Ground Vibration Testing of Airplane Pylon-Store Dynamics using …ufdcimages.uflib.ufl.edu/UF/E0/00/06/77/00001/dupuis_j.pdf · 2010-05-11 · ground vibration testing of airplane

GROUND VIBRATION TESTING OF AIRPLANE PYLON-STORE DYNAMICSUSING LASER DOPPLER VIBROMETER AND ACCELEROMETER

TECHNIQUES

By

JOSEPH DUPUIS

A THESIS PRESENTED TO THE GRADUATE SCHOOLOF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OFMASTER 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.

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TABLE OF CONTENTSpage

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

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

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Test Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 TEST HARDWARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1 Test Article . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Accelerometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4 Laser Doppler Vibrometer . . . . . . . . . . . . . . . . . . . . . . . . 142.5 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.6 Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 DATA ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1 Modal Analysis Software . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Using Laser and Accelerometer Data Cooperatively: Method 1 . . . . 203.3 Using Laser and Accelerometer Data Cooperatively: Method 2 . . . . 25

4 GVT ON PIDS-3 AND MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.1 Test Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2 Consideration of Excitation Signals . . . . . . . . . . . . . . . . . . . 304.3 Accelerometer Response to Vertical Excitation . . . . . . . . . . . . . 324.4 Accelerometer Response to Lateral Excitation . . . . . . . . . . . . . . 404.5 Laser Response to Lateral Excitation . . . . . . . . . . . . . . . . . . 464.6 Scan Response to Lateral Excitation . . . . . . . . . . . . . . . . . . . 50

5 GVT ON PIDS-3 AND GBU-10 . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.1 Test Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.2 Accelerometer Response to Lateral Excitation . . . . . . . . . . . . . . 56

iii

6 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

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

iv

LIST OF TABLESTable 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

v

LIST OF FIGURESFigure page

2–1 MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2–2 GBU-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 Vibrometer . . . . . . . . . . . . . . . . . 14

2–8 IOtech Data Acquisition System . . . . . . . . . . . . . . . . . . . . . . . 15

2–9 STEM Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3–1 Laser and Accelerometer Frequency Response Functions . . . . . . . . . . 21

3–2 Beam Second-Bending Mode Shape . . . . . . . . . . . . . . . . . . . . . 22

3–3 Effect of FFT Size on FRF of Laser Data . . . . . . . . . . . . . . . . . . 22

3–4 Effect of FFT Size on Curve Fit . . . . . . . . . . . . . . . . . . . . . . . 23

3–5 Poorly Animated Mode Shape . . . . . . . . . . . . . . . . . . . . . . . . 24

3–6 Frequency Response Function at Various 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 Vibrometer . . . . . . 30

4–5 Transfer Functions for Random Burst and Sine Sweep Excitation . . . . . 31

4–6 Transfer Functions for 10 and 35 lb Force Excitation . . . . . . . . . . . . 31

4–7 Transfer Functions for 1024 and 2048 Point Transforms . . . . . . . . . . 32

vi

4–8 Transfer Functions at Representative Locations . . . . . . . . . . . . . . . 33

4–9 Mode Shape at 46 Hz Measured by Accelerometer for Vertical Excita-tion to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4–10 Mode Shape at 183 Hz Measured by Accelerometers for Vertical Excita-tion to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36









4–19 Mode Shape at 186.3 Hz Measured by Accelerometers for Lateral Exci-tation to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4–20 Mode Shape at 296.9 Hz Measured by Accelerometers for Lateral Exci-tation to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4–21 Mode Shape at 356.59 Hz Measured by Accelerometers for Lateral Ex-citation to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43




vii



4–27 Mode Shape at 86.41 Hz Measured by Laser for Lateral Excitation toMK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48






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 GBU-10 . . . . . . . . . . . . . . . . . . 55

