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Ground vibration testing of airplane pylon-store dynamics using laser doppler vibrometer and accelerometer techniques

University of Florida Institutional Repository

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GR OUND VIBRA TION TESTING OF AIRPLANE PYLON-ST ORE D YN AMICS USING LASER DOPPLER VIBR OMETER AND A CCELER OMETER TECHNIQ UES By JOSEPH DUPUIS A THESIS PRESENTED T O THE GRADU A TE SCHOOL OF THE UNIVERSITY OF FLORID A IN P AR TIAL FULFILLMENT OF THE REQ UIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORID A 2003

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A CKNO WLEDGMENTS I w ould lik e e xpress my sincere gratitude to all of my committee members for their support on this project. In particular I w ould lik e to thank Dr Richard Lind for pro viding daily guidance throughout the course of the entire project without which success w ould ne v er ha v e been realized. I w ould lik e to thank Dr Andre w K urdila and Roque Salas from SEEK EA GLE for arranging the project and pro viding logistic support. I w ould also lik e to thank Dr Christopher Niezrecki for of fering his suggestions for impro ving the quality of the w ork presented. I of fer special thanks to the technicians at the STEM f acility at Eglin Air F orce Base for their assistance in implementing the test. Finally I w ould lik e to thank all my friends, f amily and co w ork ers for their support in v arious w ays throughout the years. ii

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T ABLE OF CONTENTS page A CKNO WLEDGMENTS . . . . . . . . . . . . . . . . ii LIST OF T ABLES . . . . . . . . . . . . . . . . . v LIST OF FIGURES . . . . . . . . . . . . . . . . . vi ABSTRA CT . . . . . . . . . . . . . . . . . . . x 1 INTR ODUCTION . . . . . . . . . . . . . . . . 1 1.1 T est Ov ervie w . . . . . . . . . . . . . . . 1 1.2 Background . . . . . . . . . . . . . . . . 2 2 TEST HARD W ARE . . . . . . . . . . . . . . . 8 2.1 T est Article . . . . . . . . . . . . . . . . 8 2.2 Excitation . . . . . . . . . . . . . . . . 11 2.3 Accelerometers . . . . . . . . . . . . . . . 12 2.4 Laser Doppler V ibrometer . . . . . . . . . . . . 14 2.5 Data Acquisition . . . . . . . . . . . . . . 15 2.6 F acility . . . . . . . . . . . . . . . . . 16 3 D A T A AN AL YSIS . . . . . . . . . . . . . . . . 17 3.1 Modal Analysis Softw are . . . . . . . . . . . . 17 3.2 Using Laser and Accelerometer Data Cooperati v ely: Method 1 . . 20 3.3 Using Laser and Accelerometer Data Cooperati v ely: Method 2 . . 25 4 GVT ON PIDS-3 AND MK-84 . . . . . . . . . . . . 28 4.1 T est Conguration . . . . . . . . . . . . . . 28 4.2 Consideration of Excitation Signals . . . . . . . . . 30 4.3 Accelerometer Response to V ertical Excitation . . . . . . 32 4.4 Accelerometer Response to Lateral Excitation . . . . . . . 40 4.5 Laser Response to Lateral Excitation . . . . . . . . . 46 4.6 Scan Response to Lateral Excitation . . . . . . . . . 50 5 GVT ON PIDS-3 AND GB U-10 . . . . . . . . . . . . 55 5.1 T est Conguration . . . . . . . . . . . . . . 55 5.2 Accelerometer Response to Lateral Excitation . . . . . . . 56 iii

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6 SUMMAR Y . . . . . . . . . . . . . . . . . . 67 REFERENCES . . . . . . . . . . . . . . . . . . 69 BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . 72 i v

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LIST OF T ABLES T able page 2–1 Dimensions for the MK-84 and GB U-10 Munitions . . . . . . 9 3–1 Ef fect of FFT Size on Modal P arameters . . . . . . . . . 24 4–1 Modes Measured by Accelerometers for V ertical Excitation to MK-84 . 33 4–2 AutoMA C of Accelerometer Response for V ertical Excitation to MK-84 . 34 4–3 Modes Measured by Accelerometers for Lateral Excitation to MK-84 . 41 4–4 AutoMA C of Accelerometer Response for Lateral Excitation to MK-84 . 42 4–5 Modes Measured by Laser for Lateral Excitation to MK-84 . . . . 47 4–6 AutoMA C of Laser Response for Lateral Excitation to MK-84 . . . 48 5–1 Modes Measured for Lateral Excitation to GB U-10 . . . . . . 57 5–2 AutoMA C of Accelerometer Response for Lateral Excitation to GB U-10 57 v

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LIST OF FIGURES Figure page 2–1 MK-84 . . . . . . . . . . . . . . . . . . 8 2–2 GB U-10 . . . . . . . . . . . . . . . . . . 9 2–3 PIDS-3 . . . . . . . . . . . . . . . . . . 10 2–4 Excitation System for GVT . . . . . . . . . . . . . 12 2–5 PCB Accelerometer Model 352C67 . . . . . . . . . . 13 2–6 Accelerometer Schematic . . . . . . . . . . . . . 13 2–7 Polytec Scanning Laser Doppler V ibrometer . . . . . . . . 14 2–8 IOtech Data Acquisition System . . . . . . . . . . . 15 2–9 STEM F acility . . . . . . . . . . . . . . . . 16 3–1 Laser and Accelerometer Frequenc y Response Functions . . . . . 21 3–2 Beam Second-Bending Mode Shape . . . . . . . . . . 22 3–3 Ef fect of FFT Size on FRF of Laser Data . . . . . . . . . 22 3–4 Ef fect of FFT Size on Curv e Fit . . . . . . . . . . . 23 3–5 Poorly Animated Mode Shape . . . . . . . . . . . . 24 3–6 Frequenc y Response Function at V arious Locations . . . . . . 25 3–7 Separate Subsection FRFs . . . . . . . . . . . . . 26 4–1 Excitation Points for GVT of MK-84 . . . . . . . . . . 28 4–2 Measurement Points for GVT of MK-84 with Accelerometers . . . 29 4–3 Measurement Points for GVT of MK-84 with Accelerometers . . . 29 4–4 Measurement Points for GVT of MK-84 with Laser V ibrometer . . . 30 4–5 T ransfer Functions for Random Burst and Sine Sweep Excitation . . 31 4–6 T ransfer Functions for 10 and 35 lb F orce Excitation . . . . . . 31 4–7 T ransfer Functions for 1024 and 2048 Point T ransforms . . . . . 32 vi

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4–8 T ransfer Functions at Representati v e Locations . . . . . . . 33 4–9 Mode Shape at 46 Hz Measured by Accelerometer for V ertical Excitation to MK-84 . . . . . . . . . . . . . . . 35 4–10 Mode Shape at 183 Hz Measured by Accelerometers for V ertical Excitation to MK-84 . . . . . . . . . . . . . . . 36 4–11 Mode Shape at 312 Hz Measured by Accelerometers for V ertical Excitation to MK-84 . . . . . . . . . . . . . . . 36 4–12 Mode Shape at 443 Hz Measured by Accelerometers for V ertical Excitation to MK-84 . . . . . . . . . . . . . . . 37 4–13 Mode Shape at 507 Hz Measured by Accelerometers for V ertical Excitation to MK-84 . . . . . . . . . . . . . . . 38 4–14 Mode Shape at 671 Hz Measured by Accelerometers for V ertical Excitation to MK-84 . . . . . . . . . . . . . . . 38 4–15 Mode Shape at 831 Hz Measured by Accelerometers for V ertical Excitation to MK-84 . . . . . . . . . . . . . . . 39 4–16 Mode Shape at 899 Hz Measured by Accelerometers for V ertical Excitation to MK-84 . . . . . . . . . . . . . . . 39 4–17 Mode Shape at 946 Hz Measured by Accelerometers for V ertical Excitation to MK-84 . . . . . . . . . . . . . . . 40 4–18 T ransfer Functions at Representati v e Locations . . . . . . . 40 4–19 Mode Shape at 186.3 Hz Measured by Accelerometers for Lateral Excitation to MK-84 . . . . . . . . . . . . . . . 42 4–20 Mode Shape at 296.9 Hz Measured by Accelerometers for Lateral Excitation to MK-84 . . . . . . . . . . . . . . . 43 4–21 Mode Shape at 356.59 Hz Measured by Accelerometers for Lateral Excitation to MK-84 . . . . . . . . . . . . . . 43 4–22 Mode Shape at 548.51 Hz Measured by Accelerometers for Lateral Excitation to MK-84 . . . . . . . . . . . . . . 44 4–23 Mode Shape at 680.64 Hz Measured by Accelerometers for Lateral Excitation to MK-84 . . . . . . . . . . . . . . 45 4–24 Mode Shape at 858.42 Hz Measured by Accelerometers for Lateral Excitation to MK-84 . . . . . . . . . . . . . . 46 vii

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4–25 Mode Shape at 969.66 Hz Measured by Accelerometers for Lateral Excitation to MK-84 . . . . . . . . . . . . . . 46 4–26 T ransfer Functions at Representati v e Locations . . . . . . . 47 4–27 Mode Shape at 86.41 Hz Measured by Laser for Lateral Excitation to MK-84 . . . . . . . . . . . . . . . . . 48 4–28 Mode Shape at 135.71 Hz Measured by Laser for Lateral Excitation to MK-84 . . . . . . . . . . . . . . . . . 49 4–29 Mode Shape at 189.05 Hz Measured by Laser for Lateral Excitation to MK-84 . . . . . . . . . . . . . . . . . 49 4–30 Mode Shape at 239.73 Hz Measured by Laser for Lateral Excitation to MK-84 . . . . . . . . . . . . . . . . . 50 4–31 Mode Shape at 239.73 Hz Measured by Laser for Lateral Excitation to MK-84 . . . . . . . . . . . . . . . . . 51 4–32 Mode Shape at 293.35 Hz Measured by Laser for Lateral Excitation to MK-84 . . . . . . . . . . . . . . . . . 51 4–33 Mode Shape at 185 Hz Measured by Laser Scan on Fin of MK-84 . . 52 4–34 Mode Shape at 185 Hz Measured by Laser Scan on PIDS-3 Pylon . . 53 4–35 Mode Shape at 290 Hz Measured by Laser Scan on Fin of MK-84 . . 54 5–1 Measurement Points for GVT of GB U-10 . . . . . . . . . 55 5–2 Measurement Points for GVT of GB U-10 . . . . . . . . . 56 5–3 T ransfer Functions at Representati v e Locations . . . . . . . 56 5–4 Mode Shape at 35.78 Hz Measured for Lateral Excitation to GB U-10 . 58 5–5 Mode Shape at 84.71 Hz Measured for Lateral Excitation to GB U-10 . 59 5–6 Mode Shape at 169.71 Hz Measured for Lateral Excitation to GB U-10 . 59 5–7 Mode Shape at 275.53 Hz Measured for Lateral Excitation to GB U-10 . 60 5–8 Mode Shape at 288.44 Hz Measured for Lateral Excitation to GB U-10 . 61 5–9 Mode Shape at 358.7 Hz Measured for Lateral Excitation to GB U-10 . 61 5–10 Mode Shape at 535.62 Hz Measured for Lateral Excitation to GB U-10 . 62 5–11 Mode Shape at 571.56 Hz Measured for Lateral Excitation to GB U-10 . 63 5–12 Mode Shape at 650.52 Hz Measured for Lateral Excitation to GB U-10 . 63 viii

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5–13 Mode Shape at 719.88 Hz Measured for Lateral Excitation to GB U-10 . 64 5–14 Mode Shape at 838.73 Hz Measured for Lateral Excitation to GB U-10 . 64 5–15 Mode Shape at 882.25 Hz Measured for Lateral Excitation to GB U-10 . 65 5–16 Mode Shape at 953.44 Hz Measured for Lateral Excitation to GB U-10 . 66 ix

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Abstract of Thesis Presented to the Graduate School of the Uni v ersity of Florida in P artial Fulllment of the Requirements for the De gree of Master of Science GR OUND VIBRA TION TESTING OF AIRPLANE PYLON-ST ORE D YN AMICS USING LASER DOPPLER VIBR OMETER AND A CCELER OMETER TECHNIQ UES By Joseph Dupuis May 2003 Chair: Dr Richard C. Lind Major Department: Mechanical and Aerospace Engineering Ground vibration testing is the process of determining a structure' s dynamic response to a force input. This information is useful for model de v elopment and stability analysis. Modal analysis is performed to e xtract modal parameters, such as natural frequencies, dampings and mode shapes, from measured responses. These responses are typically measured using either a laser Doppler vibrometer or accelerometers. The U.S. Air F orce is interested in performing a ground vibration test or GVT on F-16 wing stores. T w o stores of particular concern are the the MK-84 and the GB U-10 bombs when these munitions are attached to the wing with a Pylon Inte grated Dispenser also kno wn as a PIDS-3. During recent ight tests this conguration w as observ ed to sustain damage in the form of cracks in v arious places on the stores and p ylon. This thesis documents a ground vibration test performed on this coupled structure using laser and accelerometer measurements to determine the modal parameters and underlying dynamics of the structure. x

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CHAPTER 1 INTR ODUCTION 1.1 T est Ov ervie w The United States Air F orce is interested in in v estigating coupled p ylon-store dynamics. The dynamics of MK-84 and GB U-10 bombs while mounted to a PIDS3 p ylon are of particular interest. Recent ight tests ha v e noted that the ns of these bombs were sometimes damaged during ights in which the ordnance w as not e xpended. The occurrence of this damage w as restricted to ights with the bombs mounted onto the PIDS-3 p ylon so a study of the coupled p ylon-store dynamics for these specic units w as be gun. Eglin Air F orce Base (EAFB) and the Uni v ersity of Florida (UF) collaborated to conduct a ground vibration test (GVT) in support of the p ylon-store in v estigation. The test w as managed by personnel from the SEEK EA GLE of ce of EAFB. Assistance w as pro vided by f aculty and students from the Department of Mechanical and Aerospace Engineering at UF The testing w as conducted using f acilities at EAFB during the week of July 15-19, 2002. The objecti v e of this testing w as to e xperimentally identify the structural dynamics of the p ylon-store couplings. The test article w as mounted to a massi v e stand that could be considered rigid. A vibration shak er w as attached to the test article to pro vide e xcitation. The resulting responses were recorded using accelerometers and a laser Doppler vibrometer Modal parameters of natural frequencies and dampings along with associated mode shapes were e xtracted from the data using ST AR-MOD AL softw are. Se v eral modes were identied from the data. Man y of the modes were dominated by motion of the ns on the bombs; ho we v er some modes also had signicant motion of the p ylon. The damage observ ed in ight w as restricted to use of the PIDS-3 p ylon 1

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2 so an y modes in v olving the p ylon are of particular interest. Most of the mode shapes with p ylon motion demonstrated bending dynamics such that the leading-edge and trailing-edge ends of the p ylon mo v ed laterally or v ertically Another mode shape in v olving the p ylon sho wed a localized bending in which motion w as restricted to a small area. The laser Doppler vibrometer pro v ed especially useful for this GVT The noise le v el in the measurements w as noticeably reduced for the laser measurements as compared to accelerometer measurements. The modal analysis, which uses transfer functions from these measurements, w as easier for the laser data than for the accelerometer data. Consequently the analysis identied se v eral more modes using laser data than accelerometer data. These additional modes were accepted with a high le v el of condence based on standard metrics such as modal assurance criterion. This report presents the results of the GVT for the MK-84 and GB U-10 mounted on a PIDS-3 p ylon. The setup for the test is e xplained along with descriptions of the equipment. Modal parameters and mode shapes are gi v en for separate test articles of a MK-84 mounted on a PIDS-3 p ylon and a GB U-10 mounted on a PIDS-3 p ylon. 1.2 Background The entire subject of modal analysis has man y dif ferent f acets and renements of the v arious subject areas are continuously being e xplored. Current literature is replete with ne w ideas and strate gies for solving old problems as well as the ne w problems which arise e v eryday Although man y techniques are considered standard and essentially undisputed as acceptable testing procedure after enduring years of v alidation, there is no one technique that is superior in all situations. This section is a discussion of some of the current w ork being done in the modal analysis community and some of the w ork which has helped to shape the current state of the eld. The data collection methods for vibration testing can be brok en into tw o major cate gories dened by the type of sensor(s) used, being either a laser or accelerometers.

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3 When using accelerometers certain obstacles arise that must be considered in order to obtain the highest quality data possible. It is important to note the mass loading ef fects an accelerometer may ha v e on the system. W alter [ 1 ] relates the ratio of measured v elocity Vs to true v elocity V s through the concept of mechanical impedance and denes this quantity as VsV sZ sZ sZ anwhere Z s is the mechanical impedance of the structure. Further noting that Z a can be written as j w m Notice that since the impedance of the accelerometer depends on the mass; small, light-weight accelerometers will only ne gligibly inuence the dynamics of the structure. Although this result w ould tend to indicate that smaller accelerometers w ould simply be a better choice W alter also notes that smaller accelerometers are not as internally strain isolated as are lar ger ones. This will result in a lar ger base strain coupling in the sensing element and hence more error Further conclusions re v eal that shear mode accelerometers don' t ha v e a shear path into the crystal thereby minimizing the amount of error A short comparison of accelerometer selection is gi v en in W alter [ 1 ] and in Ref. 2 The laser Doppler vibrometer (LD V) is an important tool for the measurement of a system' s dynamic response. It is no surprise that there is a great deal of interest in it' s use and a wealth of literature dedicated to this subject alone. It' s non-intrusi v e nature mak es the LD V in v aluable when e v en the smallest of accelerometers w ould produce profound mass loading ef fects or when sensor contact could pro v e harmful to the test article. In general the accelerometer test requires more setup time b ut less acquisition time than the LD V with the LD V test usually being more time ef cient o v erall [ 3 ]. Other comparisons can be made b ut both methods still remain useful with neither technique being better in all situations. The LD V is an interferometer based signal detection system that measures the v elocity at a point parallel to the beam. The measurements are usually tak en in a

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4 step-wise f ashion at se v eral points dening a surf ace. The ne west type of LD V will scan continuously across a surf ace with the adv antage of needing fe wer data for an accurate depiction of the mode shapes and an impro v ement in the speckle noise which often plagues the traditional LD V An in depth look at ho w one implements this ne w type of data collection with a constant sinusoidal input force can be found in Ref. 4 Current w ork stri v es to e xtend the usage of the continuously scanning LD V from line scans to area scans [ 5 ]. Another a v enue along which current in v estigations are tra v eling is using this type of laser for impact testing [ 6 ]. Impact testing is not usually done when using a step-wise LD V because it requires a ne w impact at each point, so when a lar ge number of scans is required it becomes rather impractical. W ith the continuous scanning LD V only one impact w ould be required for each scan line. The dra wback of using a continuously scanning LD V is that sine sweeps cannot be used. Some other ne w approaches to laser testing include the de v elopment of a homodyne interferometer in conjunction with a ne w photodetector W ith the instrument proposed, it w ould be possible to measure in-plane and out-of-plane v elocities with a single laser beam [ 7 ]. There are other laser techniques being used for vibration analysis such as holographic interferometry and electronic speckle pattern interferometry which ha v e the adv antage of measuring the entire surf ace displacement at once, a so called whole-eld method. The limiting f actor in the usage of these techniques has been that the y pro vide little quantitati v e measure of the system, b ut the use of modal analysis softw are has been sho wn to alle viate this shortcoming [ 8 ]. Experimental w ork in an y eld can sometimes be problematic in areas of data collection, data analysis, and noise reduction as well as other aspects of the process. An ytime one can gain insight into the type and possible cause for error it is a w orthwhile in v estment of ef fort. In modal analysis, one usually collects response data in the time domain and con v erts it to the frequenc y domain to produce frequenc y response functions (FRFs) which are used to determine the mode shapes. If a model e xists

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5 the modes can be compared by use of the Modal Assurance Criterion (MA C). Also, the measure of ho w well each of the modes across a set of FRFs compare and can be distinguished from each other is kno wn as an auto-Modal Assurance Criterion. A detailed e xplanation of these parameters can be found in Ref. 9 Recently w ork has been done to de v elop a ne w data plotting technique, FMA C, that mak es use of mode shape correlation and natural frequencies on the same plot which can be useful in visualizing the modal density and the determining the nature of lar ge of f diagonal v alues in the MA C matrix [ 10 ]. In man y testing congurations the data is collected consecuti v ely in dif ferent sections which can result in at least a slight change in test conditions o v er the whole test. These changes could be in the form of temperature v ariations or accelerometer mass loading or mounting compliance, if used, all of which could result in slightly dif ferent resonant frequencies in that testing section. F or lar ge structures the number of dif ferent sections can become lar ge and a global modal analysis may result in ille gitimate results. Auweaer et al. [ 11 ] of fer one possible solution by performing modal analysis on each section, mer ging the results then doing some a v eraging o v er the entire data, or using one section as a reference. Another problem is addressed in Ref. 12 which determines that the presence of transient ef fects during the test performance will result in an o v erestimation of the damping v alues. Of course this only applies to randomly e xcited structures so one remedy as stated in the w ork, is the use of only periodic signals, b ut for those persistent types who insist on using random e xcitations, an algorithm is presented which w orks to eliminate this problem. Another solution w ould be the use of e xponential windo wing which is kno wn to aid in leakage reduction by adding damping to the system [ 13 ]. This articial damping will of course decrease the amplitude of the resonant frequenc y b ut this decrease can be accounted for since the amount of e xtra damping can be e xactly determined. The issues presented here are only a small sample of the kinds of problems that can arise in data processing. This is an entire subject on it' s o wn and an important one at that

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6 as it may be necessary to adjust the data acquisition process in an ef fort to compensate for an y data processing problems that are kno wn to result from a particular collection technique. The application of vibration testing is wide ranging and certainly a necessity for structures whose loss of inte grity can ha v e dire consequences. One such area is in the de v elopment of aircraft where the distinction is made between laboratory tests and in ight tests, the former being called a ground vibration test or GVT The N ASA Dryden Flight Research F acility has a well established procedure for implementing these tests and man y of their standards can be found in the literature [ 14 15 16 17 18 ]. The GVT is typically used for analysis such as utter prediction, nite-element model updating, comparing modal changes resulting from structural modications, and deciphering irre gularities encountered during ight [ 14 ]. In nearly all GVT testing of lar ge aircraft it is desired to simulate free-free boundary conditions so the aircraft is supported through some soft support system. This can be done by reducing the tire pressure to minimize stif fness and allo wing the airplane to rest on its landing gear [ 14 ]. The plane may also be supported with b ungee cords along with the deated tire technique [ 19 ]. A ne wer strate gy for implementing the soft support system is using pneumatic springs to support the aircraft from underneath at a fe w jack points [ 15 ]. T ypical e xcitation signals for the GVT include random or b urst random, slo w sine sweep and sine dwell. Lar ge aircraft and e v en spacecraft ground vibration tests can be rather time consuming. It is al w ays of interest to nd w ays in which test time can be reduced without compromising the quality of the data collected. Current tests ha v e included as man y as 400 accelerometers with a test time ranging an ywhere from ten days to a month [ 19 20 ]. One series of tests performed by the Modal and Control Dynamics T eam at N ASA s Marshall Space Flight Center on se v en lar ge elements of the Inter national Space Station included up to 1,251 accelerometer channels. The tests were performed o v er a period of about four and a half years although each separate test took

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7 tw o to three weeks [ 21 ]. In an ef fort to reduce the time to perform a lar ge scale GVT Gloth et al. [ 22 ] of fer some interesting strate gies including impro v ed test preparation in the form of selecting test parameters using insight from a FE model. These parameters might include accelerometer and e xciter locations or particular frequenc y ranges. Another technique of fered is to use high frequenc y resolution only around modes thought to be highly af fected by utter or when precise model updating is desired. There is certainly f ar more w ork being done in vibration testing and modal analysis than can in whole be adequately co v ered in this report. The information pro vided here merely establishes justication for the use of the procedures and techniques emplo yed for this e xperiment.

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CHAPTER 2 TEST HARD W ARE 2.1 T est Article The test article for the GVT consists of a munition mounted to a p ylon. Specically a separate GVT w as performed for a MK-84 and a GB U-10 munition. Each of these munitions were mounted onto a Pylon Inte grated Dispenser PIDS-3, p ylon. The MK-84 is a 2,000-pound class bomb This bomb is a ballistic munition with no acti v e propulsion or control system to guide the bomb onto a tar get. The bomb, as sho wn in Figure 2–1 is essentially a main body with a tail assembly The main body w as lled with an inert solid for the testing to match mass properties of the e xplosi v e used in an actual MK-84 bomb The tail assembly contains a ballute, essentially a combination of balloon and parachute, that slo ws the munition and pro vides some measure of open-loop control. These internal masses will are of note since it has been sho wn that internal response can transmit suf cient ener gy to the surf ace where the measurements are made [ 23 ]. Also, 4 ns are part of the tail assembly Figure 2–1: MK-84 The GB U-10 is also a 2,000-pound class bomb This bomb is a smart munition designed to operate in conjunction with additional personnel. A laser designator must 8

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9 illuminate a tar get to pro vide reference for the acti v e control system that guides the munition. The article to be tested, as sho wn in Figure 2–2 is the P a v e w ay-II v ersion of the GB U-10. Figure 2–2: GB U-10 The test article had the ns retracted inside the tail assembly during the GVT The production v ersion of the GB U-10 actually consists of an instrument package on the nose, a main body and a tail assembly; ho we v er the instrument package w as not attached for the GVT Also, the main body contained inert material that matched mass properties of the e xplosi v e in the production v ersion. Some basic dimensions of these munitions are gi v en in T able 2–1 T able 2–1: Dimensions for the MK-84 and GB U-10 Munitions P arameter MK-84 GB U-10 W eight (lbs) 2039 2562 Length (in) 129 172 Diameter (in) 18 18 Se v eral features of these munitions may af fect the modal testing. The main body of each munition is relati v ely solid so this portion is e xpected to be quite stif f. The tail assemblies are more complicated with v arying le v els of stif fness and so must be carefully considered when analyzing data. The tail assemblies ha v e a metal shell surrounding internal components. This shell comprises the e xterior surf ace upon which accelerometers are mounted. The shell itself is a c ylinder of relati v ely thin metal. Man y of the components attached to this shell

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10 in v olv e springs and rods of v arying stif fness. Thus, the responses measured along the shell may be signicantly af fected by local modes associated with the thin c ylinder and the components. The ns are another part of the tail assemblies that must be considered. The ns on each munition are metal sheets; ho we v er these ns ha v e considerably dif ferent dimensions. The ns on the MK-84 ha v e half-span of roughly 14 in. (35.56 cm) and a chord length than ranges from 17 in. (43.18 cm) near the root to 7.5 in. (19.05 cm) near the tip. Con v ersely the ns on the GB U-10 ha v e half-span of only 8 in. (20.32 cm) and chord length of roughly 33 in. (83.82 cm) throughout. These dimensions imply the MK-84 may sho w lar ge deections due to chord-wise and span-wise mode shapes of the ns b ut the GB U-10 will probably sho w only small deections. The p ylon to which these bombs will be attached is sho wn in Figure 2–3 This p ylon is a length of 101 in. (256.54 cm) at the bottom and a height of 15.8 in. (40.132 cm) at the center The width of the p ylon ranges from 9 in. (22.86 cm) to 12 in. (30.48 cm) throughout most of the structure. Included in the p ylon are 3 chaf f dispensers. Figure 2–3: PIDS-3 The test article consists of the MK-84 or GB U-10 bomb attached to the PIDS-3 p ylon. This attachment is pro vided by hooks on the underside of the p ylon. Also, 4 sw ay braces on the p ylon contact the bomb to pro vide some stabilization. The top of the p ylon contains 3 points at which the test article is connected to an aircraft wing or for this test, the mounting f acility

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11 2.2 Excitation A source of e xcitation w as needed for ground vibration testing. The mass and stif fness properties of the test articles made use of impact hammers questionable; therefore, an electromechanical shak er w as used for testing [ 15 ]. The shak er w as manuf actured by Ling corporation and could output up to 100 lbf (444.8 N) of force at frequencies up to the desired 2,000 Hz. The shak er w as cooled using an ordinary Hoo v er brand v acuum. The shak er w as mounted in the f acility using tw o dif ferent strate gies depending on the type of e xcitation to be considered. The shak er w as placed directly under the test article to allo w e xcitation in the v ertical direction. Alternati v ely the shak er w as tightly clamped to a lar ge metal frame which w as itself attached to a boom on a v ehicle to allo w e xcitation in the horizontal direction. The amount of force that the shak er actually applied to the test article w as measured by a force transducer The transducer used for this GVT w as a PCB Piezotronics model 208C02 ICP quartz sensor with a dynamic range of 100 lbf (444.8 N) of force. Mounting blocks for this transducer were attached underneath and on the side of the munitions using dental cement [ 24 ]. The shak er w as then connected to the transducer using a mechanical fuse or stinger Since this test is only concerned with approximate mode shapes and natural frequencies and w on' t be used for model updating it is safe to ignore the ef fects of stinger resonance which has been kno wn to cause problems when this resonance is in the test frequenc y range [ 25 ]. The measurement of the transducer w as amplied by a PCB 482A16 line-po wered signal conditioner This unit also pro vided the necessary ICP circuit e xcitation required by the force transducer The amplied signal w as then sent to the appropriate data acquisition system.

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12 The shak er w as operated to output a force signal with commanded properties. The random and sine sweep signals were commanded by connecting the shak er to an Agilent 33120A function generator The e xcitation system is sho wn in Figure 2–4 The force transducer stinger shak er and cooling system can be identied along with some accelerometers. This gure demonstrates the actual setup used for testing the MK-84 in response to lateral e xcitation. Figure 2–4: Excitation System for GVT 2.3 Accelerometers The accelerometers used were PCB Piezotronics miniature ceramic shear ICP accelerometers Model 352C67. Figure 2–5 sho ws a close-up vie w of one of these sensors. This shear mode accelerometer is characterized by ha ving a seismic mass mounted on the side of a piezoelectric material as sho wn in Figure 2–6 Applying an acceler ation to the mass causes a shear stress on the f ace of the crystal and, consequently a proportional electric signal. This signal generated is v ery small b ut is then amplied by the internal signal conditioning of the ICP or ”Inte grated Circuit Piezoelectric, ” after which it becomes an actual usable signal [ 2 ]. This particular model of accelerometer has a x ed v oltage sensiti vity a force measurement range up to 50g peak, and a

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13 Figure 2–5: PCB Accelerometer Model 352C67 frequenc y range from 0.5 to 10,000 Hz, which made them a suitable choice for this particular application. A study of the noise oor of se v eral accelerometers sho ws that a similar model, 352C65 which dif fers only in the connector pins, performs quite well in comparison with other currently a v ailable models of the same v oltage sensiti vity The range of noise oors across the 5-800 Hz range v aries from 8-45 Vrms with the 352C65 operating at 9 Vrms [ 26 ]. In addition, the y are small and lightweight so an y mass loading ef fect on the test article is ne gligible [ 27 ]. Figure 2–6: Accelerometer Schematic This model of accelerometer measures acceleration in only one direction so care w as tak en to mount the sensors perpendicular to the surf ace at each point. This mounting ensures that an y transv erse motion is not misinterpreted as an axial vibration.

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14 The accelerometers were mounted to the test subject with petro w ax because of ease of application and inconsequential ef fect on the surf ace of the test subject. 2.4 Laser Doppler V ibrometer A Polytec PSV -300 scanning laser Doppler vibrometer system w as also used to measure vibrations during the GVT The system consists of an OFV -055 scanning head, an OFV -303.8 class II helium neon laser and an OFV -3001 S processor/controller Figure 2–7 sho ws the laser mounted on the tripod in typical operating f ashion. Figure 2–7: Polytec Scanning Laser Doppler V ibrometer This laser measures v elocity parallel to the beam so optimal results are obtained by placing that beam perpendicular to the scan surf ace. Arranging the vibrometer in this f ashion automatically accounts for an y angle of the scanning head in the resulting analysis. The laser/scanning head w as mounted on a tripod and care w as tak en to eliminate an y incorrect measurement which can result from beam angles incurred from improper tripod setup. These measures include le v eling the tripod le gs with the b uilt in le v eling de vices, estimating the scan surf ace angle and visually matching this angle with the scanning head by tilting the scan head mounting brack et appropriately It is also important that the test object be located at a point of maximum

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15 laser intensity The rst of these occurs at 0.55 in. (1.397 cm) and e v ery 8.08 in. (20.52 cm) thereafter A laser position of approximately 24 in. (60.96 cm) from the desired point of measurement w as the most suitable choice for this test since a longer distance from the surf ace results in a lar ger depth of focus and wider scan eld [ 28 ]. The vibrometer is actually part of an entire measurement system. The use of the vibrometer is dependent on a dedicated computer for both e xcitation and measurement. This computer controlled the function generator and, consequently the signal sent to the e xcitation shak er This computer also recorded the measurements from the vibrometer 2.5 Data Acquisition An IOtech W a v eBook data acquisition system w as used to collect the accelerometer data. This is comprised of a W a v eBook 516 and four WBK 14 e xpansion modules which interf ace into a laptop computer via a PCMCIA card. Figure 2–8 sho ws the IOtech system and laptop with no accelerometers attached. Figure 2–8: IOtech Data Acquisition System Each of the e xpansion modules has eight input channels which pro vide the constant current e xcitation po wer required by the ICP circuitry The W a v eBook also has eight input channels, ho we v er these channels do not pro vide an output current and as such cannot be used for ICP accelerometers. The hardw are is controlled from

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16 the laptop using a softw are package called D ASYLab to perform data acquisition and process control along with real-time analysis. 2.6 F acility The GVT w as conducted using the STEM f acility at Eglin Air F orce Base. The STEM f acility pro vides a dedicated b uilding which w as used e xclusi v ely for the GVT during the test period. The b uilding is isolated from other b uildings; ho we v er residual vibrations were often recorded resulting from ights of F-15 aircraft o v er the area. The main component of the STEM f acility is a static ejection stand. This stand is essentially a lar ge column under which the test article could be mounted. The column, as sho wn in Figure 2–9 is e xtremely massi v e and strong. This column did not pro vide a perfectly rigid mounting point for the GVT b ut the modes associated with the column had only minor contrib utions to the measured responses. Thus, the dynamics of the column were ignored for modal analysis. Figure 2–9: STEM F acility

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CHAPTER 3 D A T A AN AL YSIS 3.1 Modal Analysis Softw are The Spectral Dynamics softw are package ST ARModal w as used to animate the response of the structure. The procedure for using ST ARModal be gins with creating the geometry of the structure by dening the coordinates for each of the points tested and then supplying corresponding data for each of these points. ST ARModal can import dif ferent types of data including time domain, cross po wer auto po wer and coherence spectra as well as frequenc y response functions, or FRFs. It is adv antageous to preprocess the data in MA TLAB to produce the FRF le with the proper header in SMS ASCII, a ST ARModal specic ASCII format. Once imported into ST ARModal, the transfer function estimation can be produced by loading a measurement le into a “data block”, highlighting the desired frequenc y band, and choosing the curv e tting method. The polynomial method ts a polynomial function to the data o v er the highlighted frequenc y range in a least-squared error f ashion. This method is appropriate for either lightly-coupled or hea vily-coupled modes and so it is an ef fecti v e choice for this e xperiment. Also called the rational fraction polynomial method, this curv e tting routine w orks as follo ws. Each measured point has an FRF called H k where k corresponds to each frequenc y location. The error between the curv e-t and the measured v alue is then dened as e k b 0b 1i w k2 b 2 mr1i w k2 mr1 a 0a 1i w ka 2i w k2 a 2 mi w k2 mH k (3.1) 17

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18 where a 0a 1 a 2 mb 0b 1 b 2 mr1are the polynomial coef cients related to the modal parameters and m being the number of modes. This equation can be re written in matrix form as ek 1i w k i w k2 i w k2 mr1 b 0 b 1b 2 mr1 H k1i w k i w k2 i w k2 mr1 a 0 a 1a 2 mr1 H ki w k2 m a 2 m (3.2) The unkno wn coef cients are determined by minimizing the error function gi v en by J J"!E$#T!E#(3.3) The resulting coef cients are used to deri v e a set of modal parameters. The parameters are then displayed in a tab ular format listing the frequenc y and damping percentage. Also, for each point magnitude and phase information at each mode is presented. The Auto Modal Assurance Criterion is also presented as a measure of ho w the mode shapes are correlated with each other The AutoMA C matrix has v alues of unity along the diagonal indicating that each mode correlates perfectly with itself. All other entries of f the main diagonal range from zero to one indicating the le v el of similarity between the modes from orthogonal to identical respecti v ely [ 29 ].

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19 The percentage damping is determined from the go v erning dif ferential equation for a vibratory system [ 30 ]. m d 2 x d t 2c d x d tk xFt(3.4) Here c stands for the damping coef cient. The solution to this dif ferential equation is xAe l t (3.5) yielding the characteristic equation l 2c m lk m0 (3.6) The roots of this equation are l 1%2 c 2 m&(' )c 2 m*2k m (3.7) If we consider the case where+c 2 m, .k m kno wn as critically damped motion, the roots of the characteristic equation are identical. The general solution then is xt/ C 1C 2 te l t (3.8) F or the critically damped case we can dene c cr20 k m (3.9) then the damping ratio is dened as zc c cr (3.10)

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20 and then e xpressed as a percentage zc c cr1100% (3.11) Equation 3.11 is the v alue reported for damping by ST ARModal and is gi v en in this report for all modes identied by the analysis. 3.2 Using Laser and Accelerometer Data Cooperati v ely: Method 1 The GVT needed to consider both accelerometer and laser measurements; therefore, a procedure for combining these data needed to be de v eloped. Certain practices specic to each method will inuence the quality of the data b ut, be yond these e xperimental techniques, further analysis techniques must be considered when generating and animating mode shapes. A simple beam e xperiment w as performed in an ef fort to determine whether or not data from the tw o techniques could be successfully combined. This e xperiment utilized a aluminum beam of modest dimensions, 19x2.25x0.125 in. (48.26x5.715x0.3175 cm), cantile v ered to a relati v ely massi v e supporting frame. Eight points were chosen for the location of the accelerometers starting 3 in. (7.62 cm) from the clamped edge and continuing out e v ery tw o inches. Eight laser points were selected 0.5 in. (1.27 cm) further out from each accelerometer point. The slight dif ference in laser and accelerometer points w as moti v ated by a desire to k eep the accelerometers mounted during the e x ecution of the laser test. K eeping all the sensors mounted during the tests ensures that an y ef fect the accelerometers ha v e on the structure will be measured by both collection procedures. Also, since the mounting base of the accelerometer is 0.25 in. (0.635 cm) there needed to be suf cient room for the laser beam to contact the surf ace without being disturbed by an y nearby accelerometer The beam w as e xcited 0.5 in. (1.27 cm) from the free end with a Ling shak er/amplier system and a command signal from a Agilent 33120A function generator Se v eral dif ferent sine

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21 sweep ranges were used with a typical maximum input of just under 1.0 lbf (4.448 N) force. The data collected using the laser w as rst con v erted from a v elocity response to an acceleration response in order to correspond with the data collected using the accelerometers. This con v ersion w as performed by taking a simple numerical deri v ati v e of the v elocity [ 31 ]. Figure 3–1 sho ws a comparison of frequenc y response functions of one of the lar ger amplitude points using both the laser and an accelerometer 10 0 10 1 10 2 Absolute Magnitude (g/lbf) 20 30 40 50 60 70 80 90 -500 0 500 Phase (degrees)Frequency (Hz) Accel Laser Figure 3–1: Laser and Accelerometer Frequenc y Response Functions This gure sho ws that the response functions match v ery closely to one another Consistent results were also observ ed among the other sets of paired points including other resonant frequencies. This particular response function w as the result of a 20 to 100 Hz sine sweep o v er 8 seconds sampled at 1,024 Hz. A 2,048-point FFT with 256 points of o v erlap w as used with a Hanning windo w applied to the input data. Figure 3–2 sho ws the resulting mode shape of the beam from the analysis in ST ARModal. The clamped edge is to the right side while the e xcited edge is to the left. The gure sho ws a smooth animation with the clear presence of a second-bending mode at 68.69 Hz.

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22 Figure 3–2: Beam Second-Bending Mode Shape This testing re v ealed a couple of data processing problems. The rst of these is a proper choice of a windo wing function. This problem is e xpected b ut still mentioned here merely as a matter of thoroughness. Although it is already kno wn to be a major consideration in signal processing, the proper choice of FFT size w as the most inuential parameter causing the results from the dif ferent data collection techniques to di v er ge. This inuence is demonstrated in the frequenc y response functions of laser data from a single point on the beam as sho wn in Figure 3–3 10 1 10 2 Absolute Magnitude (g/lbf) 40 50 60 70 80 90 500 1000 Phase (degrees) Frequency (Hz) 2048 4096 Figure 3–3: Ef fect of FFT Size on FRF of Laser Data The processing w as done in MA TLAB using thevspectcommand with FFT sizes of 2,048 points and 4,096 points. A Hanning windo w with 256 points of o v erlap w as

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23 used in both cases. There is a clear dif ference in the magnitude of the curv e at the peak, the 4,096 size maximum with a v alue of 252 g/lbf (56.65 g/N) being more than twice as lar ge as the 2,048 size maximum of 105 g/lbf (23.60 g/N). In order to animate these frequenc y responses, a curv e t is performed on the data to produce a transfer function. Figure 3–4 sho ws a typical curv e t using the MA TLABfitsyscommand. 10 0 10 1 10 2 Absolute Magnitude (g/lbf) 2048 4096 20 30 40 50 60 70 80 90 -150 -100 -50 0 Phase (degrees)Frequency (Hz) Figure 3–4: Ef fect of FFT Size on Curv e Fit These transfer functions sho w a small yet signicant dif ference in magnitude. This dif ference is not necessarily all that alarming because it is common among all points along the beam b ut when mer ging accelerometer and laser data it becomes the dif ference between smooth and chopp y animations. Figure 3–5 sho ws the outline of an animation where laser and accelerometer data match rather poorly due to signal processing issues. No w that the transfer functions ha v e been generated we can look at the dif fer ences in the frequenc y and damping. T able 3–1 summarizes the dif ferences in these parameters for the indi vidual techniques. This table sho ws that, for a similar location on the beam, the dif ference in damping and magnitude between accelerometer data and laser data is lar ger for the 4,096-size FFT F or the 2,048-size FFT the accelerometer damping estimation is 6% greater and peak magnitude is 5% greater than that of the laser W ith an FFT

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24 Figure 3–5: Poorly Animated Mode Shape T able 3–1: Ef fect of FFT Size on Modal P arameters Frequenc y(Hz) Damping Magnitude Laser 2,048 68.71 9.14E-003 102.50 4,096 68.76 2.56E-003 315.40 Accel 2,048 68.69 1.00E-002 107.90 4,096 68.67 2.96E-003 295.10 size of 4,096 the accelerometer damping is 16% lar ger while the peak magnitude is no w 6% smaller than the same v alues calculated using laser data. No signicant dif ference w as detected in the location of the resonant frequencies. All this does not necessarily mean that a smaller FFT size will pro vide better matching of the data only that it is an important f actor for consideration. The lar gest de viation in the data occurred in the damping parameter estimation which is a direct result of the curv e tting process. Consequently the ability of the softw are to closely match the transfer functions will depend on the choice of FFT size. A frequenc y response function may visually appear acceptable b ut the resulting curv e t is not guaranteed to compute a damping consistent with other data. This problem w as identied in all the numerous trials of this e xperiment. A suitable choice of FFT size must be selected by comparing estimates of transfer functions and modal parameters from se v eral measurements.

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25 3.3 Using Laser and Accelerometer Data Cooperati v ely: Method 2 While the modications to the data processing procedure mentioned in the pre vious section can be useful for obtaining a more precise damping estimate in a simple plate model, the procedure may pro v e quite onerous for a structure with multibody coupled dynamics. Damping v alues may v ary across the dif ferent subsections and only after the mode shape animations are vie wed and determined to be erroneous w ould one be alerted to the need for an adjustment to the FFT size. F or lar ge numbers of subsections or number of test points this procedure w ould be a rather lar ge imposition on the o v erall test time constraints. An alternati v e approach which combines both data acquisition procedures w as de v eloped during the testing of the MK-84 and pro v ed to be quite useful. Accelerometers were used to quickly generate FRF plots in MA TLAB o v er the entire structure through a sweep of sine w a v e frequencies. The FRFs produced tended to be rather dif cult to interpret and lack ed a clear o v erall picture of the structure' s response as sho wn in Figure 3–6 This gure sho ws FRFs for points at v arious locations on the test structure. 50 100 150 200 250 300 350 400 10 -6 10 -4 10 -2 10 0 Frequency (Hz)Magnitude (g/lbf) bomb pylon fin Figure 3–6: Frequenc y Response Function at V arious Locations

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26 By visually e xamining the FRFs of dif ferent subsections of the structure it becomes more clear where in the spectrum local resonant frequencies reside. Figures 3–7 sho w FRFs from tw o of the constituent sections of the test article those being one of the ns and the side of the p ylon. Although these are clearly less than perfect transfer functions it can be observ ed that there are possible resonances. Most notably is the peak near 185 Hz and another near 290 Hz. These suspect frequencies were then e xcited with a sine dwell and a full laser scan o v er that particular subsection w as emplo yed. 50 100 150 200 250 300 350 10 -5 10 -4 10 -3 10 -2 10 -1 Frequency (Hz)Magnitude (g/lbf) (a) Fin 50 100 150 200 250 300 350 10 -6 10 -5 10 -4 10 -3 10 -2 Frequency (Hz)Magnitude (g/lbf) (b) Pylon Figure 3–7: Separate Subsection FRFs By implementing this type of procedure it is possible to identify certain frequencies of interest from relati v ely poor quality data and then focus the rest of the test time on those frequencies in an ef fort to produce results superior to those obtained in the preliminary testing phase. The resulting mode shape animations produced by the Polytec softw are at the aforementioned sine dwell frequencies and the ef fecti v eness of this technique are presented in Section 4.6 of this report. A similar technique has been used in Ref. 21 where a ”common set” of measurements is selected to be acquired from each patch of accelerometers. This common set is then e v aluated to determine

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27 appropriate force le v els and frequenc y resolution. This idea is e xtended in this report to include the selection of the e xcitation function. Using a specic sine frequenc y is especially useful for separating closely spaced modes and for identifying nonlinear beha vior particularly when the structures character istics are unkno wn [ 32 ]. It should be noted ho we v er that by using sine dwell e xcitation much of the damping information is lost. If we let Q be a measure of resonance peak sharpness which is related to the damping it can be sho wn that Qw w 2w 11 g (3.12) where w 2 and w 1 are located to either side of resonance and representing the full width at half maximum and g is thestructural damping f actor[ 30 ]. It is clear that an y of the side band information has been compromised especially when the choice of dwell frequenc y lies further a w ay from resonance. Also, the frequenc y resolution of the FRFs obtained during the preliminary accelerometers test becomes an important f actor in the resulting amplitude of the response at the selected frequenc y In this test the resulting frequenc y resolution w as 1 Hz and although it is concei v able that the amplitude could ha v e v aried within this resolution range it is rather unlik ely that the amount w ould be of an y consequence. Ho we v er this will be an important consideration when the frequenc y resolution w ould allo w for poor peak amplitude location estimation.