5–2 Measurement Points for GVT of GBU-10 . . . . . . . . . . . . . . . . . . 56


5–4 Mode Shape at 35.78 Hz Measured for Lateral Excitation to GBU-10 . . . 58


5–6 Mode Shape at 169.71 Hz Measured for Lateral Excitation to GBU-10 . . 59







viii





ix

Abstract of Thesis Presented to the Graduate Schoolof the University of Florida in Partial Fulfillment of the

Requirements for the Degree of Master of Science

GROUND VIBRATION TESTING OF AIRPLANE PYLON-STORE DYNAMICSUSING LASER DOPPLER VIBROMETER AND ACCELEROMETER

TECHNIQUES

By

Joseph Dupuis

May 2003

Chair: Dr. Richard C. LindMajor 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.

x

CHAPTER 1INTRODUCTION

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

1

2

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 sensor(s) used, being either a laser or accelerometers.

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 effects

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

velocity V�

s to true velocity Vs through the concept of mechanical impedance and

defines this quantity as

V�

s�Vs �� Zs

��Zs � Za �

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

written as jωm. 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

4

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

5

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

6

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

7

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 2TEST 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

8

9

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-10Weight (lbs) 2039 2562Length (in) 129 172Diameter (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

10

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.

11

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.

12

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

13

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 8-45µVrms with the

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

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

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.

14

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

15

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

16

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 3DATA 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

ek � �b0 � b1

�iωk � 2 �� b2m 1

�iωk � 2m 1 ��

a0 � a1�iωk �� a2

�iωk � 2 �� a2m

�iωk � 2m �� Hk (3.1)

17

18

where a0 � a1 � �� a2m � b0 � b1 � �� 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

e �k � �1

�iωk � �

iωk � 2 �� iωk � 2m 1 �

�� b0

b1��b2m 1

�� Hk

�1

�iωk � �

iωk � 2 �� iωk � 2m 1 �

�� a0

a1��a2m 1

�� Hk�iωk � 2ma2m

(3.2)

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].

19

The percentage damping is determined from the governing differential equation for

a vibratory system [30].

md2xdt2 � c

dxdt � kx � F

�t � (3.4)

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

equation is

x � Aeλt (3.5)

yielding the characteristic equation

λ2 � cm

λ � km � 0 (3.6)

The roots of this equation are

λ1 % 2 � � c2m &(' ) c

2m * 2 � km

(3.7)

If we consider the case where + c2m , �.- k

m , known as critically damped motion,

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

x�t �/� �

C1 � C2t � eλt (3.8)

For the critically damped case we can define

ccr � 2 0 km (3.9)

then the damping ratio is defined as

ζ � cccr

(3.10)

20

and then expressed as a percentage

ζ � cccr 1 100% (3.11)

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

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 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.

100

101

102

Abs

olut

e M

agni

tude

(g/

lbf)

20 30 40 50 60 70 80 90

−500

0

500

Pha

se (

degr

ees)

Frequency (Hz)

AccelLaser

Figure 3–1: 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.

22

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

101

102

Abs

olut

e M

agni

tude

(g/

lbf)

40 50 60 70 80 90500

1000

Pha

se (

degr

ees)

Frequency (Hz)

20484096

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

23

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.

100

101

102

Abs

olut

e M

agni

tude

(g/

lbf)

20484096

20 30 40 50 60 70 80 90−150−100−50

0

Pha

se (

degr

ees)

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

24

Figure 3–5: Poorly Animated Mode Shape

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

Frequency(Hz) Damping MagnitudeLaser2,048 68.71 9.14E-003 102.504,096 68.76 2.56E-003 315.40Accel2,048 68.69 1.00E-002 107.904,096 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.

25

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.

50 100 150 200 250 300 350 40010

−6

10−4

10−2

100

Frequency (Hz)

Mag

nitu

de (

g/lb

f)

bombpylonfin

Figure 3–6: Frequency Response Function at Various Locations

26

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.

50 100 150 200 250 300 35010

−5

10−4

10−3

10−2

10−1

Frequency (Hz)

Mag

nitu

de (

g/lb

f)

(a) Fin

50 100 150 200 250 300 35010

−6

10−5

10−4

10−3

10−2

Frequency (Hz)

Mag

nitu

de (

g/lb

f)

(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

27

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

Q � ωω2 � ω1

� 1γ

(3.12)

where ω2 and ω1 are located to either side of resonance and representing the full

width at half maximum and γ 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 4GVT 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.

28

29

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

30

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.

31

0 200 400 600 800 100010

−4

10−3

10−2

10−1

100

Frequency (Hz)

Mag

nitu

de (

g/lb

f)

random burstsine sweep

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

0 200 400 600 800 100010

−4

10−3

10−2

10−1

100

Frequency (Hz)

Mag

nitu

de (

g/lb

f)

10 lbf35 lbf

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

32

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.

0 200 400 600 800 100010

−4

10−3

10−2

10−1

100

101

Frequency (Hz)

Mag

nitu

de (

g/lb

f)

10242048

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

33

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

of the measurements.

0 200 400 600 800 100010

−6

10−4

10−2

100

102

Frequency (Hz)

Mag

nitu

de (

g/lb

f)

bombpylonfin

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 7.632 183.32 1.893 312.53 1.744 443.16 0.2475 507.61 0.3726 525.03 -0.8127 671.99 0.9398 831.16 0.9339 899.67 0.241

10 946.22 1.14

34

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 9 101 1.00 0.09 0.00 0.03 0.03 0.02 0.03 0.01 0.02 0.022 0.09 1.00 0.02 0.01 0.02 0.03 0.02 0.01 0.02 0.013 0.00 0.02 1.00 0.01 0.13 0.01 0.05 0.01 0.00 0.014 0.03 0.01 0.01 1.00 0.02 0.04 0.00 0.01 0.02 0.045 0.03 0.02 0.13 0.02 1.00 0.13 0.00 0.00 0.04 0.046 0.02 0.03 0.01 0.04 0.13 1.00 0.02 0.05 0.07 0.007 0.03 0.02 0.05 0.00 0.00 0.02 1.00 0.04 0.04 0.018 0.01 0.01 0.01 0.01 0.00 0.05 0.04 1.00 0.15 0.019 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

35

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.

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


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.


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

36

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.



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

37

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

motion which correlates with a chord-wise bending mode.



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.


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

38



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

on the lower fins show small modal displacements.


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

39


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

and torsion.



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.


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.

0 200 400 600 800 100010

−6

10−4

10−2

100

102

Frequency (Hz)

Mag

nitu

de (

g/lb

f)

bombpylonfin


41

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 0.619082 296.90 1.100003 356.59 0.993784 548.51 0.306215 680.64 0.409616 858.42 0.628677 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.


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

42

Table 4–4: AutoMAC of Accelerometer Response for Lateral Excitation to MK-84

Modes 1 2 3 4 5 6 71 1.00 0.01 0.00 0.09 0.00 0.01 0.002 0.01 1.00 0.13 0.16 0.04 0.08 0.013 0.00 0.13 1.00 0.08 0.02 0.04 0.034 0.09 0.16 0.08 1.00 0.01 0.09 0.035 0.00 0.04 0.02 0.01 1.00 0.13 0.046 0.01 0.08 0.04 0.09 0.13 1.00 0.017 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. Another feature is bending

localized around the mid-span point of the pylon.

Figure 4–19: Mode Shape at 186.3 Hz Measured by Accelerometers for Lateral Excita-tion to MK-84


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.


mode shape for this dynamic involves mostly the fin with very small motions of the

43

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.

Figure 4–21: Mode Shape at 356.59 Hz Measured by Accelerometers for Lateral Exci-tation to MK-84

44


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.



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

45

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 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.


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.