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CHAPTER 4 GVT ON PIDS-3 AND MK-84 4.1 T est Conguration A set of ground vibration tests were conducted on the test article composed of the MK-84 and PIDS-3 p ylon. This set of tests used accelerometers and the laser Doppler vibrometer to measure motion at distinct points on the article. The motions were responses to separate lateral or v ertical e xcitation. The e xcitation used for each GVT w as applied 112 in. (284.48 cm) aft of the nose of the MK-84 bomb The lateral e xcitation w as applied in a horizontal direction at the centerline on the port side of the bomb Similarly the v ertical e xcitation w as applied in a v ertical direction at the centerline under the bomb The points at which e xcitation w as applied are sho wn in Figure 4–1 Each point of e xcitation w as actually between the leading-edge root of a pair of ns. Figure 4–1: Excitation Points for GVT of MK-84 The signals commanded to pro vide the e xcitation force v aried for the tests. Some tests for accelerometer measurements used a series of b urst random signals with random ener gy for approximately 0.8 s follo wed by approximately 0.9 s of zeromagnitude signal. Other series of tests for accelerometer measurement used 60 s sine sweeps from 20 to 1,000 Hz or 20 to 300 Hz. The testing for laser measurements used a sine sweep from 20 to 600 Hz that lasted for 8 s. 28

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29 Accelerometer measurements at 55 locations on the test article were tak en in response to the e xcitation. As noted earlier the data acquisition system w as not capable of recording 55 measurements simultaneously; therefore, the tests were conducted using 2 congurations of 28 and 27 accelerometers. The resulting data points included 10 lateral and 9 v ertical measurements on the main body of the bomb, 11 lateral and 4 v ertical measurements on the p ylon, and 21 measurements on the ns. Se v eral of the accelerometer locations are sho wn in Figure 4–2 This dra wing indicates the locations of accelerometers measuring lateral motion on the p ylon and bomb Also, the accelerometers on the lo wer n on the port side are mark ed. Figure 4–2: Measurement Points for GVT of MK-84 with Accelerometers The remaining accelerometers are sho wn in Figure 4–3 The left dra wing vie ws the test article from near the bottom such that the accelerometers measuring both lateral and v ertical motion can be seen. The right dra wing vie ws the test article from directly abo v e to sho w the accelerometers on the top of the p ylon and the accelerometers on the upper ns for both port and starboard sides. Figure 4–3: Measurement Points for GVT of MK-84 with Accelerometers

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30 The laser took measurements at 91 locations on the test article. These locations were restricted to the PIDS-3 p ylon and to the ns on the tail assembly of the MK84. The measurements included 38 points on the upper n on the starboard side of the MK-84. Also, the measurements included 53 points on the starboard side of the PIDS-3 p ylon. Figure 4–4 sho ws the locations at which these measurements were tak en. Figure 4–4: Measurement Points for GVT of MK-84 with Laser V ibrometer 4.2 Consideration of Excitation Signals Se v eral types of e xcitation signals were a v ailable for testing; therefore, the ef fects of these signals must be noted when analyzing response data. Some of the properties that are of particular interest are the ef fects of damping mechanisms and nonlinearities in the dynamics. A comparison of representati v e transfer functions for random b urst and sine sweep signals is sho wn in Figure 4–5 as measured by an accelerometer on a n. The transfer functions are slightly dif ferent b ut these dif ferences are mostly minor In particular the dif ferences at the peaks, which presumably indicate modal properties, are generally small e xcepting near 525 Hz and 945 Hz. The issue of nonlinearities w as in v estigated by using e xcitation at dif ferent force le v els. Figure 4–6 presents transfer functions from n accelerometer to e xcitation with 10 and 35 lb (44.48 and 155.69 N) of force. In this case, the e xcitation w as the b urst random signal. These transfer functions are quite similar e xcept near 525 Hz.

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31 0 200 400 600 800 1000 10 -4 10 -3 10 -2 10 -1 10 0 Frequency (Hz)Magnitude (g/lbf) random burst sine sweep Figure 4–5: T ransfer Functions for Random Burst and Sine Sweep Excitation 0 200 400 600 800 1000 10 -4 10 -3 10 -2 10 -1 10 0 Frequency (Hz)Magnitude (g/lbf) 10 lbf 35 lbf Figure 4–6: T ransfer Functions for 10 and 35 lb F orce Excitation The comparisons in Figure 4–5 and Figure 4–6 are representati v e of the testing. T ransfer functions could be sho wn to compare sensors at dif ferent locations. T ransfer functions could also be sho wn to compare signals for lateral e xcitation instead of the v ertical e xcitation. In each case, the comparisons w ould be similar to those already presented. Another comparison w as made to in v estigate the relationship between e xcitation and signal processing. Essentially transfer functions were computed from accelerometer measurements to dif ferent e xcitations using dif ferent dif ferent parameters for the signal processing. Figure 4–7 presents transfer functions that were computed using

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32 1,024 and 2,048 points in the F ourier transform. These results indicate only small ef fect on the transfer function for dif ferent size transforms. Some transfer functions noted dif ferences at limited frequencies; ho we v er the comparisons ne v er noted a consistent ef fect of FFT size. 0 200 400 600 800 1000 10 -4 10 -3 10 -2 10 -1 10 0 10 1 Frequency (Hz)Magnitude (g/lbf) 1024 2048 Figure 4–7: T ransfer Functions for 1024 and 2048 Point T ransforms The result of comparing these e xcitation signals w as a noted similarity in transfer functions. Essentially the transfer functions can be generated using an y of the e xcitation signals under consideration without greatly af fecting the results. All the data w as used for modal analysis b ut this report will restrict the presentation to data from sine sweep testing. This does not conict with an y current industry standards of testing and since the structure displayed a rather lar ge modal density the sine sweep w ould be more lik ely to pro vide an adequate force input and frequenc y resolution to properly characterize the response [ 33 ]. Furthermore, the data analysis will be based on analysis of F ourier transforms with 2,048 points. 4.3 Accelerometer Response to V ertical Excitation A GVT w as performed by measuring accelerometers in response to v ertical e xcitation. T esting w as performed using using b urst random and sine sweep signals. The resulting transfer functions were similar such that no noticeable dif ferences were

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33 noted. A set of these transfer functions are sho wn in Figure 4–8 as being representati v e of the measurements. 0 200 400 600 800 1000 10 -6 10 -4 10 -2 10 0 10 2 Frequency (Hz)Magnitude (g/lbf) bomb pylon fin Figure 4–8: T ransfer Functions at Representati v e Locations Clearly these transfer functions demonstrate a lo w signal to noise ratio. This ef fect is caused by issues such as measurement noise and aliasing. Ne v ertheless, the transfer functions had se v eral peaks that indicated modes. The v alues of natural frequencies and dampings for the modes identied by this GVT are gi v en in T able 4–1 The analysis indicated 9 modes were present between 20 and 1,000 Hz. The damping le v els sho wed lar ge v ariations b ut most modes had relati v ely lo w damping with le v els less than 1%. T able 4–1: Modes Measured by Accelerometers for V ertical Excitation to MK-84 Mode Frequenc y Hz Damping, % 1 46.53 7.63 2 183.32 1.89 3 312.53 1.74 4 443.16 0.247 5 507.61 0.372 6 525.03 -0.812 7 671.99 0.939 8 831.16 0.933 9 899.67 0.241 10 946.22 1.14

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34 A feature of particular interest in T able 4–1 is the mode with natural frequenc y at 525.03 Hz. The modal analysis w as not able to identify the properties of this mode with an y condence. Specically the mode w as identied as being unstable with ne gati v e damping. Such an unstable mode is not physically realistic so further analysis w as done that focused on this mode. Modal analysis using dif ferent parameters, such as number of poles, w as performed using se v eral sets of response data b ut the resulting damping w as al w ays ne gati v e. Thus, the data indicates something of interest at this frequenc y b ut its properties could not be condently identied. It should be noted that the dynamics at 525.03 Hz were noted as being sensiti v e to type of sweep in Figure 4–5 and le v el of force in Figure 4–6 The remaining modes in T able 4–1 were e xtracted as stable modes. The majority of modes shapes in v olv ed signicant displacement of the ns and cone of the tail assembly Some of the mode shapes also in v olv ed motion of the p ylon. Interestingly enough, the main body of the bomb w as rarely observ ed to mo v e much for an y of these modes. The AutoMA C matrix sho wn in T able 4–2 conrms that each of the modes identied are separate distinct modes with the lar gest correlation of 15% between modes 8 and 9. T able 4–2: AutoMA C of Accelerometer Response for V ertical Excitation to MK-84 Modes 1 2 3 4 5 6 7 8 9 10 1 1.00 0.09 0.00 0.03 0.03 0.02 0.03 0.01 0.02 0.02 2 0.09 1.00 0.02 0.01 0.02 0.03 0.02 0.01 0.02 0.01 3 0.00 0.02 1.00 0.01 0.13 0.01 0.05 0.01 0.00 0.01 4 0.03 0.01 0.01 1.00 0.02 0.04 0.00 0.01 0.02 0.04 5 0.03 0.02 0.13 0.02 1.00 0.13 0.00 0.00 0.04 0.04 6 0.02 0.03 0.01 0.04 0.13 1.00 0.02 0.05 0.07 0.00 7 0.03 0.02 0.05 0.00 0.00 0.02 1.00 0.04 0.04 0.01 8 0.01 0.01 0.01 0.01 0.00 0.05 0.04 1.00 0.15 0.01 9 0.02 0.02 0.00 0.02 0.04 0.07 0.04 0.15 1.00 0.04 10 0.02 0.01 0.01 0.04 0.04 0.00 0.01 0.01 0.04 1.00

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35 The mode shape for the dynamics at 46.53 Hz is sho wn in Figure 4–9 This mode, which has the lo west frequenc y of an y mode noted by the testing, appears to be similar in nature to a rigid-body mode. Essentially the bomb and p ylon are rotating longitudinally about their interf ace mounting points. The ns sho w a small amount of bending b ut the mode shape is dominated by the pitch rotation of the p ylon and bomb The trailing-edge ends of the bomb and p ylon sho w the most mo v ement in this mode shape. Furthermore, these trailing-edge ends are mo ving out of phase for the bomb and p ylon. Figure 4–9: Mode Shape at 46 Hz Measured by Accelerometer for V ertical Excitation to MK-84 The mode shape for the dynamics at 183.32 Hz is sho wn in Figure 4–10 This mode shape sho ws little motion of the bomb or p ylon. Instead, the mode shape is dominated by the ns. This mode appears to be a rst-bending mode in the span-wise direction for the ns. The ns sho w v ery little twisting at either the root or tip so the mode appears to be span-wise bending. The mode shape for the dynamics at 312.53 Hz is sho wn in Figure 4–11 This mode in v olv es motion of the p ylon and ns b ut v ery little motion of the main body of the bomb The p ylon motion is a longitudinal bending with the leading-edge and trailing-edge ends mo ving in phase along the v ertical direction. Also, the ns ha v e a

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36 Figure 4–10: Mode Shape at 183 Hz Measured by Accelerometers for V ertical Excitation to MK-84 torsion motion that is characterized by little twist angle near the root b ut increasing twist angle near the tip. Figure 4–11: Mode Shape at 312 Hz Measured by Accelerometers for V ertical Excitation to MK-84 The mode shape for the dynamics at 443.16 Hz is sho wn in Figure 4–12 This mode also in v olv es the p ylon and ns b ut includes little motion of the main body of the bomb The motion of p ylon is restricted to v ertical mo v ement of the leading-edge

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37 end with little corresponding mo v ement of the trailing-edge end. The ns sho w a motion which correlates with a chord-wise bending mode. Figure 4–12: Mode Shape at 443 Hz Measured by Accelerometers for V ertical Excitation to MK-84 The mode shape for the dynamics at 507.61 Hz is sho wn in Figure 4–13 This mode shape is characterized by some motion at the nose of the p ylon along with lar ge motion in v olving the ns and cone of the tail assembly The tail cone demonstrates a rst-bending type of motion. This bending is e vident in measurements from accelerometers on the cone and at the root of the ns. Also, the ns sho w some torsional motion in this mode shape. The p ylon motion is small and constrained mainly to v ertical oscillations at the leading-edge end. The mode shape for the dynamics at 671.99 Hz is sho wn in Figure 4–14 The mode shape for this dynamic is almost purely af fecting the ns. The lar gest motion is seen by the trailing-edge mid-span point on the ns. Con v ersely the leading-edge point at the root of the ns sho ws almost no motion. The mode shape for the dynamics at 831.16 Hz is sho wn in Figure 4–15 This mode shape sho ws a some what complicated relationship between the ns and the cone of the tail assembly The leading-edge end of the cone sho ws signicant in-phase v ertical and lateral motion. The complication arises when considering the ns. The

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38 Figure 4–13: Mode Shape at 507 Hz Measured by Accelerometers for V ertical Excitation to MK-84 Figure 4–14: Mode Shape at 671 Hz Measured by Accelerometers for V ertical Excitation to MK-84 trailing-edge root of the upper ns sho w lar ge modal displacements b ut the same points on the lo wer ns sho w small modal displacements. The mode shape for the dynamics at 899.67 Hz is sho wn in Figure 4–16 This mode shape again sho ws v ery little motion of the p ylon or the main body of the bomb The tail cone sho ws bending in both v ertical and lateral direction which is also demonstrated in the measurements tak en at the root of the ns. The outer portions of

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39 Figure 4–15: Mode Shape at 831 Hz Measured by Accelerometers for V ertical Excitation to MK-84 the ns appear as a higher -order modal shape that has contrib utions of both bending and torsion. Figure 4–16: Mode Shape at 899 Hz Measured by Accelerometers for V ertical Excitation to MK-84 The mode shape for the dynamics at 946.22 Hz is sho wn in Figure 4–17 This mode shape is v ery similar in nature to the dynamic at 899.67 Hz. The only noticeable dif ference between these tw o modes is the motion of the lo wer ns. The motion at

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40 946.22 Hz sho ws both bending and torsion motion b ut it appears slightly dif ferent than the motion at 899.67 Hz. Figure 4–17: Mode Shape at 946 Hz Measured by Accelerometers for V ertical Excitation to MK-84 4.4 Accelerometer Response to Lateral Excitation A GVT w as performed using accelerometers to measure response to lateral e xcitation. Again, testing w as performed using b urst random and sine sweep signals b ut the resulting transfer functions sho wed little appreciable dif ferences. A set of these transfer functions are sho wn in Figure 4–18 as being representati v e of the measurements. 0 200 400 600 800 1000 10 -6 10 -4 10 -2 10 0 10 2 Frequency (Hz)Magnitude (g/lbf) bomb pylon fin Figure 4–18: T ransfer Functions at Representati v e Locations

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41 These transfer functions demonstrate a lo w signal to noise ratio that is similar to that in Figure 4–8 This high le v el of noise corrupts the modal analysis some what b ut se v eral modes can still be distinguished in the transfer functions. The transfer functions were analyzed to obtain parameters associated with modal dynamics of the test article. These parameters are gi v en in T able 4–3 T able 4–3: Modes Measured by Accelerometers for Lateral Excitation to MK-84 Mode Frequenc y Hz Damping, % 1 186.30 0.61908 2 296.90 1.10000 3 356.59 0.99378 4 548.51 0.30621 5 680.64 0.40961 6 858.42 0.62867 7 969.66 0.31425 Only 7 modes were identied between 20 and 1000 Hz using lateral e xcitation. Se v eral of these modes ha v e natural frequencies close to the modes identied from v ertical e xcitation. In particular the natural frequencies of 186.3 and 680.64 Hz in T able 4–3 are close to the natural frequencies of 183.32 and 671.99 Hz in T able 4–1 The lateral mode at 186.3 Hz and the v ertical mode at 183.3 Hz actually ha v e similar mode shapes so these modes may be caused by the same dynamic. Con v ersely the modes are quite dif ferent for the lateral mode at 680.6 Hz and the v ertical mode at 671.9 Hz so the underlying dynamics are probably distinct. The AutoMA C matrix sho wn in T able 4–4 assures that the modes identied are distinct with the highest de gree of being between modes 4 and 2. The mode shape for the dynamics at 186.3 Hz is sho wn in Figure 4–19 This mode sho ws motion in both the ns and p ylon b ut little motion in the main body of the bomb The n motion is similar in nature to a span-wise bending mode. The p ylon is some what more complicated with distinct features. One feature of the mode shape is a

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42 T able 4–4: AutoMA C of Accelerometer Response for Lateral Excitation to MK-84 Modes 1 2 3 4 5 6 7 1 1.00 0.01 0.00 0.09 0.00 0.01 0.00 2 0.01 1.00 0.13 0.16 0.04 0.08 0.01 3 0.00 0.13 1.00 0.08 0.02 0.04 0.03 4 0.09 0.16 0.08 1.00 0.01 0.09 0.03 5 0.00 0.04 0.02 0.01 1.00 0.13 0.04 6 0.01 0.08 0.04 0.09 0.13 1.00 0.01 7 0.00 0.01 0.03 0.03 0.04 0.01 1.00 slight lateral motion of the leading-edge nose of the p ylon. Another feature is bending localized around the mid-span point of the p ylon. Figure 4–19: Mode Shape at 186.3 Hz Measured by Accelerometers for Lateral Excitation to MK-84 The mode shape for the dynamics at 296.9 Hz is sho wn in Figure 4–20 This mode is characterized by a torsion motion of the ns. The tip of each n is clearly twisting in comparison to the root of each n. Also, the leading-edge end of the p ylon sho ws some oscillation in both lateral and v ertical directions. The trailing-edge end of the p ylon and the main body of the bomb sho w almost no motion. The mode shape for the dynamics at 356.59 Hz is sho wn in Figure 4–21 The mode shape for this dynamic in v olv es mostly the n with v ery small motions of the

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43 Figure 4–20: Mode Shape at 296.9 Hz Measured by Accelerometers for Lateral Excitation to MK-84 bomb and p ylon. The ns are sho wing a some what complicated motion. Specically the leading-edge mid-span point is mo ving more than the rest of the n. Also, this point is mo ving out of phase with the other points on the n. Figure 4–21: Mode Shape at 356.59 Hz Measured by Accelerometers for Lateral Excitation to MK-84

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44 The mode shape for the dynamics at 548.51 Hz is sho wn in Figure 4–22 This mode shape is particularly complicated to describe. The ns appear to mo v e as a bending mode; ho we v er the upper and lo wer ns demonstrate some dif ferent motion. The lo wer ns sho w more of a classical rst-bending shape whereas the upper ns indicate similarity to a second-bending shape. The motion is further complicated by noting the trailing-edge root of each n seems to be out of phase with the trailing-edge end of the tail assembly on the bomb Figure 4–22: Mode Shape at 548.51 Hz Measured by Accelerometers for Lateral Excitation to MK-84 The mode shape for the dynamics at 680.64 Hz is sho wn in Figure 4–23 The p ylon and main body of the bomb sho w minor motion in this mode shape; therefore, the Figure sho ws only the tail assembly to allo w detailed consideration of its motion. The mode shape is seen to in v olv e complicated interactions between the n and cone components of the tail assembly on the bomb The ns demonstrate a b ubble-type mode in which the mid-span mid-chord points, at the center of the ns, sho w the lar gest deections. Furthermore, these center points mo v e out of phase with the other points on the ns. The cone of the tail assembly sho ws bending-type motion. In

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45 particular the leading-edge end of the cone sho ws lar ge lateral motion b ut the trailingedge end of the cone sho ws lar ge v ertical motion. Each bending, v ertical and lateral, sho ws a nodal point at which little motion is observ ed. Figure 4–23: Mode Shape at 680.64 Hz Measured by Accelerometers for Lateral Excitation to MK-84 The mode shape for the dynamics at 858.42 Hz is sho wn in Figure 4–24 This Figure again sho ws only the tail assembly to simplify the analysis. This mode shape actually appears to be a higher -order v ersion of the dynamics at 680.64 Hz. The midspan mid-chord point at the center of the ns mo v es a lot b ut no w the leading-edge and trailing-edge points at mid-span locations also mo v e. The entire set of mid-span points are mo ving out of phase with the points at the root and tip of the ns. Also, the tail cone again sho ws bending motion b ut the nodal points ha v e changed between 680.64 Hz mode and this mode. The lateral motion does not sho w a nodal point and the v ertical motion sho ws a nodal point that has mo v ed to w ards the trailing-edge end of the cone. The mode shape for the dynamics at 969.66 Hz is sho wn in Figure 4–25 This mode presents some dif culty for analysis. Essentially the mode shape at 969.66 Hz is quite similar to the mode shape at 858.42 Hz. The dif ferences are slight so distinguishing between the modes is dif cult.

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46 Figure 4–24: Mode Shape at 858.42 Hz Measured by Accelerometers for Lateral Excitation to MK-84 Figure 4–25: Mode Shape at 969.66 Hz Measured by Accelerometers for Lateral Excitation to MK-84 4.5 Laser Response to Lateral Excitation A GVT w as also performed using the laser Doppler vibrometer to measure responses to lateral e xcitation. The testing only considered sine sweep signals. A set of these transfer functions are sho wn in Figure 4–26 as being representati v e of the measurements. The transfer functions from the laser measurements clearly ha v e a higher signal to noise ratio than the data resulting from accelerometers. The reduction in noise is

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47 0 50 100 150 200 250 300 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 Frequency (Hz)Magnitude (g/lbf) fin pylon Figure 4–26: T ransfer Functions at Representati v e Locations almost certainly related to the non-contact nature of the measurement obtained from the laser Noise related to the sensor mounting and wiring are inherently a v oided with this type of measurement. Modal dynamics were e xtracted from these transfer functions. The parameters for the resulting modes are presented in T able 4–5 T able 4–5: Modes Measured by Laser for Lateral Excitation to MK-84 Mode Frequenc y (Hz) Damping 1 86.41 1.64 2 135.71 1.05 3 189.05 2.12 4 239.73 1.82 5 293.35 0.323 The modes identied from the laser dif fer from those identied by the accelerometers e v en though both used similar e xcitation. Specically the laser data indicated 5 modes between 86 and 300 Hz whereas the accelerometer data indicated only 2 modes in this range. This discrepanc y lik ely results from the better data obtained using the laser Se v eral modes are probably hidden in the noise le v el of the accelerometer data b ut are easily seen in the laser data. The AutoMA C matrix sho wn in T able 4–6 re v eals

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48 a correlation of 28% between modes 2 and 3 which indicates that the modes are f airly correlated and may display a de gree of similarity in mode shape. T able 4–6: AutoMA C of Laser Response for Lateral Excitation to MK-84 Modes 1 2 3 4 5 1 1.00 0.02 0.02 0.06 0.04 2 0.02 1.00 0.28 0.06 0.01 3 0.02 0.28 1.00 0.01 0.01 4 0.06 0.06 0.01 1.00 0.06 5 0.04 0.01 0.01 0.06 1.00 The mode shape for the dynamics at 86.41 Hz is sho wn in Figure 4–27 This mode is some what dif cult to characterize because of the disparity between the ns and the p ylon. The ns are clearly under going a smooth bending motion; ho we v er the p ylon is not easy to understand. The points on the p ylon sho w small amounts of lateral motion that appears almost random in terms of both magnitude and phase. Figure 4–27: Mode Shape at 86.41 Hz Measured by Laser for Lateral Excitation to MK-84 The mode shape for the dynamics at 135.71 Hz is sho wn in Figure 4–28 This mode is predominately a bending mode for the ns. The mid-point area on the p ylon sho ws some bending b ut the p ylon displacement is considerably smaller than the n displacement.

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49 Figure 4–28: Mode Shape at 135.71 Hz Measured by Laser for Lateral Excitation to MK-84 The mode shape for the dynamics at 189.05 Hz is sho wn in Figure 4–29 The main feature of this mode is some localized motion on the p ylon. The area around the mid-point location of the p ylon is mo ving laterally in response to this e xcitation. The ns also sho w some bending motion b ut clearly the p ylon motion is the dominate part of this mode. An additional feature of this mode is a slight rotation of the entire p ylon about the mounting point. The trailing-edge end of the p ylon is in phase with the localized mid-point locations and out of phase with the leading-edge end during this rotation. Figure 4–29: Mode Shape at 189.05 Hz Measured by Laser for Lateral Excitation to MK-84

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50 The mode shape for the dynamics at 239.73 Hz is sho wn for the test article in Figure 4–30 and for the ns in Figure 4–31 This mode contains interesting features for both the ns and p ylon. The p ylon motion is dominated by a lateral bending at the leading-edge nose. The remaining areas of the p ylon sho w some motion b ut these motions are clearly smaller than the nose displacement. Figure 4–30: Mode Shape at 239.73 Hz Measured by Laser for Lateral Excitation to MK-84 The motion of the ns is e xpanded in Figure 4–31 This motion clearly correlates to a chord-wise bending mode. The mid-chord line is sho wn to ha v e v ery little displacement while the leading-edge and trailing-edge points ha v e lar ge displacements. The mode shape for the dynamics at 293.35 Hz is sho wn in Figure 4–32 This mode shape might indicate some higher -order dynamics for both the p ylon and ns. The ns sho w some chord-wise bending b ut the motion is complicated and not v ery smooth. The p ylon sho ws the localized mid-point bending b ut also motion near the ends. Specically the leading-edge ends are mo ving out of phase with the trailing-edge ends. This bending motion is localized to only the ends so the mode does not appear to be a rotation; rather the mode in v olv es bending of only the ends. 4.6 Scan Response to Lateral Excitation The transfer functions and associated mode shapes, sho wn in Figure 4–26 to Figure 4–32 indicated the laser w as capable of determining information about se v eral modes. These rst set of data were collected by taking data at widely-space discrete points and analyzing using ST ARModal; ho we v er information with ner

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51 Figure 4–31: Mode Shape at 239.73 Hz Measured by Laser for Lateral Excitation to MK-84 Figure 4–32: Mode Shape at 293.35 Hz Measured by Laser for Lateral Excitation to MK-84 resolution could also be obtained using scanning. This scanning w as done to co v er a limited portion of the test article with man y closed-spaced measurements. Also, the

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52 scanning w as restricted to single frequencies to allo w maximum information about a specic mode to be obtained. The resulting mode shapes were identied by softw are proprietary to the PolyT ec system. The scan w as or ganized to focus on either the port-side upper n or the midsection of the p ylon. The scan of the n used 247 points whereas the scan of the p ylon used 279 points. The measurements of responses on the n where tak en at 512 Hz for 2 s. Con v ersely the measurements of the responses on the p ylon were tak en at 1024 Hz for 1 s. A scan w as performed to concentrate on the modal dynamics near 185 Hz. The resulting mode shape is sho wn through 2-dimensional intensity shading in Figure 4–33 This mode is clearly a span-wise rst-bending dynamic. This mode shape agrees with the mode shapes determined by accelerometer measurements in Figure 4–19 and determined by laser measurements in Figure 4–29 The only dif ference is the higher resolution resulting from scanning the surf ace. Figure 4–33: Mode Shape at 185 Hz Measured by Laser Scan on Fin of MK-84

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53 The p ylon w as also tested at this frequenc y The resulting mode shape is sho wn in Figure 4–34 The p ylon motion agrees well with the modes shapes obtained by the accelerometer measurements in Figure 4–19 and determined by laser measurements in Figure 4–29 Again, the dif ference between the closely-spaced scanning data and the widely-spaced data is the increased resolution of the scanning data. The scanning data deniti v ely notes that the p ylon vibration is isolated to a local re gion of the p ylon. Figure 4–34: Mode Shape at 185 Hz Measured by Laser Scan on PIDS-3 Pylon Finally a scan of just the n w as done with an e xcitation frequenc y of 290 Hz. Figure 4–35 sho ws the result as being similar in nature to a chord-wise bending mode. The actual mode shape sho ws the greatest deection occurs about 3 in. a w ay from the leading-edge and trailing-edge ends of the n.

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54 Figure 4–35: Mode Shape at 290 Hz Measured by Laser Scan on Fin of MK-84

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CHAPTER 5 GVT ON PIDS-3 AND GB U-10 5.1 T est Conguration A set of ground vibration tests were conducted on the test article composed of the GB U-10 and PIDS-3 p ylon. This set of tests used only the accelerometers to measure motion at distinct points on the article. Also, the e xcitation w as limited to lateral input at 95 in. aft of the nose. Accelerometers were mounted at 73 locations on the test article during 3 tests. The rst test used 12 measurements of lateral motion on the bomb, 12 measurements of v ertical motion on the bomb, and 3 measurements of lateral motion on the p ylon. The second test used 26 measurements of motion on the ns. The nal test used 17 measurements of lateral motion on the p ylon and 3 measurements of v ertical motion on the p ylon. Se v eral of the accelerometer locations are sho wn in Figure 5–1 This dra wing indicates the accelerometers measuring lateral motion on the p ylon and bomb Figure 5–1: Measurement Points for GVT of GB U-10 The remainder of the accelerometer locations are sho wn in Figure 5–2 The left dra wing sho ws the vie w from under the test article. This vie w sho ws locations of the v ertical measurements on the bomb and the locations of measurements on the lo wer ns. The right dra wing sho ws the vie w from o v er the test article. This vie w sho ws 55

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56 locations of the v ertical measurements on the p ylon and the locations of measurements on the upper ns. Figure 5–2: Measurement Points for GVT of GB U-10 5.2 Accelerometer Response to Lateral Excitation A GVT w as performed by measuring accelerometers in response to v ertical e xcitation. T esting w as performed using using b urst random and sine sweep signals. The resulting transfer functions were similar such that no noticeable dif ferences were noted. The high le v el of noise in the measurements is sho wn for a representati v e set of transfer functions in Figure 5–3 0 200 400 600 800 1000 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 Frequency (Hz)Magnitude (g/lbf) bomb pylon fin Figure 5–3: T ransfer Functions at Representati v e Locations The v alues of natural frequencies and dampings for the modes identied by this GVT are gi v en in T able 4–1 The analysis indicated 13 modes were present between 20 and 1000 Hz. The damping le v els sho wed lar ge v ariations b ut most modes had relati v ely lo w damping with le v els less than 1%.

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57 T able 5–1: Modes Measured for Lateral Excitation to GB U-10 Mode Frequenc y Hz Damping, % 1 35.78 4.86 2 84.71 6.11 3 169.71 1.57 4 275.53 -0.547 5 288.44 0.106 6 358.70 0.829 7 535.62 0.479 8 571.56 0.332 9 650.52 -0.270 10 719.88 0.098 11 838.73 0.407 12 882.25 -0.505 13 953.44 0.263 The analysis of the accelerometer data for the GB U-10, similar to some data for the MK-84, generated some unstable modes. These modes are again not considered to be physical realistic b ut the instabilities could not be remo v ed despite v arying the number of poles, adjusting the frequenc y limits, and changing the curv e tting routine. The AutoMA C matrix sho wn in T able 5–2 indicates that modes 4 and 6 are quite similar with a 52% correlation between them. T able 5–2: AutoMA C of Accelerometer Response for Lateral Excitation to GB U-10 Modes 1 2 3 4 5 6 7 8 9 10 11 12 13 1 1.00 0.01 0.05 0.01 0.02 0.00 0.10 0.10 0.04 0.01 0.02 0.02 0.00 2 0.01 1.00 0.12 0.22 0.09 0.21 0.01 0.00 0.09 0.03 0.00 0.02 0.01 3 0.05 0.12 1.00 0.06 0.10 0.09 0.05 0.05 0.10 0.00 0.00 0.03 0.01 4 0.01 0.22 0.06 1.00 0.01 0.52 0.05 0.03 0.21 0.00 0.00 0.02 0.04 5 0.02 0.09 0.10 0.01 1.00 0.06 0.02 0.04 0.03 0.14 0.01 0.02 0.01 6 0.00 0.21 0.09 0.52 0.06 1.00 0.14 0.00 0.18 0.05 0.01 0.01 0.01 7 0.10 0.01 0.05 0.05 0.02 0.14 1.00 0.09 0.11 0.11 0.04 0.02 0.05 8 0.10 0.00 0.05 0.03 0.04 0.00 0.09 1.00 0.11 0.07 0.15 0.09 0.01 9 0.04 0.09 0.10 0.21 0.03 0.18 0.11 0.11 1.00 0.01 0.06 0.16 0.05 10 0.01 0.03 0.00 0.00 0.14 0.05 0.11 0.07 0.01 1.00 0.02 0.02 0.04 11 0.02 0.00 0.00 0.00 0.01 0.01 0.04 0.15 0.06 0.02 1.00 0.12 0.04 12 0.02 0.02 0.03 0.02 0.02 0.01 0.02 0.09 0.16 0.02 0.12 1.00 0.08 13 0.00 0.01 0.01 0.04 0.01 0.01 0.05 0.01 0.05 0.04 0.04 0.08 1.00

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58 The mode shape for the dynamics at 35.78 Hz is sho wn in Figure 5–4 The p ylon e xhibits a lar ge amount of motion characterized by out of phase bending of the leading-edge and trailing-edge ends. This p ylon displacement is a rotation, or rocking motion, about the center The ns sho w a bending motion with only the trailing-edge root x ed while all other points mo v e uniformly around the body of the tail cone in an angular f ashion. The tail cone itself sho ws only slight deformation. Figure 5–4: Mode Shape at 35.78 Hz Measured for Lateral Excitation to GB U-10 The mode shape for the dynamics at 84.71 Hz is sho wn in Figure 5–5 The p ylon sho ws only minor displacement b ut the bomb sho ws f airly lar ge displacement. One type of motion is a bending of the main body of the bomb that causes the displacement of the nose and tail cone. Another type of motion is a combination of bending and torsion of the ns. The root and leading-edge ends of the ns are nearly motionless such that the mode shape is dominated by lar ge displacements at the trailing-edge tip of the ns. The mode shape for the dynamics at 169.71 Hz is sho wn in Figure 5–6 This mode sho ws the same n motion as the 84.71 Hz mode. The motion in the tail cone is of the same amplitude as the pre vious mode b ut has additional nodes at one-third and tw o-thirds of the length of that section. Moreo v er the p ylon motion is no w quite

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59 Figure 5–5: Mode Shape at 84.71 Hz Measured for Lateral Excitation to GB U-10 drastic such that it sho ws bending about the center as in the rst mode. Also, the local mode near the horizontal and v ertical center of the p ylon disco v ered in the MK-84 test near 186 Hz is present and out of phase with the o v erall motion of the p ylon. Figure 5–6: Mode Shape at 169.71 Hz Measured for Lateral Excitation to GB U-10 The mode shape for the dynamics at 275.53 Hz is sho wn in Figure 5–7 The most interesting feature of this mode shape is the distinctly dif ferent motion of the upper and lo wer ns. Specically the lo wer ns sho w a bending motion similar to the mode shape at 84.71 Hz b ut the upper ns sho w bending about the trailing-edge

PAGE 70

60 mid-span point. Also, the mode shape is dominated by lar ge displacement of the tail cone of the bomb The leading-edge nose of the p ylon sho ws additional displacement with moderate magnitude. Most importantly this mode w as identied with ne gati v e damping; therefore, the mode shape may not be physically realistic. Figure 5–7: Mode Shape at 275.53 Hz Measured for Lateral Excitation to GB U-10 The mode shape for the dynamics at 288.44 Hz is sho wn in Figure 5–8 The only motion for this mode shape is a small displacement of the cone and reasonable displacement of the ns of the tail assembly Again, the motion of the ns is distinct between the upper and lo wer ns. The lo wer ns sho w rst-order displacement only at the trailing-edge tip while the upper ns sho w second-order bending with the trailing-edge end out of phase with the mid-chord line. The mode shape for the dynamics at 358.7 Hz is sho wn in Figure 5–9 The only motion is again associated with the cone and ns of the tail assembly; ho we v er the motion is each part is changed from the pre vious mode shape. The tail cone seems to deform laterally such that the side of the cone sho ws displacements much lar ger than an y displacement of the bottom of the cone. The lo wer ns sho w bending dominated by the trailing-edge tip b ut this bending includes a node point just inside the mid-span

PAGE 71

61 Figure 5–8: Mode Shape at 288.44 Hz Measured for Lateral Excitation to GB U-10 point. The upper ns sho w bending at the trailing-edge and mid-chord locations b ut the mid-span points are out of phase with the root and tip. Figure 5–9: Mode Shape at 358.7 Hz Measured for Lateral Excitation to GB U-10 The mode shape for the dynamics at 535.62 Hz is sho wn in Figure 5–10 The displacement due to this mode shape is restricted to the cone and ns of the tail assembly Each n sho wed similar motion of the trailing-edge tip. The upper n also sho wed motion of the mid-span mid-chord point b ut no sensor w as a v ailable at this

PAGE 72

62 location on the lo wer ns to allo w comparison. The tail cone w as moderately displaced in this mode shape. Figure 5–10: Mode Shape at 535.62 Hz Measured for Lateral Excitation to GB U-10 The mode shape for the dynamics at 571.56 Hz is sho wn in Figure 5–11 This mode shape in v olv es displacements of e v ery part of the test article. The p ylon sho ws motion that is restricted to the leading-edge and trailing-edge ends. The tail cone sho ws v ery lar ge displacements both on the side and on the bottom. Furthermore, the upper ns and lo wer ns are mo ving b ut in dif ferent f ashion. The upper ns ha v e lar ge trailing-edge mid-span and mid-chord tip motion, relati v ely little motion at the leading-edge end, and moderate motion at mid-chord mid-span points and mid-chord root points. The lo wer ns sho w no leading-edge motion and moderate to lar ge trailing-edge motion. The mode shape for the dynamics at 650.52 Hz is sho wn in Figure 5–12 This mode is suspiciously similar to the pre vious mode at 571.56 Hz. The similarity coupled with its unstable ne gati v e damping, may indicate that the modal analysis at this frequenc y is unreliable. The mode shape for the dynamics at 719.88 Hz is sho wn in Figure 5–13 This mode sho ws the lar ge motion in the tail cone appearing to bend about its attachment

PAGE 73

63 Figure 5–11: Mode Shape at 571.56 Hz Measured for Lateral Excitation to GB U-10 Figure 5–12: Mode Shape at 650.52 Hz Measured for Lateral Excitation to GB U-10 point to the main body of the bomb The underside of the tail section sho ws no node point b ut the side sho ws a node approximately tw o-thirds of the w ay back from the attachment point. Also, the motion of the lo wer ns is minor in comparison to the motion of the upper ns. Specically the upper ns ha v e lar ge trailing-edge mid-span motion that is out of phase with the lar ge mid-chord mid-span motion. The mode shape for the dynamics at 838.73 Hz is sho wn in Figure 5–14 The tail sho ws lar ge motion with a node on the underneath side at nearly the mid-length point

PAGE 74

64 Figure 5–13: Mode Shape at 719.88 Hz Measured for Lateral Excitation to GB U-10 of the tail section. The upper ns sho w lar ge motion at the root and tip mid-chord location that is out of phase with the lar ge mid-chord/mid-span motion. The trailingedge mid-span motion is also lar ge and in phase with the root and tip mid-chord motion. The lo wer ns sho w only modest trailing-edge motion. No notable p ylon motion is observ ed for this mode. Figure 5–14: Mode Shape at 838.73 Hz Measured for Lateral Excitation to GB U-10 The mode shape for the dynamics at 882.25 Hz is sho wn in Figure 5–15 The tail cone motion is similar to the pre vious mode e xcept that the node appears to ha v e mo v ed back to nearly tw o-thirds of the total length from the attachment point. The

PAGE 75

65 upper ns are the same as the pre vious mode with slightly smaller amplitude whereas the lo wer ns are the same as in the pre vious mode with slightly lar ger amplitude. Note that this is mode w as identied with ne gati v e damping so the mode shape is not condently accepted and may not be physically realistic. Figure 5–15: Mode Shape at 882.25 Hz Measured for Lateral Excitation to GB U-10 The mode shape for the dynamics at 953.44 Hz is sho wn in Figure 5–16 The tail section sho ws moderate motion whereas the p ylon and main body of the bomb are relati v ely motionless. The upper ns sho w quite a bit of comple xity in their motion. The leading-edge sho ws moderate motion with all locations from root to tip in phase. Also, lar ge mid-chord motion e xists at the tip and mid-span points while only little motion e xists at the root. All points at the mid-chord line are out of phase with the leading-edge and trailing-edge ends. The motions at the trailing-edge root and tip are of small amplitude while the motion at mid-span points is lar ge and in phase with the mid-span mid-chord point. In sharp contrast, the lo wer ns sho w only small motions with no out of phase motion at mid-span.

PAGE 76

66 Figure 5–16: Mode Shape at 953.44 Hz Measured for Lateral Excitation to GB U-10

PAGE 77

CHAPTER 6 SUMMAR Y The p ylon-store dynamics are quite interesting for the MK-84 and GB U-10 munitions mounted to a PIDS-3 p ylon. In particular the GVT of these test articles indicates the p ylon and tail assemblies on the bombs are highly coupled. This coupling relates the p ylon with both the cone and ns of the tail assemblies. The nature of the mode shapes included in phase and out of phase motion of the v arious components. An especially interesting feature of the GVT results is the dif ferent beha viors observ ed between the upper and lo wer ns. These ns had distinctly dif ferent motions for se v eral modes. The mode shape for the MK-84 mounted to a PIDS-3 in response to lateral e xcitation sho wed dif ferences between upper and lo wer ns at 548.31 Hz More importantly the mode shapes for the GB U-10 mounted to a PIDS-3 in response to lateral e xcitation sho wed dif ferences between upper and lo wer ns for all 10 modes with natural frequencies abo v e 275.53 Hz These dif ferences v aried from similar motion with dif ferent magnitudes to drastically dif ferent motion with dif ferent magnitudes. Another interesting feature of the GVT results is the local mode af fecting the p ylon at 186.30 Hz The mode shape for this dynamic is characterized by a lateral bending af fecting only a small portion of the p ylon. The ns on the munitions were also bending some what b ut the dominant feature w as clearly the displacement of the p ylon re gion. Finally the performance of the GVT is itself interesting to e v aluate. In particular the use of accelerometers and a laser Doppler vibrometer is w orth noting. The data measured by the laser had signicantly less noise and w as easier to analyze than the data measured by the accelerometers. Con v ersely the preparation time w as 67

PAGE 78

68 signicantly less for the accelerometers than for the laser These dif ferences suggest the laser is an e xcellent tool for GVT of the test articles as long as suf cient time is allocated for the test. The modes shapes obtained by the GVT may be indicati v e of dynamics related to the n damage that w as recently observ ed. Ob viously the modes in v olving p ylon-store coupling are potential indicators of the damage-inducing dynamics. The mode shapes in v olving dif ferent motions between the upper and lo wer also ha v e strong potential to be related to the damage. The parameters and mode shapes identied from the GVT should be used as a foundation to continue further e xperimental and computational studies into the coupled p ylon-store dynamics.