46



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

47

0 50 100 150 200 250 30010

−5

10−4

10−3

10−2

10−1

100

Frequency (Hz)

Mag

nitu

de (

g/lb

f)

finpylon


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) Damping1 86.41 1.642 135.71 1.053 189.05 2.124 239.73 1.825 293.35 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

48

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 51 1.00 0.02 0.02 0.06 0.042 0.02 1.00 0.28 0.06 0.013 0.02 0.28 1.00 0.01 0.014 0.06 0.06 0.01 1.00 0.065 0.04 0.01 0.01 0.06 1.00


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 toMK-84


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.

49



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.


50

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.


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.


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

51



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

52

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.

Figure 4–33: Mode Shape at 185 Hz Measured by Laser Scan on Fin of MK-84

53

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.

54

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

CHAPTER 5GVT 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

55

56

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.

0 200 400 600 800 100010

−5

10−4

10−3

10−2

10−1

100

Frequency (Hz)

Mag

nitu

de (

g/lb

f)

bombpylonfin


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%.

57

Table 5–1: Modes Measured for Lateral Excitation to GBU-10

Mode Frequency, Hz Damping, %1 35.78 4.862 84.71 6.113 169.71 1.574 275.53 -0.5475 288.44 0.1066 358.70 0.8297 535.62 0.4798 571.56 0.3329 650.52 -0.270

10 719.88 0.09811 838.73 0.40712 882.25 -0.50513 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 12 131 1.00 0.01 0.05 0.01 0.02 0.00 0.10 0.10 0.04 0.01 0.02 0.02 0.002 0.01 1.00 0.12 0.22 0.09 0.21 0.01 0.00 0.09 0.03 0.00 0.02 0.013 0.05 0.12 1.00 0.06 0.10 0.09 0.05 0.05 0.10 0.00 0.00 0.03 0.014 0.01 0.22 0.06 1.00 0.01 0.52 0.05 0.03 0.21 0.00 0.00 0.02 0.045 0.02 0.09 0.10 0.01 1.00 0.06 0.02 0.04 0.03 0.14 0.01 0.02 0.016 0.00 0.21 0.09 0.52 0.06 1.00 0.14 0.00 0.18 0.05 0.01 0.01 0.017 0.10 0.01 0.05 0.05 0.02 0.14 1.00 0.09 0.11 0.11 0.04 0.02 0.058 0.10 0.00 0.05 0.03 0.04 0.00 0.09 1.00 0.11 0.07 0.15 0.09 0.019 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 0.0411 0.02 0.00 0.00 0.00 0.01 0.01 0.04 0.15 0.06 0.02 1.00 0.12 0.0412 0.02 0.02 0.03 0.02 0.02 0.01 0.02 0.09 0.16 0.02 0.12 1.00 0.0813 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

58


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.


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

59


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.



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

60

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.



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

61


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.



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

62

location on the lower fins to allow comparison. The tail cone was moderately displaced

in this mode shape.



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.


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.


mode shows the large motion in the tail cone appearing to bend about its attachment

63



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

64


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.



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

65

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.



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.

66


CHAPTER 6SUMMARY

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

67

68

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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[4] A. B. Stanbridge and D. J. Ewins. “Modal Testing Using a Scanning LaserDoppler Vibrometer.” Mechanical Systems and Signal Processing, 13, 1999.

[5] A. B. Stanbridge, M. Martarelli, and D. J. Ewins. “Measuring Area Mode Shapeswith a Scanning Laser Doppler Vibrometer.” IMAC XVII Proceedings, 1999.

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[10] D. Fotsch and D. J. Ewins. “Application of MAC in the Frequency Domain.”IMAC XVIII Proceedings, 2000.

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[12] P. Guillaume, P. Verboven, S. Vanlanduit, and E. Parloo. “Accurate DampingEstimates Using Adapted Frequency-Domain Identification Techniques.” IMACXVIII Proceedings, 2000.

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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.

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