PAGE 79

REFERENCES [1] P L. W alter “ Accelerometer Selection for and Application to Modal Analysis. ” IMA C XVII Pr oceedings 1999. [2] PCB Piezotronics Inc. Shoc k and V ibr ation Sensor s Catalo g Depe w Ne w Y ork, PCB Piezotronics Inc., 1999. [3] R. I. Le vin, N. A. J. Lie v en, and G. W Skingle. “Comparison of Accelerometer and Laser Doppler V ibrometer Measurement T echniques for a V ibration T est of a Lar ge Aerospace Structure. ” Pr oceedings of SPIE Thir d International Confer ence on V ibr ation Measur ements by Laser T ec hniques: Advances and Applications v olume 3411, 1998. [4] A. B. Stanbridge and D. J. Ewins. “Modal T esting Using a Scanning Laser Doppler V ibrometer ” Mec hanical Systems and Signal Pr ocessing 13, 1999. [5] A. B. Stanbridge, M. Martarelli, and D. J. Ewins. “Measuring Area Mode Shapes with a Scanning Laser Doppler V ibrometer ” IMA C XVII Pr oceedings 1999. [6] A. B. Stanbridge, M. Martarelli, and D. J. Ewins. “The Scanning Laser Doppler V ibrometer Applied to Impact Modal T esting. ” IMA C XVII Pr oceedings 1999. [7] M. B. Klein and G. D. Bacher “No v el Single-Beam V ector V elocity V ibrometer for Modal Analysis. ” IMA C XVII Pr oceedings 1999. [8] G. Graham, J. Petzing, M. Lucas, and J. T yrer “Quantitati v e modal Analysis Using Electronic Speckle P attern Interferometry ” Optics and Laser s in Engineering 31, 1999. [9] D. J. Ewins. Modal T esting Baldock, Hertfordshire, England, Research Studies Press Ltd., 2000. [10] D. F otsch and D. J. Ewins. “ Application of MA C in the Frequenc y Domain. ” IMA C XVIII Pr oceedings 2000. [11] H. V an der Auweraer W Leurs, P Mas, and L. Hermans. “Modal P arameter Estimation From inconsistent Data Sets. ” IMA C XVIII Pr oceedings 2000. [12] P Guillaume, P V erbo v en, S. V anlanduit, and E. P arloo. “ Accurate Damping Estimates Using Adapted Frequenc y-Domain Identication T echniques. ” IMA C XVIII Pr oceedings 2000. 69

PAGE 80

70 [13] P V erbo v en, P Guillaume, and M. V an Ov ermeire. “Impro v ed Modal P arameter Estimation Using Exponential W indo wing and Non-parametric Instrumental V ariables T echniqus. ” IMA C XVIII Pr oceedings 2000. [14] M. W K ehoe. “ Aircraft Ground V ibration T esting at N ASA Ames-Dryden Flight Research F acility ” T echnical Report 88272, N ASA, July 1987. [15] M. W K ehoe and L. C. Freudinger “ Aircraft Ground V ibration T esting at the N ASA-Dryden Flight Research F acility 1993. ” T echnical Report 104275, N ASA, June 1994. [16] M. W K ehoe and D. F V oracek. “Ground V ibration T est Results of a JetStar Airplane Using Impulsi v e Sine Excitation. ” T echnical Report 100448, N ASA, Feb 1989. [17] M. W K ehoe. “Modied U.S. Army U-8F Ground V ibration T est. ” T echnical Report 86741, N ASA, Aug. 1986. [18] D. F V oracek. “Ground V ibration and Flight FLutter T est of a Single-Seat F16XL Aircraft with a Modied W ing. ” T echnical Report 104269, N ASA, June 1993. [19] W Lo, C. Shih, and G. Hinote. “Ground V ibration T est of a Commerical Aircraft. ” IMA C XIX Pr oceedings 2001. [20] M. Sano, K. K omatsu, and M. Mine gishi. “Comparison of Modal T esting Methods of Aircraft. ” IMA C XVII Pr oceedings 1999. [21] K. O. Kappus, T C. Driskill, and R. A. P arks. “Modal T esting of Se v en Shuttle Car go Elements for Space Station. ” IMA C XX Pr oceedings 2002. [22] G. Gloth, M. De gener U. Fullekrug, J. Gschwilm, M. Sinapius, P .F ar gette, B. Le v adoux, and P Lubrina. “Experimental In v estigation of Ne w GVT Concepts for Lar ge Aircraft. ” IMA C XIX Pr oceedings 2001. [23] B. R. Jor gensen, T W oehrle, M. Eli, and C. T Cho w “ Modal Response of Interior Mass Based Upon External Measurements. ” IMA C XVII Pr oceedings 1999. [24] He wlett-P ackard Co. Fundamentals of Modal T esting Application Note 243-3 He wlett-P ackard Co., 1991. [25] K. G. McConnell and P aolo Cappa. “T ransducer Inertia and Stinger Stif fness Ef fects on FRF Measurements. ” IMA C XVII Pr oceedings 1999. [26] G. C. F oss. “Measurement System Noise. ” IMA C XX Pr oceedings 2002. [27] M. R. Ashory “ Assessment of the Mass-Loading Ef fects of Accelerometers in Modal T esting. ” IMA C XX Pr oceedings 2002.

PAGE 81

71 [28] S. Gade, N. B. Moller N. Jacobsen, and B. Hardonk. “Modal Analysis Using a Scanning Laser Doppler V ibrometer ” IMA C XX Pr oceedings 2002. [29] Inc. Spectral Dynamics. The ST AR System Manuals, Refer ence Manual 34050114 San Jose, California, Spectral Dynamics, Inc., 2001. [30] W T Thomson. Theory of V ibr ation with Applications, 2nd edition Engle w ood Clif fs, Ne w Jerse y Prentice Hall, Inc., 1981. [31] D. Kincaid and W Chene y Numerical Analysis P acic Gro v e, California, Brooks/Cole Publishing Compan y 1991. [32] K. G. McConnell. V ibr ation T esting: Theory and Pr actice Ne w Y ork, John W ile y & Sons, Inc., 1995. [33] R. J. Dieck elman, A. J. Hauenstein, and R. P Ritzel. “Modern Sine Excitation GVT T echniques. ” IMA C XX Pr oceedings 2002.

PAGE 82

BIOGRAPHICAL SKETCH Joseph Dupuis w as born in Bethesda, Maryland, on December 3 r d 1971. The Dupuis f amily mo v ed to the W est P alm Beach, Florida, area where Joseph w as to spend his formati v e years. His colle ge studies be gan at the P alm Beach Community Colle ge in Lak e W orth, Florida, in 1989 where he recei v ed an A.A. de gree in music. He later changed majors and went on to recei v e a B.S. de gree in physics from the Uni v ersity of Florida in Gainesville. Since 2002, Joseph has attended the Colle ge of Engineering at the Uni v ersity of Florida to pursue his M.S. de gree in aerospace engineering. During this time he has w ork ed part-time as a teaching and research assistant in the Department of Mechanical and Aerospace Engineering. He has also w ork ed as a medical laboratory assistant in the Blood Bank at Shands hospital at U.F His research interests focus on structural dynamics. 72


Permanent Link: http://ufdc.ufl.edu/UFE0000677/00001

Material Information

Title: Ground vibration testing of airplane pylon-store dynamics using laser doppler vibrometer and accelerometer techniques
Physical Description: Mixed Material
Creator: Duphuis, Joseph ( Author, Primary )
Publication Date: 2003
Copyright Date: 2003

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0000677:00001

Permanent Link: http://ufdc.ufl.edu/UFE0000677/00001

Material Information

Title: Ground vibration testing of airplane pylon-store dynamics using laser doppler vibrometer and accelerometer techniques
Physical Description: Mixed Material
Creator: Duphuis, Joseph ( Author, Primary )
Publication Date: 2003
Copyright Date: 2003

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0000677:00001


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GROUND VIBRATION TESTING OF AIRPLANE PYLON-STORE DYNAMICS
USING LASER DOPPLER VIBROMETER AND ACCELEROMETER
TECHNIQUES















By

JOSEPH DUPUIS


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2003















ACKNOWLEDGMENTS

I would like express my sincere gratitude to all of my committee members for

their support on this project. In particular I would like to thank Dr. Richard Lind

for providing daily guidance throughout the course of the entire project without

which success would never have been realized. I would like to thank Dr. Andrew

Kurdila and Roque Salas from SEEK EAGLE for arranging the project and providing

logistic support. I would also like to thank Dr. Christopher Niezrecki for offering his

suggestions for improving the quality of the work presented.

I offer special thanks to the technicians at the STEM facility at Eglin Air Force

Base for their assistance in implementing the test.

Finally I would like to thank all my friends, family and coworkers for their

support in various ways throughout the years.
















TABLE OF CONTENTS


ACKNOWLEDGMENTS . ...

LIST OF TABLES ...........

LIST OF FIGURES . ......

ABSTRACT . ........

1 INTRODUCTION .. ...

1.1 Test Overview . ..
1.2 Background . ....

2 TEST HARDWARE .......

2.1 Test Article ........
2.2 Excitation .........
2.3 Accelerometers ......
2.4 Laser Doppler Vibrometer
2.5 Data Acquisition .....
2.6 Facility . . .

3 DATA ANALYSIS ........

3.1 Modal Analysis Software .
3.2 Using Laser and Acceleron
3.3 Using Laser and Acceleron

4 GVT ON PIDS-3 AND MK-84 .

4.1 Test Configuration . .
4.2 Consideration of Excitation
4.3 Accelerometer Response to
4.4 Accelerometer Response to
4.5 Laser Response to Lateral
4.6 Scan Response to Lateral E

5 GVT ON PIDS-3 AND GBU-10 .

5.1 Test Configuration . .
5.2 Accelerometer Response to


1
1








E


eter Data Cooperatively:
eter Data Cooperatively:




Signals .........
Vertical Excitation .
Lateral Excitation ...
citation ........
citation . . .




Lateral Excitation ..


Method 1
Method 2


page

. ii

SV

. vi

. x

. 1

. 1
S2

S8

S8
. 11
. 12
. 14
. 15
. 16

. 17

. 17
. 20
. 25

. 28

. 28
. 30
. 32
. 40
. 46
. 50

. 55

. 55
. 56


x










6 SU M M ARY . . . . . . . . 67

REFEREN CE S . . . . . . .. . . 69

BIOGRAPHICAL SKETCH ............................. 72















LIST OF TABLES
Table page

2-1 Dimensions for the MK-84 and GBU-10 Munitions.... . . 9

3-1 Effect of FFT Size on Modal Parameters . . . . 24

4-1 Modes Measured by Accelerometers for Vertical Excitation to MK-84 33

4-2 AutoMAC of Accelerometer Response for Vertical Excitation to MK-84 34

4-3 Modes Measured by Accelerometers for Lateral Excitation to MK-84 41

4-4 AutoMAC of Accelerometer Response for Lateral Excitation to MK-84 42

4-5 Modes Measured by Laser for Lateral Excitation to MK-84 . ... 47

4-6 AutoMAC of Laser Response for Lateral Excitation to MK-84 ...... 48

5-1 Modes Measured for Lateral Excitation to GBU-10 . . 57

5-2 AutoMAC of Accelerometer Response for Lateral Excitation to GBU-10 57
















Figure

2-1

2-2

2-3

2-4

2-5

2-6

2-7

2-8

2-9

3-1

3-2

3-3

3-4

3-5

3-6

3-7

4-1


LIST OF FIGURES
page

M K-84......... 8
GBU -1 .. ...... ..... . . . . . 9
G B U -10 . . . . . . . . . 9

P ID S -3 . . . . . . . . . 10

Excitation System for GVT ......................... .. 12

PCB Accelerometer Model 352C67 . . . . . 13

Accelerometer Schematic . . . . . . 13

Polytec Scanning Laser Doppler Vibrometer. . . . 14

IOtech Data Acquisition System . . . .. . . 15

STEM Facility . . . . . . . . 16

Laser and Accelerometer Frequency Response Functions . . 21

Beam Second-Bending Mode Shape . . . . . 22

Effect of FFT Size on FRF of Laser Data . . . . 22

Effect of FFT Size on Curve Fit . . .. . . 23

Poorly Animated Mode Shape . . . . . .... 24

Frequency Response Function at Various Locations ... . ...... 25

Separate Subsection FRFs . . . . . . 26

Excitation Points for GVT of MK-84 . . . . 28

Measurement Points for GVT of MK-84 with Accelerometers . 29

Measurement Points for GVT of MK-84 with Accelerometers . 29

Measurement Points for GVT of MK-84 with Laser Vibrometer .. . 30

Transfer Functions for Random Burst and Sine Sweep Excitation . 31

Transfer Functions for 10 and 35 lb Force Excitation . ..... 31

Transfer Functions for 1024 and 2048 Point Transforms . . 32









Transfer Functions at Representative Locations .. ............

Mode Shape at 46 Hz Measured by Accelerometer for Vertical Excita-
tion to M K -84 . . . . . . . .


4-10 Mode Shape at 183 Hz Measured by
tion to MK-84 .. ........

4-11 Mode Shape at 312 Hz Measured by
tion to MK-84 .. ........

4-12 Mode Shape at 443 Hz Measured by
tion to MK-84 .. ........

4-13 Mode Shape at 507 Hz Measured by
tion to MK-84 .. ........

4-14 Mode Shape at 671 Hz Measured by
tion to MK-84 .. ........

4-15 Mode Shape at 831 Hz Measured by
tion to MK-84 .. ........

4-16 Mode Shape at 899 Hz Measured by
tion to MK-84 .. ........

4-17 Mode Shape at 946 Hz Measured by
tion to MK-84 .. ........


Accelerometers for


Accelerometers for


Accelerometers for


Accelerometers for


Accelerometers for


Accelerometers for


Accelerometers for


Accelerometers for


Vertical Excita-


Vertical Excita-


Vertical Excita-


Vertical Excita-


Vertical Excita-


Vertical Excita-


Vertical Excita-


Vertical Excita-


4-18 Transfer Functions at Representative Locations .. ..........

4-19 Mode Shape at 186.3 Hz Measured by Accelerometers for Lateral Exci-
tation to M K-84 ..............

4-20 Mode Shape at 296.9 Hz Measured by Accelerometers for Lateral Exci-
tation to M K-84 ..............

4-21 Mode Shape at 356.59 Hz Measured by Accelerometers for Lateral Ex-
citation to M K-84 .............

4-22 Mode Shape at 548.51 Hz Measured by Accelerometers for Lateral Ex-
citation to M K-84 .............

4-23 Mode Shape at 680.64 Hz Measured by Accelerometers for Lateral Ex-
citation to M K-84 .............

4-24 Mode Shape at 858.42 Hz Measured by Accelerometers for Lateral Ex-
citation to M K-84 ..............









4-25 Mode Shape at 969.66 Hz Measured by Accelerometers for Lateral Ex-
citation to M K-84 ...............

4-26 Transfer Functions at Representative Locations .. ............

4-27 Mode Shape at 86.41 Hz Measured by Laser for Lateral Excitation to


MK-84

4-28 Mode Shape
MK-84

4-29 Mode Shape
MK-84

4-30 Mode Shape
MK-84

4-31 Mode Shape
MK-84

4-32 Mode Shape
MK-84

4-33 Mode Shape

4-34 Mode Shape

4-35 Mode Shape


at 135.71 Hz Measured by Laser for Lateral Excitation to


at 189.05 Hz Measured by Laser for Lateral Excitation to


at 239.73 Hz Measured by Laser for Lateral Excitation to


at 239.73 Hz Measured by Laser for Lateral Excitation to


at 293.35 Hz Measured by Laser for Lateral Excitation to


at 185 Hz Measured by Laser Scan on Fin of MK-84 .

at 185 Hz Measured by Laser Scan on PIDS-3 Pylon .

at 290 Hz Measured by Laser Scan on Fin of MK-84 .


-1 Measurement Points for GVT of GBU-10 . . . . .

-2 Measurement Points for GVT of GBU-10 ..................

-3 Transfer Functions at Representative Locations ...............

-4 Mode Shape at 35.78 Hz Measured for Lateral Excitation to GBU-10 .

-5 Mode Shape at 84.71 Hz Measured for Lateral Excitation to GBU-10 .

-6 Mode Shape at 169.71 Hz Measured for Lateral Excitation to GBU-10

-7 Mode Shape at 275.53 Hz Measured for Lateral Excitation to GBU-10

-8 Mode Shape at 288.44 Hz Measured for Lateral Excitation to GBU-10 .

-9 Mode Shape at 358.7 Hz Measured for Lateral Excitation to GBU-10 ..

-10 Mode Shape at 535.62 Hz Measured for Lateral Excitation to GBU-10

-11 Mode Shape at 571.56 Hz Measured for Lateral Excitation to GBU-10

-12 Mode Shape at 650.52 Hz Measured for Lateral Excitation to GBU-10









5-13 Mode Shape at 719.88 Hz Measured for Lateral Excitation to GBU-10 64

5-14 Mode Shape at 838.73 Hz Measured for Lateral Excitation to GBU-10 64

5-15 Mode Shape at 882.25 Hz Measured for Lateral Excitation to GBU-10 65

5-16 Mode Shape at 953.44 Hz Measured for Lateral Excitation to GBU-10 66















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

GROUND VIBRATION TESTING OF AIRPLANE PYLON-STORE DYNAMICS
USING LASER DOPPLER VIBROMETER AND ACCELEROMETER
TECHNIQUES

By

Joseph Dupuis

May 2003

Chair: Dr. Richard C. Lind
Major Department: Mechanical and Aerospace Engineering

Ground vibration testing is the process of determining a structure's dynamic re-

sponse to a force input. This information is useful for model development and stability

analysis. Modal analysis is performed to extract modal parameters, such as natural

frequencies, dampings and mode shapes, from measured responses. These responses

are typically measured using either a laser Doppler vibrometer or accelerometers.

The U.S. Air Force is interested in performing a ground vibration test or GVT

on F-16 wing stores. Two stores of particular concern are the the MK-84 and the

GBU-10 bombs when these munitions are attached to the wing with a Pylon Integrated

Dispenser, also known as a PIDS-3. During recent flight tests this configuration was

observed to sustain damage in the form of cracks in various places on the stores and

pylon. This thesis documents a ground vibration test performed on this coupled struc-

ture using laser and accelerometer measurements to determine the modal parameters

and underlying dynamics of the structure.















CHAPTER 1
INTRODUCTION

1.1 Test Overview

The United States Air Force is interested in investigating coupled pylon-store

dynamics. The dynamics of MK-84 and GBU-10 bombs while mounted to a PIDS-

3 pylon are of particular interest. Recent flight tests have noted that the fins of

these bombs were sometimes damaged during flights in which the ordnance was not

expended. The occurrence of this damage was restricted to flights with the bombs

mounted onto the PIDS-3 pylon so a study of the coupled pylon-store dynamics for

these specific units was begun.

Eglin Air Force Base (EAFB) and the University of Florida (UF) collaborated

to conduct a ground vibration test (GVT) in support of the pylon-store investigation.

The test was managed by personnel from the SEEK EAGLE office of EAFB. Assis-

tance was provided by faculty and students from the Department of Mechanical and

Aerospace Engineering at UF. The testing was conducted using facilities at EAFB

during the week of July 15-19, 2002.

The objective of this testing was to experimentally identify the structural dynamics

of the pylon-store couplings. The test article was mounted to a massive stand that

could be considered rigid. A vibration shaker was attached to the test article to provide

excitation. The resulting responses were recorded using accelerometers and a laser

Doppler vibrometer. Modal parameters of natural frequencies and dampings along with

associated mode shapes were extracted from the data using STAR-MODAL software.

Several modes were identified from the data. Many of the modes were dominated

by motion of the fins on the bombs; however, some modes also had significant motion

of the pylon. The damage observed in flight was restricted to use of the PIDS-3 pylon









so any modes involving the pylon are of particular interest. Most of the mode shapes

with pylon motion demonstrated bending dynamics such that the leading-edge and

trailing-edge ends of the pylon moved laterally or vertically. Another mode shape

involving the pylon showed a localized bending in which motion was restricted to a

small area.

The laser Doppler vibrometer proved especially useful for this GVT. The noise

level in the measurements was noticeably reduced for the laser measurements as

compared to accelerometer measurements. The modal analysis, which uses transfer

functions from these measurements, was easier for the laser data than for the ac-

celerometer data. Consequently, the analysis identified several more modes using laser

data than accelerometer data. These additional modes were accepted with a high level

of confidence based on standard metrics such as modal assurance criterion.

This report presents the results of the GVT for the MK-84 and GBU-10 mounted

on a PIDS-3 pylon. The setup for the test is explained along with descriptions of the

equipment. Modal parameters and mode shapes are given for separate test articles of a

MK-84 mounted on a PIDS-3 pylon and a GBU-10 mounted on a PIDS-3 pylon.

1.2 Background

The entire subject of modal analysis has many different facets and refinements

of the various subject areas are continuously being explored. Current literature is

replete with new ideas and strategies for solving old problems as well as the new

problems which arise everyday. Although many techniques are considered standard

and essentially undisputed as acceptable testing procedure after enduring years of

validation, there is no one technique that is superior in all situations. This section is a

discussion of some of the current work being done in the modal analysis community

and some of the work which has helped to shape the current state of the field.

The data collection methods for vibration testing can be broken into two major

categories defined by the type of sensors) used, being either a laser or accelerometers.









When using accelerometers certain obstacles arise that must be considered in order to

obtain the highest quality data possible. It is important to note the mass loading effects

an accelerometer may have on the system. Walter [1] relates the ratio of measured

velocity V~ to true velocity V, through the concept of mechanical impedance and

defines this quantity as

V/V =[Z, /(Z +Z,)]

where Z, is the mechanical impedance of the structure. Further noting that Za can be

written as jozm. Notice that since the impedance of the accelerometer depends on the

mass; small, light-weight accelerometers will only negligibly influence the dynamics of

the structure. Although this result would tend to indicate that smaller accelerometers

would simply be a better choice Walter also notes that smaller accelerometers are

not as internally strain isolated as are larger ones. This will result in a larger base

strain coupling in the sensing element and hence more error. Further conclusions

reveal that shear mode accelerometers don't have a shear path into the crystal thereby

minimizing the amount of error. A short comparison of accelerometer selection is

given in Walter [1] and in Ref 2.

The laser Doppler vibrometer (LDV) is an important tool for the measurement of a

system's dynamic response. It is no surprise that there is a great deal of interest in it's

use and a wealth of literature dedicated to this subject alone. It's non-intrusive nature

makes the LDV invaluable when even the smallest of accelerometers would produce

profound mass loading effects or when sensor contact could prove harmful to the test

article. In general the accelerometer test requires more setup time but less acquisition

time than the LDV with the LDV test usually being more time efficient overall [3].

Other comparisons can be made but both methods still remain useful with neither

technique being better in all situations.

The LDV is an interferometer based signal detection system that measures the

velocity at a point parallel to the beam. The measurements are usually taken in a









step-wise fashion at several points defining a surface. The newest type of LDV will

scan continuously across a surface with the advantage of needing fewer data for an

accurate depiction of the mode shapes and an improvement in the speckle noise which

often plagues the traditional LDV. An in depth look at how one implements this new

type of data collection with a constant sinusoidal input force can be found in Ref 4.

Current work strives to extend the usage of the continuously scanning LDV from line

scans to area scans [5]. Another avenue along which current investigations are traveling

is using this type of laser for impact testing [6]. Impact testing is not usually done

when using a step-wise LDV because it requires a new impact at each point, so when

a large number of scans is required it becomes rather impractical. With the continuous

scanning LDV only one impact would be required for each scan line. The drawback of

using a continuously scanning LDV is that sine sweeps cannot be used.

Some other new approaches to laser testing include the development of a homo-

dyne interferometer in conjunction with a new photodetector. With the instrument

proposed, it would be possible to measure in-plane and out-of-plane velocities with a

single laser beam [7]. There are other laser techniques being used for vibration anal-

ysis such as holographic interferometry and electronic speckle pattern interferometry

which have the advantage of measuring the entire surface displacement at once, a so

called whole-field method. The limiting factor in the usage of these techniques has

been that they provide little quantitative measure of the system, but the use of modal

analysis software has been shown to alleviate this shortcoming [8].

Experimental work in any field can sometimes be problematic in areas of data

collection, data analysis, and noise reduction as well as other aspects of the process.

Anytime one can gain insight into the type and possible cause for error it is a worth-

while investment of effort. In modal analysis, one usually collects response data in the

time domain and converts it to the frequency domain to produce frequency response

functions (FRFs) which are used to determine the mode shapes. If a model exists









the modes can be compared by use of the Modal Assurance Criterion (MAC). Also,

the measure of how well each of the modes across a set of FRFs compare and can

be distinguished from each other is known as an auto-Modal Assurance Criterion.

A detailed explanation of these parameters can be found in Ref 9. Recently work

has been done to develop a new data plotting technique, FMAC, that makes use of

mode shape correlation and natural frequencies on the same plot which can be useful

in visualizing the modal density and the determining the nature of large off diagonal

values in the MAC matrix [10]. In many testing configurations the data is collected

consecutively in different sections which can result in at least a slight change in test

conditions over the whole test. These changes could be in the form of temperature

variations or, accelerometer mass loading or mounting compliance, if used, all of which

could result in slightly different resonant frequencies in that testing section. For large

structures the number of different sections can become large and a global modal anal-

ysis may result in illegitimate results. Auweaer et al. [11] offer one possible solution

by performing modal analysis on each section, merging the results then doing some

averaging over the entire data, or using one section as a reference. Another problem

is addressed in Ref. 12 which determines that the presence of transient effects during

the test performance will result in an overestimation of the damping values. Of course

this only applies to randomly excited structures so one remedy, as stated in the work,

is the use of only periodic signals, but for those persistent types who insist on using

random excitations, an algorithm is presented which works to eliminate this problem.

Another solution would be the use of exponential windowing which is known to aid

in leakage reduction by adding damping to the system [13]. This artificial damping

will of course decrease the amplitude of the resonant frequency, but this decrease can

be accounted for since the amount of extra damping can be exactly determined. The

issues presented here are only a small sample of the kinds of problems that can arise

in data processing. This is an entire subject on it's own and an important one at that









as it may be necessary to adjust the data acquisition process in an effort to compensate

for any data processing problems that are known to result from a particular collection

technique.

The application of vibration testing is wide ranging and certainly a necessity for

structures whose loss of integrity can have dire consequences. One such area is in the

development of aircraft where the distinction is made between laboratory tests and in

flight tests, the former being called a ground vibration test or GVT. The NASA Dryden

Flight Research Facility has a well established procedure for implementing these tests

and many of their standards can be found in the literature [14,15, 16,17, 18]. The GVT

is typically used for analysis such as flutter prediction, finite-element model updating,

comparing modal changes resulting from structural modifications, and deciphering

irregularities encountered during flight [14]. In nearly all GVT testing of large aircraft

it is desired to simulate free-free boundary conditions so the aircraft is supported

through some soft support system. This can be done by reducing the tire pressure to

minimize stiffness and allowing the airplane to rest on its landing gear [14]. The plane

may also be supported with bungee cords along with the deflated tire technique [19].

A newer strategy for implementing the soft support system is using pneumatic springs

to support the aircraft from underneath at a few jack points [15]. Typical excitation

signals for the GVT include random or burst random, slow sine sweep and sine dwell.

Large aircraft and even spacecraft ground vibration tests can be rather time

consuming. It is always of interest to find ways in which test time can be reduced

without compromising the quality of the data collected. Current tests have included

as many as 400 accelerometers with a test time ranging anywhere from ten days to a

month [19, 20]. One series of tests performed by the Modal and Control Dynamics

Team at NASA's Marshall Space Flight Center on seven large elements of the Inter-

national Space Station included up to 1,251 accelerometer channels. The tests were

performed over a period of about four and a half years although each separate test took









two to three weeks [21]. In an effort to reduce the time to perform a large scale GVT,

Gloth et al. [22] offer some interesting strategies including improved test preparation in

the form of selecting test parameters using insight from a FE model. These parameters

might include accelerometer and exciter locations or particular frequency ranges. An-

other technique offered is to use high frequency resolution only around modes thought

to be highly affected by flutter or when precise model updating is desired.

There is certainly far more work being done in vibration testing and modal

analysis than can in whole be adequately covered in this report. The information

provided here merely establishes justification for the use of the procedures and

techniques employed for this experiment.















CHAPTER 2
TEST HARDWARE

2.1 Test Article

The test article for the GVT consists of a munition mounted to a pylon. Specifi-

cally, a separate GVT was performed for a MK-84 and a GBU-10 munition. Each of

these munitions were mounted onto a Pylon Integrated Dispenser, PIDS-3, pylon.

The MK-84 is a 2,000-pound class bomb. This bomb is a ballistic munition with

no active propulsion or control system to guide the bomb onto a target. The bomb, as

shown in Figure 2-1, is essentially a main body with a tail assembly. The main body

was filled with an inert solid for the testing to match mass properties of the explosive

used in an actual MK-84 bomb. The tail assembly contains a ballute, essentially a

combination of balloon and parachute, that slows the munition and provides some

measure of open-loop control. These internal masses will are of note since it has been

shown that internal response can transmit sufficient energy to the surface where the

measurements are made [23]. Also, 4 fins are part of the tail assembly.













Figure 2-1: MK-84


The GBU-10 is also a 2,000-pound class bomb. This bomb is a smart munition

designed to operate in conjunction with additional personnel. A laser designator must









illuminate a target to provide reference for the active control system that guides the

munition. The article to be tested, as shown in Figure 2-2, is the Paveway-II version of

the GBU-10.










Figure 2-2: GBU-10


The test article had the fins retracted inside the tail assembly during the GVT.

The production version of the GBU-10 actually consists of an instrument package on

the nose, a main body, and a tail assembly; however, the instrument package was not

attached for the GVT. Also, the main body contained inert material that matched mass

properties of the explosive in the production version. Some basic dimensions of these

munitions are given in Table 2-1.

Table 2-1: Dimensions for the MK-84 and GBU-10 Munitions

Parameter MK-84 GBU-10
Weight (lbs) 2039 2562
Length (in) 129 172
Diameter (in) 18 18



Several features of these munitions may affect the modal testing. The main body

of each munition is relatively solid so this portion is expected to be quite stiff. The

tail assemblies are more complicated with varying levels of stiffness and so must be

carefully considered when analyzing data.

The tail assemblies have a metal shell surrounding internal components. This shell

comprises the exterior surface upon which accelerometers are mounted. The shell itself

is a cylinder of relatively thin metal. Many of the components attached to this shell









involve springs and rods of varying stiffness. Thus, the responses measured along the

shell may be significantly affected by local modes associated with the thin cylinder and

the components.

The fins are another part of the tail assemblies that must be considered. The fins

on each munition are metal sheets; however, these fins have considerably different

dimensions. The fins on the MK-84 have half-span of roughly 14 in. (35.56 cm) and

a chord length than ranges from 17 in. (43.18 cm) near the root to 7.5 in. (19.05 cm)

near the tip. Conversely, the fins on the GBU-10 have half-span of only 8 in. (20.32

cm) and chord length of roughly 33 in. (83.82 cm) throughout. These dimensions

imply the MK-84 may show large deflections due to chord-wise and span-wise mode

shapes of the fins but the GBU-10 will probably show only small deflections.

The pylon to which these bombs will be attached is shown in Figure 2-3. This

pylon is a length of 101 in. (256.54 cm) at the bottom and a height of 15.8 in.

(40.132 cm) at the center. The width of the pylon ranges from 9 in. (22.86 cm) to

12 in. (30.48 cm) throughout most of the structure. Included in the pylon are 3 chaff

dispensers.






Figure 2-3: PIDS-3


The test article consists of the MK-84 or GBU-10 bomb attached to the PIDS-3

pylon. This attachment is provided by hooks on the underside of the pylon. Also, 4

sway braces on the pylon contact the bomb to provide some stabilization. The top of

the pylon contains 3 points at which the test article is connected to an aircraft wing or,

for this test, the mounting facility.









2.2 Excitation

A source of excitation was needed for ground vibration testing. The mass and

stiffness properties of the test articles made use of impact hammers questionable;

therefore, an electromechanical shaker was used for testing [15]. The shaker was

manufactured by Ling corporation and could output up to 100 lbf (444.8 N) of force

at frequencies up to the desired 2,000 Hz. The shaker was cooled using an ordinary

Hoover brand vacuum.

The shaker was mounted in the facility using two different strategies depending on

the type of excitation to be considered. The shaker was placed directly under the test

article to allow excitation in the vertical direction. Alternatively, the shaker was tightly

clamped to a large metal frame which was itself attached to a boom on a vehicle to

allow excitation in the horizontal direction.

The amount of force that the shaker actually applied to the test article was

measured by a force transducer. The transducer used for this GVT was a PCB

Piezotronics model 208C02 ICP quartz sensor with a dynamic range of 100 lbf

(444.8 N) of force. Mounting blocks for this transducer were attached underneath

and on the side of the munitions using dental cement [24]. The shaker was then

connected to the transducer using a mechanical fuse or stinger. Since this test is only

concerned with approximate mode shapes and natural frequencies and won't be used

for model updating it is safe to ignore the effects of stinger resonance which has been

known to cause problems when this resonance is in the test frequency range [25]. The

measurement of the transducer was amplified by a PCB 482A16 line-powered signal

conditioner. This unit also provided the necessary ICP circuit excitation required by the

force transducer. The amplified signal was then sent to the appropriate data acquisition

system.









The shaker was operated to output a force signal with commanded properties.

The random and sine sweep signals were commanded by connecting the shaker to an

Agilent 33120A function generator.

The excitation system is shown in Figure 2-4. The force transducer, stinger,

shaker, and cooling system can be identified along with some accelerometers. This

figure demonstrates the actual setup used for testing the MK-84 in response to lateral

excitation.















Figure 2-4: Excitation System for GVT


2.3 Accelerometers

The accelerometers used were PCB Piezotronics miniature ceramic shear ICP

accelerometers Model 352C67. Figure 2-5 shows a close-up view of one of these

sensors.

This shear mode accelerometer is characterized by having a seismic mass mounted

on the side of a piezoelectric material as shown in Figure 2-6. Applying an acceler-

ation to the mass causes a shear stress on the face of the crystal and, consequently, a

proportional electric signal. This signal generated is very small but is then amplified

by the internal signal conditioning of the ICP, or "Integrated Circuit Piezoelectric,"

after which it becomes an actual usable signal [2]. This particular model of accelerom-

eter has a fixed voltage sensitivity, a force measurement range up to 50g peak, and a
























Figure 2-5: PCB Accelerometer Model 352C67


frequency range from 0.5 to 10,000 Hz, which made them a suitable choice for this

particular application. A study of the noise floor of several accelerometers shows that

a similar model, 352C65 which differs only in the connector pins, performs quite well

in comparison with other currently available models of the same voltage sensitivity.

The range of noise floors across the 5-800 Hz range varies from 8-45p/Vrms with the

352C65 operating at 9/,Vrms [26]. In addition, they are small and lightweight so any

mass loading effect on the test article is negligible [27].


Piezelectric crystal Direction of acceleration
Seismic mass






Base --



Figure 2-6: Accelerometer Schematic


This model of accelerometer measures acceleration in only one direction so

care was taken to mount the sensors perpendicular to the surface at each point. This

mounting ensures that any transverse motion is not misinterpreted as an axial vibration.









The accelerometers were mounted to the test subject with petro wax because of ease of

application and inconsequential effect on the surface of the test subject.

2.4 Laser Doppler Vibrometer

A Polytec PSV-300 scanning laser Doppler vibrometer system was also used to

measure vibrations during the GVT. The system consists of an OFV-055 scanning head,

an OFV-303.8 class II helium neon laser, and an OFV-3001 S processor/controller.

Figure 2-7 shows the laser mounted on the tripod in typical operating fashion.



....... ...















Figure 2-7: Polytec Scanning Laser Doppler Vibrometer


This laser measures velocity parallel to the beam so optimal results are obtained

by placing that beam perpendicular to the scan surface. Arranging the vibrometer

in this fashion automatically accounts for any angle of the scanning head in the

resulting analysis. The laser/scanning head was mounted on a tripod and care was

taken to eliminate any incorrect measurement which can result from beam angles

incurred from improper tripod setup. These measures include leveling the tripod

legs with the built in leveling devices, estimating the scan surface angle and visually

matching this angle with the scanning head by tilting the scan head mounting bracket

appropriately. It is also important that the test object be located at a point of maximum









laser intensity. The first of these occurs at 0.55 in. (1.397 cm) and every 8.08 in.

(20.52 cm) thereafter. A laser position of approximately 24 in. (60.96 cm) from the

desired point of measurement was the most suitable choice for this test since a longer

distance from the surface results in a larger depth of focus and wider scan field [28].

The vibrometer is actually part of an entire measurement system. The use of the

vibrometer is dependent on a dedicated computer for both excitation and measurement.

This computer controlled the function generator and, consequently, the signal sent

to the excitation shaker. This computer also recorded the measurements from the

vibrometer.

2.5 Data Acquisition

An IOtech WaveBook data acquisition system was used to collect the accelerome-

ter data. This is comprised of a WaveBook 516 and four WBK 14 expansion modules

which interface into a laptop computer via a PCMCIA card. Figure 2-8 shows the

IOtech system and laptop with no accelerometers attached.















Figure 2-8: IOtech Data Acquisition System


Each of the expansion modules has eight input channels which provide the

constant current excitation power required by the ICP circuitry. The WaveBook also

has eight input channels, however these channels do not provide an output current

and as such cannot be used for ICP accelerometers. The hardware is controlled from









the laptop using a software package called DASYLab to perform data acquisition and

process control along with real-time analysis.

2.6 Facility

The GVT was conducted using the STEM facility at Eglin Air Force Base. The

STEM facility provides a dedicated building which was used exclusively for the GVT

during the test period. The building is isolated from other buildings; however, residual

vibrations were often recorded resulting from flights of F-15 aircraft over the area.

The main component of the STEM facility is a static ejection stand. This stand is

essentially a large column under which the test article could be mounted. The column,

as shown in Figure 2-9, is extremely massive and strong. This column did not provide

a perfectly rigid mounting point for the GVT but the modes associated with the column

had only minor contributions to the measured responses. Thus, the dynamics of the

column were ignored for modal analysis.


Figure 2-9: STEM Facility














CHAPTER 3
DATA ANALYSIS

3.1 Modal Analysis Software

The Spectral Dynamics software package STARModal was used to animate the

response of the structure. The procedure for using STARModal begins with creating

the geometry of the structure by defining the coordinates for each of the points tested

and then supplying corresponding data for each of these points. STARModal can

import different types of data including time domain, cross power, auto power and

coherence spectra as well as frequency response functions, or FRFs. It is advantageous

to preprocess the data in MATLAB to produce the FRF file with the proper header in

SMS ASCII, a STARModal specific ASCII format. Once imported into STARModal,

the transfer function estimation can be produced by loading a measurement file into a

"data block", highlighting the desired frequency band, and choosing the curve fitting

method.

The polynomial method fits a polynomial function to the data over the highlighted

frequency range in a least-squared error fashion. This method is appropriate for

either lightly-coupled or heavily-coupled modes and so it is an effective choice for

this experiment. Also called the rational fraction polynomial method, this curve

fitting routine works as follows. Each measured point has an FRF called Hk where

k corresponds to each frequency location. The error between the curve-fit and the

measured value is then defined as

(bo + bl (iCk)2... + b2m-1 (iOk)2m- 1)
S(ao+al(i0ok) +a2(iCok)2... +a2m(iOk)2m)









where (I,,.(I,...,a2m,bo,bl,...,b2m-1, are the polynomial coefficients related to the

modal parameters and m being the number of modes. This equation can be rewritten in

matrix form as



bo

ek= 1 (iok) (10k)2 (... k)2m-1 b


b2m-1
(3.2)
a0

Hk 1 (iOk) (10ok)2 ... (i0k)2m-1 Hk(ij(k)2ma2m


a2m-1

The unknown coefficients are determined by minimizing the error function given

by J.


J= {E*}T{E} (3.3)

The resulting coefficients are used to derive a set of modal parameters. The

parameters are then displayed in a tabular format listing the frequency and damping

percentage. Also, for each point magnitude and phase information at each mode is

presented. The Auto Modal Assurance Criterion is also presented as a measure of

how the mode shapes are correlated with each other. The AutoMAC matrix has values

of unity along the diagonal indicating that each mode correlates perfectly with itself.

All other entries off the main diagonal range from zero to one indicating the level of

similarity between the modes from orthogonal to identical respectively [29].









The percentage damping is determined from the governing differential equation for

a vibratory system [30].


d2x dx
min +c +kx= F(t) (3.4)

Here c stands for the damping coefficient. The solution to this differential

equation is


x =AeX (3.5)

yielding the characteristic equation



S+ +k- = 0 (3.6)
m m
The roots of this equation are



21,2(n)2 (3.7)
2m 2nm n

If we consider the case where (2) = 1 known as critically damped motion,

the roots of the characteristic equation are identical. The general solution then is



x(t)= (C1 +C2t)eX (3.8)

For the critically damped case we can define



ccr = 2Vkm (3.9)

then the damping ratio is defined as


=c (3.10)
Ccr









and then expressed as a percentage


c
=- x 100% (3.11)
Ccr
Equation 3.11 is the value reported for damping by STARModal and is given in

this report for all modes identified by the analysis.

3.2 Using Laser and Accelerometer Data Cooperatively: Method 1

The GVT needed to consider both accelerometer and laser measurements;

therefore, a procedure for combining these data needed to be developed. Certain

practices specific to each method will influence the quality of the data but, beyond

these experimental techniques, further analysis techniques must be considered when

generating and animating mode shapes.

A simple beam experiment was performed in an effort to determine whether or not

data from the two techniques could be successfully combined. This experiment utilized

a aluminum beam of modest dimensions, 19x2.25x0.125 in. (48.26x5.715x0.3175 cm),

cantilevered to a relatively massive supporting frame. Eight points were chosen

for the location of the accelerometers starting 3 in. (7.62 cm) from the clamped

edge and continuing out every two inches. Eight laser points were selected 0.5 in.

(1.27 cm) further out from each accelerometer point. The slight difference in laser and

accelerometer points was motivated by a desire to keep the accelerometers mounted

during the execution of the laser test. Keeping all the sensors mounted during the

tests ensures that any effect the accelerometers have on the structure will be measured

by both collection procedures. Also, since the mounting base of the accelerometer is

0.25 in. (0.635 cm) there needed to be sufficient room for the laser beam to contact

the surface without being disturbed by any nearby accelerometer. The beam was

excited 0.5 in. (1.27 cm) from the free end with a Ling shaker/amplifier system and

a command signal from a Agilent 33120A function generator. Several different sine










sweep ranges were used with a typical maximum input of just under 1.0 lbf (4.448 N)

force.

The data collected using the laser was first converted from a velocity response

to an acceleration response in order to correspond with the data collected using the

accelerometers. This conversion was performed by taking a simple numerical derivative

of the velocity [31].

Figure 3-1 shows a comparison of frequency response functions of one of the

larger amplitude points using both the laser and an accelerometer.


Figure 3-1:


S 2 Accel
. 102 Laser



101



100
50- ------------------------------ -



- 50 0

0
a -500
Io 20 30 40 50 60 70 80 90
Frequency (Hz)

Laser and Accelerometer Frequency Response Functions


This figure shows that the response functions match very closely to one another.

Consistent results were also observed among the other sets of paired points including

other resonant frequencies. This particular response function was the result of a

20 to 100 Hz sine sweep over 8 seconds sampled at 1,024 Hz. A 2,048-point FFT

with 256 points of overlap was used with a Hanning window applied to the input

data. Figure 3-2 shows the resulting mode shape of the beam from the analysis in

STARModal. The clamped edge is to the right side while the excited edge is to the

left. The figure shows a smooth animation with the clear presence of a second-bending

mode at 68.69 Hz.



























Figure 3-2: Beam Second-Bending Mode Shape


This testing revealed a couple of data processing problems. The first of these is a

proper choice of a windowing function. This problem is expected but still mentioned

here merely as a matter of thoroughness. Although it is already known to be a

major consideration in signal processing, the proper choice of FFT size was the most

influential parameter causing the results from the different data collection techniques

to diverge. This influence is demonstrated in the frequency response functions of laser

data from a single point on the beam as shown in Figure 3-3

2048
S4096
S102



10.



0)' - - -- -----------------------
1000

50
540 50 60 70 80 90
Frequency (Hz)

Figure 3-3: Effect of FFT Size on FRF of Laser Data


The processing was done in MATLAB using the vspect command with FFT sizes

of 2,048 points and 4,096 points. A Hanning window with 256 points of overlap was










used in both cases. There is a clear difference in the magnitude of the curve at the

peak, the 4,096 size maximum with a value of 252 g/lbf (56.65 g/N) being more than

twice as large as the 2,048 size maximum of 105 g/lbf (23.60 g/N). In order to animate

these frequency responses, a curve fit is performed on the data to produce a transfer

function. Figure 3-4 shows a typical curve fit using the MATLAB fitsys command.

2048
S- 4096
102



101



100
0
-100
( -150'
20 30 40 50 60 70 80 90
Frequency (Hz)

Figure 3-4: Effect of FFT Size on Curve Fit


These transfer functions show a small yet significant difference in magnitude.

This difference is not necessarily all that alarming because it is common among all

points along the beam but when merging accelerometer and laser data it becomes the

difference between smooth and choppy animations. Figure 3-5 shows the outline of

an animation where laser and accelerometer data match rather poorly due to signal

processing issues.

Now that the transfer functions have been generated we can look at the differ-

ences in the frequency and damping. Table 3-1 summarizes the differences in these

parameters for the individual techniques.

This table shows that, for a similar location on the beam, the difference in

damping and magnitude between accelerometer data and laser data is larger for the

4,096-size FFT. For the 2,048-size FFT, the accelerometer damping estimation is

6% greater and peak magnitude is 5% greater than that of the laser. With an FFT






















Figure 3-5: Poorly Animated Mode Shape

Table 3-1: Effect of FFT Size on Modal Parameters

Frequency(Hz) Damping Magnitude
Laser
2,048 68.71 9.14E-003 102.50
4,096 68.76 2.56E-003 315.40
Accel
2,048 68.69 1.00E-002 107.90
4,096 68.67 2.96E-003 295.10



size of 4,096 the accelerometer damping is 16% larger while the peak magnitude

is now 6% smaller than the same values calculated using laser data. No significant

difference was detected in the location of the resonant frequencies. All this does not

necessarily mean that a smaller FFT size will provide better matching of the data

only that it is an important factor for consideration. The largest deviation in the data

occurred in the damping parameter estimation which is a direct result of the curve

fitting process. Consequently, the ability of the software to closely match the transfer

functions will depend on the choice of FFT size. A frequency response function may

visually appear acceptable but the resulting curve fit is not guaranteed to compute a

damping consistent with other data. This problem was identified in all the numerous

trials of this experiment. A suitable choice of FFT size must be selected by comparing

estimates of transfer functions and modal parameters from several measurements.










3.3 Using Laser and Accelerometer Data Cooperatively: Method 2

While the modifications to the data processing procedure mentioned in the previ-

ous section can be useful for obtaining a more precise damping estimate in a simple

plate model, the procedure may prove quite onerous for a structure with multibody

coupled dynamics. Damping values may vary across the different subsections and only

after the mode shape animations are viewed and determined to be erroneous would

one be alerted to the need for an adjustment to the FFT size. For large numbers of

subsections or number of test points this procedure would be a rather large imposition

on the overall test time constraints.

An alternative approach which combines both data acquisition procedures was

developed during the testing of the MK-84 and proved to be quite useful. Accelerom-

eters were used to quickly generate FRF plots in MATLAB over the entire structure

through a sweep of sine wave frequencies. The FRFs produced tended to be rather

difficult to interpret and lacked a clear overall picture of the structure's response as

shown in Figure 3-6. This figure shows FRFs for points at various locations on the

test structure.

bomb
100 pylon
S fin


1 0 ;.



10



10-6
50 100 150 200 250 300 350 400
Frequency (Hz)

Figure 3-6: Frequency Response Function at Various Locations










By visually examining the FRFs of different subsections of the structure

it becomes more clear where in the spectrum local resonant frequencies reside.

Figures 3-7 show FRFs from two of the constituent sections of the test article those

being one of the fins and the side of the pylon. Although these are clearly less than

perfect transfer functions it can be observed that there are possible resonances. Most

notably is the peak near 185 Hz and another near 290 Hz. These suspect frequencies

were then excited with a sine dwell and a full laser scan over that particular subsection

was employed.




10-1 1 0 10-2

10-2 10, -3
r1o / i ,1 ,

E 10-3 I 10-4
I I
10-4 10-

10-5 10-6
50 100 150 200 250 300 350 50 100 150 200 250 300 350
Frequency (Hz) Frequency (Hz)

(a) Fin (b) Pylon


Figure 3-7: Separate Subsection FRFs


By implementing this type of procedure it is possible to identify certain frequen-

cies of interest from relatively poor quality data and then focus the rest of the test

time on those frequencies in an effort to produce results superior to those obtained in

the preliminary testing phase. The resulting mode shape animations produced by the

Polytec software at the aforementioned sine dwell frequencies and the effectiveness of

this technique are presented in Section 4.6 of this report. A similar technique has been

used in Ref 21 where a "common set" of measurements is selected to be acquired

from each patch of accelerometers. This common set is then evaluated to determine









appropriate force levels and frequency resolution. This idea is extended in this report to

include the selection of the excitation function.

Using a specific sine frequency is especially useful for separating closely spaced

modes and for identifying nonlinear behavior particularly when the structures character-

istics are unknown [32]. It should be noted however that by using sine dwell excitation

much of the damping information is lost. If we let Q be a measure of resonance peak

sharpness which is related to the damping it can be shown that

Co 1
Q = -(3.12)
(02 (1 o

where 02 and oM are located to either side of resonance and representing the full

width at half maximum and y is the structural damping factor [30]. It is clear that any

of the side band information has been compromised especially when the choice of

dwell frequency lies further away from resonance.

Also, the frequency resolution of the FRFs obtained during the preliminary

accelerometers test becomes an important factor in the resulting amplitude of the

response at the selected frequency. In this test the resulting frequency resolution was

1 Hz and although it is conceivable that the amplitude could have varied within this

resolution range it is rather unlikely that the amount would be of any consequence.

However, this will be an important consideration when the frequency resolution would

allow for poor peak amplitude location estimation.















CHAPTER 4
GVT ON PIDS-3 AND MK-84

4.1 Test Configuration

A set of ground vibration tests were conducted on the test article composed of

the MK-84 and PIDS-3 pylon. This set of tests used accelerometers and the laser

Doppler vibrometer to measure motion at distinct points on the article. The motions

were responses to separate lateral or vertical excitation.

The excitation used for each GVT was applied 112 in. (284.48 cm) aft of the nose

of the MK-84 bomb. The lateral excitation was applied in a horizontal direction at the

centerline on the port side of the bomb. Similarly, the vertical excitation was applied

in a vertical direction at the centerline under the bomb. The points at which excitation

was applied are shown in Figure 4-1. Each point of excitation was actually between

the leading-edge root of a pair of fins.









Figure 4-1: Excitation Points for GVT of MK-84


The signals commanded to provide the excitation force varied for the tests. Some

tests for accelerometer measurements used a series of burst random signals with

random energy for approximately 0.8 s followed by approximately 0.9 s of zero-

magnitude signal. Other series of tests for accelerometer measurement used 60 s sine

sweeps from 20 to 1,000 Hz or 20 to 300 Hz. The testing for laser measurements used

a sine sweep from 20 to 600 Hz that lasted for 8 s.









Accelerometer measurements at 55 locations on the test article were taken in

response to the excitation. As noted earlier, the data acquisition system was not

capable of recording 55 measurements simultaneously; therefore, the tests were

conducted using 2 configurations of 28 and 27 accelerometers. The resulting data

points included 10 lateral and 9 vertical measurements on the main body of the bomb,

11 lateral and 4 vertical measurements on the pylon, and 21 measurements on the fins.

Several of the accelerometer locations are shown in Figure 4-2. This drawing

indicates the locations of accelerometers measuring lateral motion on the pylon and

bomb. Also, the accelerometers on the lower fin on the port side are marked.








Figure 4-2: Measurement Points for GVT of MK-84 with Accelerometers


The remaining accelerometers are shown in Figure 4-3. The left drawing views

the test article from near the bottom such that the accelerometers measuring both lateral

and vertical motion can be seen. The right drawing views the test article from directly

above to show the accelerometers on the top of the pylon and the accelerometers on the

upper fins for both port and starboard sides.









Figure 4-3: Measurement Points for GVT of MK-84 with Accelerometers









The laser took measurements at 91 locations on the test article. These locations

were restricted to the PIDS-3 pylon and to the fins on the tail assembly of the MK-

84. The measurements included 38 points on the upper fin on the starboard side of

the MK-84. Also, the measurements included 53 points on the starboard side of the

PIDS-3 pylon. Figure 4-4 shows the locations at which these measurements were

taken.












Figure 4-4: Measurement Points for GVT of MK-84 with Laser Vibrometer


4.2 Consideration of Excitation Signals

Several types of excitation signals were available for testing; therefore, the effects

of these signals must be noted when analyzing response data. Some of the properties

that are of particular interest are the effects of damping mechanisms and nonlinearities

in the dynamics.

A comparison of representative transfer functions for random burst and sine sweep

signals is shown in Figure 4-5 as measured by an accelerometer on a fin. The transfer

functions are slightly different but these differences are mostly minor. In particular,

the differences at the peaks, which presumably indicate modal properties, are generally

small excepting near 525 Hz and 945 Hz.

The issue of nonlinearities was investigated by using excitation at different force

levels. Figure 4-6 presents transfer functions from fin accelerometer to excitation with

10 and 35 lb (44.48 and 155.69 N) of force. In this case, the excitation was the burst

random signal. These transfer functions are quite similar except near 525 Hz.











100



-1
10 1

10 2




S10-3

random burst
_. .......sine sweep
104
0 200 400 600 800 1000
Frequency (Hz)

Figure 4-5: Transfer Functions for Random Burst and Sine Sweep Excitation

100






-2 1
10




10 lbf
10-4 35 b
0 200 400 600 800 1000
Frequency (Hz)

Figure 4-6: Transfer Functions for 10 and 35 lb Force Excitation


The comparisons in Figure 4-5 and Figure 4-6 are representative of the testing.

Transfer functions could be shown to compare sensors at different locations. Transfer

functions could also be shown to compare signals for lateral excitation instead of the

vertical excitation. In each case, the comparisons would be similar to those already

presented.

Another comparison was made to investigate the relationship between excitation

and signal processing. Essentially, transfer functions were computed from accelerom-

eter measurements to different excitations using different different parameters for the

signal processing. Figure 4-7 presents transfer functions that were computed using










1,024 and 2,048 points in the Fourier transform. These results indicate only small

effect on the transfer function for different size transforms. Some transfer functions

noted differences at limited frequencies; however, the comparisons never noted a

consistent effect of FFT size.


-- 1024
...... 2048
100 .

10-2



103


104
0 200 400 600 800 1000
Frequency (Hz)

Figure 4-7: Transfer Functions for 1024 and 2048 Point Transforms


The result of comparing these excitation signals was a noted similarity in transfer

functions. Essentially, the transfer functions can be generated using any of the

excitation signals under consideration without greatly affecting the results. All the data

was used for modal analysis but this report will restrict the presentation to data from

sine sweep testing. This does not conflict with any current industry standards of testing

and since the structure displayed a rather large modal density the sine sweep would be

more likely to provide an adequate force input and frequency resolution to properly

characterize the response [33]. Furthermore, the data analysis will be based on analysis

of Fourier transforms with 2,048 points.

4.3 Accelerometer Response to Vertical Excitation

A GVT was performed by measuring accelerometers in response to vertical

excitation. Testing was performed using using burst random and sine sweep signals.

The resulting transfer functions were similar such that no noticeable differences were










noted. A set of these transfer functions are shown in Figure 4-8 as being representative

of the measurements.

102
--- bomb
....... pylon
fin
100


1-2


Clo"! j' f ,


10-6
0 200 400 600 800 1000
Frequency (Hz)
Figure 4-8: Transfer Functions at Representative Locations


Clearly these transfer functions demonstrate a low signal to noise ratio. This effect

is caused by issues such as measurement noise and aliasing. Nevertheless, the transfer

functions had several peaks that indicated modes.

The values of natural frequencies and dampings for the modes identified by this

GVT are given in Table 4-1. The analysis indicated 9 modes were present between

20 and 1,000 Hz. The damping levels showed large variations but most modes had

relatively low damping with levels less than 1%.

Table 4-1: Modes Measured by Accelerometers for Vertical Excitation to MK-84

Mode Frequency, Hz Damping, %
1 46.53 7.63
2 183.32 1.89
3 312.53 1.74
4 443.16 0.247
5 507.61 0.372
6 525.03 -0.812
7 671.99 0.939
8 831.16 0.933
9 899.67 0.241
10 946.22 1.14









A feature of particular interest in Table 4-1 is the mode with natural frequency

at 525.03 Hz. The modal analysis was not able to identify the properties of this mode

with any confidence. Specifically, the mode was identified as being unstable with

negative damping. Such an unstable mode is not physically realistic so further analysis

was done that focused on this mode. Modal analysis using different parameters, such

as number of poles, was performed using several sets of response data but the resulting

damping was always negative. Thus, the data indicates something of interest at this

frequency but its properties could not be confidently identified. It should be noted

that the dynamics at 525.03 Hz were noted as being sensitive to type of sweep in

Figure 4-5 and level of force in Figure 4-6.

The remaining modes in Table 4-1 were extracted as stable modes. The majority

of modes shapes involved significant displacement of the fins and cone of the tail

assembly. Some of the mode shapes also involved motion of the pylon. Interestingly

enough, the main body of the bomb was rarely observed to move much for any of

these modes. The AutoMAC matrix shown in Table 4-2 confirms that each of the

modes identified are separate distinct modes with the largest correlation of 15%

between modes 8 and 9.

Table 4-2: AutoMAC of Accelerometer Response for Vertical Excitation to MK-84

Modes 1 2 3 4 5 6 7 8 9 10
1 1.00 0.09 0.00 0.03 0.03 0.02 0.03 0.01 0.02 0.02
2 0.09 1.00 0.02 0.01 0.02 0.03 0.02 0.01 0.02 0.01
3 0.00 0.02 1.00 0.01 0.13 0.01 0.05 0.01 0.00 0.01
4 0.03 0.01 0.01 1.00 0.02 0.04 0.00 0.01 0.02 0.04
5 0.03 0.02 0.13 0.02 1.00 0.13 0.00 0.00 0.04 0.04
6 0.02 0.03 0.01 0.04 0.13 1.00 0.02 0.05 0.07 0.00
7 0.03 0.02 0.05 0.00 0.00 0.02 1.00 0.04 0.04 0.01
8 0.01 0.01 0.01 0.01 0.00 0.05 0.04 1.00 0.15 0.01
9 0.02 0.02 0.00 0.02 0.04 0.07 0.04 0.15 1.00 0.04
10 0.02 0.01 0.01 0.04 0.04 0.00 0.01 0.01 0.04 1.00









The mode shape for the dynamics at 46.53 Hz is shown in Figure 4-9. This

mode, which has the lowest frequency of any mode noted by the testing, appears to be

similar in nature to a rigid-body mode. Essentially, the bomb and pylon are rotating

longitudinally about their interface mounting points. The fins show a small amount of

bending but the mode shape is dominated by the pitch rotation of the pylon and bomb.

The trailing-edge ends of the bomb and pylon show the most movement in this mode

shape. Furthermore, these trailing-edge ends are moving out of phase for the bomb and

pylon.







~--4









Figure 4-9: Mode Shape at 46 Hz Measured by Accelerometer for Vertical Excitation
to MK-84


The mode shape for the dynamics at 183.32 Hz is shown in Figure 4-10. This

mode shape shows little motion of the bomb or pylon. Instead, the mode shape is

dominated by the fins. This mode appears to be a first-bending mode in the span-wise

direction for the fins. The fins show very little twisting at either the root or tip so the

mode appears to be span-wise bending.

The mode shape for the dynamics at 312.53 Hz is shown in Figure 4-11. This

mode involves motion of the pylon and fins but very little motion of the main body

of the bomb. The pylon motion is a longitudinal bending with the leading-edge and

trailing-edge ends moving in phase along the vertical direction. Also, the fins have a













--- A

y ,/ / ljz











Figure 4-10: Mode Shape at 183 Hz Measured by Accelerometers for Vertical Excita-
tion to MK-84


torsion motion that is characterized by little twist angle near the root but increasing

twist angle near the tip.


Figure 4-11: Mode Shape at 312 Hz Measured by Accelerometers for Vertical Excita-
tion to MK-84


The mode shape for the dynamics at 443.16 Hz is shown in Figure 4-12. This

mode also involves the pylon and fins but includes little motion of the main body of

the bomb. The motion of pylon is restricted to vertical movement of the leading-edge









end with little corresponding movement of the trailing-edge end. The fins show a

motion which correlates with a chord-wise bending mode.

















Figure 4-12: Mode Shape at 443 Hz Measured by Accelerometers for Vertical Excita-
tion to MK-84


The mode shape for the dynamics at 507.61 Hz is shown in Figure 4-13. This

mode shape is characterized by some motion at the nose of the pylon along with large

motion involving the fins and cone of the tail assembly. The tail cone demonstrates a

first-bending type of motion. This bending is evident in measurements from accelerom-

eters on the cone and at the root of the fins. Also, the fins show some torsional motion

in this mode shape. The pylon motion is small and constrained mainly to vertical

oscillations at the leading-edge end.

The mode shape for the dynamics at 671.99 Hz is shown in Figure 4-14. The

mode shape for this dynamic is almost purely affecting the fins. The largest motion is

seen by the trailing-edge mid-span point on the fins. Conversely, the leading-edge point

at the root of the fins shows almost no motion.

The mode shape for the dynamics at 831.16 Hz is shown in Figure 4-15. This

mode shape shows a somewhat complicated relationship between the fins and the cone

of the tail assembly. The leading-edge end of the cone shows significant in-phase

vertical and lateral motion. The complication arises when considering the fins. The































Figure 4-13: Mode Shape at 507 Hz Measured by Accelerometers for Vertical Excita-
tion to MK-84























Figure 4-14: Mode Shape at 671 Hz Measured by Accelerometers for Vertical Excita-
tion to MK-84


trailing-edge root of the upper fins show large modal displacements but the same points

on the lower fins show small modal displacements.

The mode shape for the dynamics at 899.67 Hz is shown in Figure 4-16. This

mode shape again shows very little motion of the pylon or the main body of the

bomb. The tail cone shows bending in both vertical and lateral direction which is also

demonstrated in the measurements taken at the root of the fins. The outer portions of


___
__
C__
__


























Figure 4-15: Mode Shape at 831 Hz Measured by Accelerometers for Vertical Excita-
tion to MK-84

the fins appear as a higher-order modal shape that has contributions of both bending

and torsion.


















Figure 4-16: Mode Shape at 899 Hz Measured by Accelerometers for Vertical Excita-
tion to MK-84


The mode shape for the dynamics at 946.22 Hz is shown in Figure 4-17. This

mode shape is very similar in nature to the dynamic at 899.67 Hz. The only noticeable

difference between these two modes is the motion of the lower fins. The motion at








40

946.22 Hz shows both bending and torsion motion but it appears slightly different than

the motion at 899.67 Hz.

















Figure 4-17: Mode Shape at 946 Hz Measured by Accelerometers for Vertical Excita-
tion to MK-84


4.4 Accelerometer Response to Lateral Excitation

A GVT was performed using accelerometers to measure response to lateral

excitation. Again, testing was performed using burst random and sine sweep signals

but the resulting transfer functions showed little appreciable differences. A set of

these transfer functions are shown in Figure 4-18 as being representative of the

measurements.


102


,10

S 2
10


10-4


0 200 400 600 800 1000
Frequency (Hz)
Figure 4-18: Transfer Functions at Representative Locations









These transfer functions demonstrate a low signal to noise ratio that is similar to

that in Figure 4-8. This high level of noise corrupts the modal analysis somewhat but

several modes can still be distinguished in the transfer functions.

The transfer functions were analyzed to obtain parameters associated with modal

dynamics of the test article. These parameters are given in Table 4-3.

Table 4-3: Modes Measured by Accelerometers for Lateral Excitation to MK-84

Mode Frequency, Hz Damping, %
1 186.30 0.61908
2 296.90 1.10000
3 356.59 0.99378
4 548.51 0.30621
5 680.64 0.40961
6 858.42 0.62867
7 969.66 0.31425



Only 7 modes were identified between 20 and 1000 Hz using lateral excitation.

Several of these modes have natural frequencies close to the modes identified from

vertical excitation. In particular, the natural frequencies of 186.3 and 680.64 Hz in

Table 4-3 are close to the natural frequencies of 183.32 and 671.99 Hz in Table 4-1.

The lateral mode at 186.3 Hz and the vertical mode at 183.3 Hz actually have similar

mode shapes so these modes may be caused by the same dynamic. Conversely, the

modes are quite different for the lateral mode at 680.6 Hz and the vertical mode at

671.9 Hz so the underlying dynamics are probably distinct. The AutoMAC matrix

shown in Table 4-4 assures that the modes identified are distinct with the highest

degree of being between modes 4 and 2.

The mode shape for the dynamics at 186.3 Hz is shown in Figure 4-19. This

mode shows motion in both the fins and pylon but little motion in the main body of the

bomb. The fin motion is similar in nature to a span-wise bending mode. The pylon is

somewhat more complicated with distinct features. One feature of the mode shape is a









Table 4-4: AutoMAC of Accelerometer Response for Lateral Excitation to MK-84

Modes 1 2 3 4 5 6 7
1 1.00 0.01 0.00 0.09 0.00 0.01 0.00
2 0.01 1.00 0.13 0.16 0.04 0.08 0.01
3 0.00 0.13 1.00 0.08 0.02 0.04 0.03
4 0.09 0.16 0.08 1.00 0.01 0.09 0.03
5 0.00 0.04 0.02 0.01 1.00 0.13 0.04
6 0.01 0.08 0.04 0.09 0.13 1.00 0.01
7 0.00 0.01 0.03 0.03 0.04 0.01 1.00


slight lateral motion of the leading-edge nose of the pylon.

localized around the mid-span point of the pylon.


Another feature is bending


Figure 4-19: Mode Shape at 186.3 Hz Measured by Accelerometers for Lateral Excita-
tion to MK-84


The mode shape for the dynamics at 296.9 Hz is shown in Figure 4-20. This

mode is characterized by a torsion motion of the fins. The tip of each fin is clearly

twisting in comparison to the root of each fin. Also, the leading-edge end of the pylon

shows some oscillation in both lateral and vertical directions. The trailing-edge end of

the pylon and the main body of the bomb show almost no motion.

The mode shape for the dynamics at 356.59 Hz is shown in Figure 4-21. The

mode shape for this dynamic involves mostly the fin with very small motions of the





















/r


.'r


Figure 4-20: Mode Shape at 296.9 Hz Measured by Accelerometers for Lateral Excita-
tion to MK-84


bomb and pylon. The fins are showing a somewhat complicated motion. Specifically,

the leading-edge mid-span point is moving more than the rest of the fin. Also, this

point is moving out of phase with the other points on the fin.










,
^,-" ---





y^^ ---'^'






Figure 4-21: Mode Shape at 356.59 Hz Measured by Accelerometers for Lateral Exci-
tation to MK-84


i
,I









The mode shape for the dynamics at 548.51 Hz is shown in Figure 4-22. This

mode shape is particularly complicated to describe. The fins appear to move as a

bending mode; however, the upper and lower fins demonstrate some different motion.

The lower fins show more of a classical first-bending shape whereas the upper fins

indicate similarity to a second-bending shape. The motion is further complicated by

noting the trailing-edge root of each fin seems to be out of phase with the trailing-edge

end of the tail assembly on the bomb.



















Figure 4-22: Mode Shape at 548.51 Hz Measured by Accelerometers for Lateral Exci-
tation to MK-84


The mode shape for the dynamics at 680.64 Hz is shown in Figure 4-23. The

pylon and main body of the bomb show minor motion in this mode shape; therefore,

the Figure shows only the tail assembly to allow detailed consideration of its motion.

The mode shape is seen to involve complicated interactions between the fin and cone

components of the tail assembly on the bomb. The fins demonstrate a bubble-type

mode in which the mid-span mid-chord points, at the center of the fins, show the

largest deflections. Furthermore, these center points move out of phase with the other

points on the fins. The cone of the tail assembly shows bending-type motion. In









particular, the leading-edge end of the cone shows large lateral motion but the trailing-

edge end of the cone shows large vertical motion. Each bending, vertical and lateral,

shows a nodal point at which little motion is observed.














Figure 4-23: Mode Shape at 680.64 Hz Measured by Accelerometers for Lateral Exci-
tation to MK-84


The mode shape for the dynamics at 858.42 Hz is shown in Figure 4-24. This

Figure again shows only the tail assembly to simplify the analysis. This mode shape

actually appears to be a higher-order version of the dynamics at 680.64 Hz. The mid-

span mid-chord point at the center of the fins moves a lot but now the leading-edge

and trailing-edge points at mid-span locations also move. The entire set of mid-span

points are moving out of phase with the points at the root and tip of the fins. Also,

the tail cone again shows bending motion but the nodal points have changed between

680.64 Hz mode and this mode. The lateral motion does not show a nodal point and

the vertical motion shows a nodal point that has moved towards the trailing-edge end of

the cone.

The mode shape for the dynamics at 969.66 Hz is shown in Figure 4-25. This

mode presents some difficulty for analysis. Essentially, the mode shape at 969.66

Hz is quite similar to the mode shape at 858.42 Hz. The differences are slight so

distinguishing between the modes is difficult.












ii / \













Figure 4-24: Mode Shape at 858.42 Hz Measured by Accelerometers for Lateral Exci-
tation to MK-84


















Figure 4-25: Mode Shape at 969.66 Hz Measured by Accelerometers for Lateral Exci-
tation to MK-84


4.5 Laser Response to Lateral Excitation

A GVT was also performed using the laser Doppler vibrometer to measure

responses to lateral excitation. The testing only considered sine sweep signals. A set

of these transfer functions are shown in Figure 4-26 as being representative of the

measurements.

The transfer functions from the laser measurements clearly have a higher signal

to noise ratio than the data resulting from accelerometers. The reduction in noise is










100

101

o-2
M10

10-3
10 4

S" [- fin
_- pylon
10-5
0 50 100 150 200 250 300
Frequency (Hz)
Figure 4-26: Transfer Functions at Representative Locations


almost certainly related to the non-contact nature of the measurement obtained from the

laser. Noise related to the sensor mounting and wiring are inherently avoided with this

type of measurement.

Modal dynamics were extracted from these transfer functions. The parameters for

the resulting modes are presented in Table 4-5.

Table 4-5: Modes Measured by Laser for Lateral Excitation to MK-84

Mode Frequency (Hz) Damping
1 86.41 1.64
2 135.71 1.05
3 189.05 2.12
4 239.73 1.82
5 293.35 0.323




The modes identified from the laser differ from those identified by the accelerom-

eters even though both used similar excitation. Specifically, the laser data indicated 5

modes between 86 and 300 Hz whereas the accelerometer data indicated only 2 modes

in this range. This discrepancy likely results from the better data obtained using the

laser. Several modes are probably hidden in the noise level of the accelerometer data

but are easily seen in the laser data. The AutoMAC matrix shown in Table 4-6 reveals









a correlation of 28% between modes 2 and 3 which indicates that the modes are fairly

correlated and may display a degree of similarity in mode shape.

Table 4-6: AutoMAC of Laser Response for Lateral Excitation to MK-84

Modes 1 2 3 4 5
1 1.00 0.02 0.02 0.06 0.04
2 0.02 1.00 0.28 0.06 0.01
3 0.02 0.28 1.00 0.01 0.01
4 0.06 0.06 0.01 1.00 0.06
5 0.04 0.01 0.01 0.06 1.00


The mode shape for the dynamics at 86.41 Hz is shown in Figure 4-27. This

mode is somewhat difficult to characterize because of the disparity between the fins

and the pylon. The fins are clearly undergoing a smooth bending motion; however, the

pylon is not easy to understand. The points on the pylon show small amounts of lateral

motion that appears almost random in terms of both magnitude and phase.


Figure 4-27: Mode Shape at 86.41 Hz Measured by Laser for Lateral Excitation to
MK-84


The mode shape for the dynamics at 135.71 Hz is shown in Figure 4-28. This

mode is predominately a bending mode for the fins. The mid-point area on the pylon

shows some bending but the pylon displacement is considerably smaller than the fin

displacement.



























Figure 4-28: Mode Shape at 135.71 Hz Measured by Laser for Lateral Excitation to
MK-84

The mode shape for the dynamics at 189.05 Hz is shown in Figure 4-29. The

main feature of this mode is some localized motion on the pylon. The area around

the mid-point location of the pylon is moving laterally in response to this excitation.

The fins also show some bending motion but clearly the pylon motion is the dominate

part of this mode. An additional feature of this mode is a slight rotation of the entire

pylon about the mounting point. The trailing-edge end of the pylon is in phase with the

localized mid-point locations and out of phase with the leading-edge end during this

rotation.







-_.-.---. __-__







Figure 4-29: Mode Shape at 189.05 Hz Measured by Laser for Lateral Excitation to
MK-84









The mode shape for the dynamics at 239.73 Hz is shown for the test article in

Figure 4-30 and for the fins in Figure 4-31. This mode contains interesting features

for both the fins and pylon. The pylon motion is dominated by a lateral bending at

the leading-edge nose. The remaining areas of the pylon show some motion but these

motions are clearly smaller than the nose displacement.











Figure 4-30: Mode Shape at 239.73 Hz Measured by Laser for Lateral Excitation to
MK-84


The motion of the fins is expanded in Figure 4-31. This motion clearly correlates

to a chord-wise bending mode. The mid-chord line is shown to have very little

displacement while the leading-edge and trailing-edge points have large displacements.

The mode shape for the dynamics at 293.35 Hz is shown in Figure 4-32. This

mode shape might indicate some higher-order dynamics for both the pylon and fins.

The fins show some chord-wise bending but the motion is complicated and not very

smooth. The pylon shows the localized mid-point bending but also motion near the

ends. Specifically, the leading-edge ends are moving out of phase with the trailing-edge

ends. This bending motion is localized to only the ends so the mode does not appear to

be a rotation; rather, the mode involves bending of only the ends.

4.6 Scan Response to Lateral Excitation

The transfer functions and associated mode shapes, shown in Figure 4-26

to Figure 4-32, indicated the laser was capable of determining information about

several modes. These first set of data were collected by taking data at widely-space

discrete points and analyzing using STARModal; however, information with finer














/ -. 1/-z
// ,





^-:-- -
// -- _
... .. / ._


4y- /











Figure 4-31: Mode Shape at 239.73 Hz Measured by Laser for Lateral Excitation to
MK-84


Figure 4-32: Mode Shape at 293.35 Hz Measured by Laser for Lateral Excitation to
MK-84


resolution could also be obtained using scanning. This scanning was done to cover a

limited portion of the test article with many closed-spaced measurements. Also, the


- --------


i------~









scanning was restricted to single frequencies to allow maximum information about a

specific mode to be obtained. The resulting mode shapes were identified by software

proprietary to the PolyTec system.

The scan was organized to focus on either the port-side upper fin or the mid-

section of the pylon. The scan of the fin used 247 points whereas the scan of the pylon

used 279 points. The measurements of responses on the fin where taken at 512 Hz for

2 s. Conversely, the measurements of the responses on the pylon were taken at 1024

Hz for 1 s.

A scan was performed to concentrate on the modal dynamics near 185 Hz. The

resulting mode shape is shown through 2-dimensional intensity shading in Figure 4-33.

This mode is clearly a span-wise first-bending dynamic. This mode shape agrees

with the mode shapes determined by accelerometer measurements in Figure 4-19 and

determined by laser measurements in Figure 4-29. The only difference is the higher

resolution resulting from scanning the surface.


J 4I~' ~ -


Figure 4-33: Mode Shape at 185 Hz Measured by Laser Scan on Fin of MK-84









The pylon was also tested at this frequency. The resulting mode shape is shown

in Figure 4-34. The pylon motion agrees well with the modes shapes obtained by the

accelerometer measurements in Figure 4-19 and determined by laser measurements in

Figure 4-29. Again, the difference between the closely-spaced scanning data and the

widely-spaced data is the increased resolution of the scanning data. The scanning data

definitively notes that the pylon vibration is isolated to a local region of the pylon.




















Figure 4-34: Mode Shape at 185 Hz Measured by Laser Scan on PIDS-3 Pylon


Finally, a scan of just the fin was done with an excitation frequency of 290 Hz.

Figure 4-35 shows the result as being similar in nature to a chord-wise bending mode.

The actual mode shape shows the greatest deflection occurs about 3 in. away from the

leading-edge and trailing-edge ends of the fin.




























Figure 4-35: Mode Shape at 290 Hz Measured by Laser Scan on Fin of MK-84















CHAPTER 5
GVT ON PIDS-3 AND GBU-10

5.1 Test Configuration

A set of ground vibration tests were conducted on the test article composed of the

GBU-10 and PIDS-3 pylon. This set of tests used only the accelerometers to measure

motion at distinct points on the article. Also, the excitation was limited to lateral input

at 95 in. aft of the nose.

Accelerometers were mounted at 73 locations on the test article during 3 tests.

The first test used 12 measurements of lateral motion on the bomb, 12 measurements

of vertical motion on the bomb, and 3 measurements of lateral motion on the pylon.

The second test used 26 measurements of motion on the fins. The final test used 17

measurements of lateral motion on the pylon and 3 measurements of vertical motion on

the pylon.

Several of the accelerometer locations are shown in Figure 5-1. This drawing

indicates the accelerometers measuring lateral motion on the pylon and bomb.







Figure 5-1: Measurement Points for GVT of GBU-10


The remainder of the accelerometer locations are shown in Figure 5-2. The left

drawing shows the view from under the test article. This view shows locations of the

vertical measurements on the bomb and the locations of measurements on the lower

fins. The right drawing shows the view from over the test article. This view shows










locations of the vertical measurements on the pylon and the locations of measurements

on the upper fins.









Figure 5-2: Measurement Points for GVT of GBU-10


5.2 Accelerometer Response to Lateral Excitation

A GVT was performed by measuring accelerometers in response to vertical

excitation. Testing was performed using using burst random and sine sweep signals.

The resulting transfer functions were similar such that no noticeable differences were

noted. The high level of noise in the measurements is shown for a representative set of

transfer functions in Figure 5-3.

100
10 bomb
Spylon
10 fin






104 I

10
0 200 400 600 800 1000
Frequency (Hz)
Figure 5-3: Transfer Functions at Representative Locations


The values of natural frequencies and dampings for the modes identified by this

GVT are given in Table 4-1. The analysis indicated 13 modes were present between

20 and 1000 Hz. The damping levels showed large variations but most modes had

relatively low damping with levels less than 1%.









Table 5-1: Modes Measured for Lateral Excitation to GBU-10


Mode
1
2
3
4
5
6
7
8
9
10
11
12
13


Frequency, Hz Damping, %
35.78 4.86
84.71 6.11
169.71 1.57
275.53 -0.547
288.44 0.106
358.70 0.829
535.62 0.479
571.56 0.332
650.52 -0.270
719.88 0.098
838.73 0.407
882.25 -0.505
953.44 0.263


The analysis of the accelerometer data for the GBU-10, similar to some data for

the MK-84, generated some unstable modes. These modes are again not considered

to be physical realistic but the instabilities could not be removed despite varying the

number of poles, adjusting the frequency limits, and changing the curve fitting routine.

The AutoMAC matrix shown in Table 5-2 indicates that modes 4 and 6 are quite

similar with a 52% correlation between them.

Table 5-2: AutoMAC of Accelerometer Response for Lateral Excitation to GBU-10

Modes 1 2 3 4 5 6 7 8 9 10 11 12 13
1 1.00 0.01 0.05 0.01 0.02 0.00 0.10 0.10 0.04 0.01 0.02 0.02 0.00
2 0.01 1.00 0.12 0.22 0.09 0.21 0.01 0.00 0.09 0.03 0.00 0.02 0.01
3 0.05 0.12 1.00 0.06 0.10 0.09 0.05 0.05 0.10 0.00 0.00 0.03 0.01
4 0.01 0.22 0.06 1.00 0.01 0.52 0.05 0.03 0.21 0.00 0.00 0.02 0.04
5 0.02 0.09 0.10 0.01 1.00 0.06 0.02 0.04 0.03 0.14 0.01 0.02 0.01
6 0.00 0.21 0.09 0.52 0.06 1.00 0.14 0.00 0.18 0.05 0.01 0.01 0.01
7 0.10 0.01 0.05 0.05 0.02 0.14 1.00 0.09 0.11 0.11 0.04 0.02 0.05
8 0.10 0.00 0.05 0.03 0.04 0.00 0.09 1.00 0.11 0.07 0.15 0.09 0.01
9 0.04 0.09 0.10 0.21 0.03 0.18 0.11 0.11 1.00 0.01 0.06 0.16 0.05
10 0.01 0.03 0.00 0.00 0.14 0.05 0.11 0.07 0.01 1.00 0.02 0.02 0.04
11 0.02 0.00 0.00 0.00 0.01 0.01 0.04 0.15 0.06 0.02 1.00 0.12 0.04
12 0.02 0.02 0.03 0.02 0.02 0.01 0.02 0.09 0.16 0.02 0.12 1.00 0.08
13 0.00 0.01 0.01 0.04 0.01 0.01 0.05 0.01 0.05 0.04 0.04 0.08 1.00









The mode shape for the dynamics at 35.78 Hz is shown in Figure 5-4. The

pylon exhibits a large amount of motion characterized by out of phase bending of the

leading-edge and trailing-edge ends. This pylon displacement is a rotation, or rocking

motion, about the center. The fins show a bending motion with only the trailing-edge

root fixed while all other points move uniformly around the body of the tail cone in an

angular fashion. The tail cone itself shows only slight deformation.

















Figure 5-4: Mode Shape at 35.78 Hz Measured for Lateral Excitation to GBU-10


The mode shape for the dynamics at 84.71 Hz is shown in Figure 5-5. The pylon

shows only minor displacement but the bomb shows fairly large displacement. One

type of motion is a bending of the main body of the bomb that causes the displacement

of the nose and tail cone. Another type of motion is a combination of bending and

torsion of the fins. The root and leading-edge ends of the fins are nearly motionless

such that the mode shape is dominated by large displacements at the trailing-edge tip

of the fins.

The mode shape for the dynamics at 169.71 Hz is shown in Figure 5-6. This

mode shows the same fin motion as the 84.71 Hz mode. The motion in the tail cone

is of the same amplitude as the previous mode but has additional nodes at one-third

and two-thirds of the length of that section. Moreover, the pylon motion is now quite


























Figure 5-5: Mode Shape at 84.71 Hz Measured for Lateral Excitation to GBU-10

drastic such that it shows bending about the center as in the first mode. Also, the local

mode near the horizontal and vertical center of the pylon discovered in the MK-84 test

near 186 Hz is present and out of phase with the overall motion of the pylon.


Figure 5-6: Mode Shape at 169.71 Hz Measured for Lateral Excitation to GBU-10


The mode shape for the dynamics at 275.53 Hz is shown in Figure 5-7. The

most interesting feature of this mode shape is the distinctly different motion of the

upper and lower fins. Specifically, the lower fins show a bending motion similar to

the mode shape at 84.71 Hz but the upper fins show bending about the trailing-edge









mid-span point. Also, the mode shape is dominated by large displacement of the tail

cone of the bomb. The leading-edge nose of the pylon shows additional displacement

with moderate magnitude. Most importantly, this mode was identified with negative

damping; therefore, the mode shape may not be physically realistic.

















Figure 5-7: Mode Shape at 275.53 Hz Measured for Lateral Excitation to GBU-10


The mode shape for the dynamics at 288.44 Hz is shown in Figure 5-8. The

only motion for this mode shape is a small displacement of the cone and reasonable

displacement of the fins of the tail assembly. Again, the motion of the fins is distinct

between the upper and lower fins. The lower fins show first-order displacement only

at the trailing-edge tip while the upper fins show second-order bending with the

trailing-edge end out of phase with the mid-chord line.

The mode shape for the dynamics at 358.7 Hz is shown in Figure 5-9. The only

motion is again associated with the cone and fins of the tail assembly; however, the

motion is each part is changed from the previous mode shape. The tail cone seems to

deform laterally such that the side of the cone shows displacements much larger than

any displacement of the bottom of the cone. The lower fins show bending dominated

by the trailing-edge tip but this bending includes a node point just inside the mid-span


























Figure 5-8: Mode Shape at 288.44 Hz Measured for Lateral Excitation to GBU-10

point. The upper fins show bending at the trailing-edge and mid-chord locations but the

mid-span points are out of phase with the root and tip.


Figure 5-9: Mode Shape at 358.7 Hz Measured for Lateral Excitation to GBU-10


The mode shape for the dynamics at 535.62 Hz is shown in Figure 5-10. The

displacement due to this mode shape is restricted to the cone and fins of the tail

assembly. Each fin showed similar motion of the trailing-edge tip. The upper fin also

showed motion of the mid-span mid-chord point but no sensor was available at this









location on the lower fins to allow comparison. The tail cone was moderately displaced

in this mode shape.


















Figure 5-10: Mode Shape at 535.62 Hz Measured for Lateral Excitation to GBU-10


The mode shape for the dynamics at 571.56 Hz is shown in Figure 5-11. This

mode shape involves displacements of every part of the test article. The pylon shows

motion that is restricted to the leading-edge and trailing-edge ends. The tail cone

shows very large displacements both on the side and on the bottom. Furthermore, the

upper fins and lower fins are moving but in different fashion. The upper fins have

large trailing-edge mid-span and mid-chord tip motion, relatively little motion at the

leading-edge end, and moderate motion at mid-chord mid-span points and mid-chord

root points. The lower fins show no leading-edge motion and moderate to large

trailing-edge motion.

The mode shape for the dynamics at 650.52 Hz is shown in Figure 5-12. This

mode is suspiciously similar to the previous mode at 571.56 Hz. The similarity,

coupled with its unstable negative damping, may indicate that the modal analysis at this

frequency is unreliable.

The mode shape for the dynamics at 719.88 Hz is shown in Figure 5-13. This

mode shows the large motion in the tail cone appearing to bend about its attachment



























Figure 5-11: Mode Shape at 571.56 Hz Measured for Lateral Excitation to GBU-10


Figure 5-12: Mode Shape at 650.52 Hz Measured for Lateral Excitation to GBU-10

point to the main body of the bomb. The underside of the tail section shows no node

point but the side shows a node approximately two-thirds of the way back from the

attachment point. Also, the motion of the lower fins is minor in comparison to the

motion of the upper fins. Specifically, the upper fins have large trailing-edge mid-span

motion that is out of phase with the large mid-chord mid-span motion.

The mode shape for the dynamics at 838.73 Hz is shown in Figure 5-14. The tail

shows large motion with a node on the underneath side at nearly the mid-length point

























Figure 5-13: Mode Shape at 719.88 Hz Measured for Lateral Excitation to GBU-10

of the tail section. The upper fins show large motion at the root and tip mid-chord

location that is out of phase with the large mid-chord/mid-span motion. The trailing-

edge mid-span motion is also large and in phase with the root and tip mid-chord

motion. The lower fins show only modest trailing-edge motion. No notable pylon

motion is observed for this mode.


Figure 5-14: Mode Shape at 838.73 Hz Measured for Lateral Excitation to GBU-10


The mode shape for the dynamics at 882.25 Hz is shown in Figure 5-15. The

tail cone motion is similar to the previous mode except that the node appears to have

moved back to nearly two-thirds of the total length from the attachment point. The









upper fins are the same as the previous mode with slightly smaller amplitude whereas

the lower fins are the same as in the previous mode with slightly larger amplitude.

Note that this is mode was identified with negative damping so the mode shape is not

confidently accepted and may not be physically realistic.
















Figure 5-15: Mode Shape at 882.25 Hz Measured for Lateral Excitation to GBU-10


The mode shape for the dynamics at 953.44 Hz is shown in Figure 5-16. The

tail section shows moderate motion whereas the pylon and main body of the bomb are

relatively motionless. The upper fins show quite a bit of complexity in their motion.

The leading-edge shows moderate motion with all locations from root to tip in phase.

Also, large mid-chord motion exists at the tip and mid-span points while only little

motion exists at the root. All points at the mid-chord line are out of phase with the

leading-edge and trailing-edge ends. The motions at the trailing-edge root and tip are

of small amplitude while the motion at mid-span points is large and in phase with the

mid-span mid-chord point. In sharp contrast, the lower fins show only small motions

with no out of phase motion at mid-span.


























Figure 516: Mode Shape at 953.44 Hz Measured for Lateral Excitation to GU-
Figure 5-16: Mode Shape at 953.44 Hz Measured for Lateral Excitation to GBU-10















CHAPTER 6
SUMMARY

The pylon-store dynamics are quite interesting for the MK-84 and GBU-10

munitions mounted to a PIDS-3 pylon. In particular, the GVT of these test articles

indicates the pylon and tail assemblies on the bombs are highly coupled. This coupling

relates the pylon with both the cone and fins of the tail assemblies. The nature of the

mode shapes included in phase and out of phase motion of the various components.

An especially interesting feature of the GVT results is the different behaviors

observed between the upper and lower fins. These fins had distinctly different motions

for several modes. The mode shape for the MK-84 mounted to a PIDS-3 in response

to lateral excitation showed differences between upper and lower fins at 548.31 Hz.

More importantly, the mode shapes for the GBU-10 mounted to a PIDS-3 in response

to lateral excitation showed differences between upper and lower fins for all 10

modes with natural frequencies above 275.53 Hz. These differences varied from

similar motion with different magnitudes to drastically different motion with different

magnitudes.

Another interesting feature of the GVT results is the local mode affecting the

pylon at 186.30 Hz. The mode shape for this dynamic is characterized by a lateral

bending affecting only a small portion of the pylon. The fins on the munitions were

also bending somewhat but the dominant feature was clearly the displacement of the

pylon region.

Finally, the performance of the GVT is itself interesting to evaluate. In particular,

the use of accelerometers and a laser Doppler vibrometer is worth noting. The data

measured by the laser had significantly less noise and was easier to analyze than

the data measured by the accelerometers. Conversely, the preparation time was









significantly less for the accelerometers than for the laser. These differences suggest

the laser is an excellent tool for GVT of the test articles as long as sufficient time is

allocated for the test.

The modes shapes obtained by the GVT may be indicative of dynamics related to

the fin damage that was recently observed. Obviously the modes involving pylon-store

coupling are potential indicators of the damage-inducing dynamics. The mode shapes

involving different motions between the upper and lower also have strong potential to

be related to the damage. The parameters and mode shapes identified from the GVT

should be used as a foundation to continue further experimental and computational

studies into the coupled pylon-store dynamics.















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BIOGRAPHICAL SKETCH

Joseph Dupuis was born in Bethesda, Maryland, on December 3rd, 1971. The

Dupuis family moved to the West Palm Beach, Florida, area where Joseph was to

spend his formative years. His college studies began at the Palm Beach Community

College in Lake Worth, Florida, in 1989 where he received an A.A. degree in music.

He later changed majors and went on to receive a B.S. degree in physics from the

University of Florida in Gainesville. Since 2002, Joseph has attended the College

of Engineering at the University of Florida to pursue his M.S. degree in aerospace

engineering. During this time he has worked part-time as a teaching and research

assistant in the Department of Mechanical and Aerospace Engineering. He has also

worked as a medical laboratory assistant in the Blood Bank at Shands hospital at U.F.

His research interests focus on structural dynamics.