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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.
ii
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
4–11 Mode Shape at 312 Hz Measured by Accelerometers for Vertical Excita-tion to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4–12 Mode Shape at 443 Hz Measured by Accelerometers for Vertical Excita-tion to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4–13 Mode Shape at 507 Hz Measured by Accelerometers for Vertical Excita-tion to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4–14 Mode Shape at 671 Hz Measured by Accelerometers for Vertical Excita-tion to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4–15 Mode Shape at 831 Hz Measured by Accelerometers for Vertical Excita-tion to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4–16 Mode Shape at 899 Hz Measured by Accelerometers for Vertical Excita-tion to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4–17 Mode Shape at 946 Hz Measured by Accelerometers for Vertical Excita-tion to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4–18 Transfer Functions at Representative Locations . . . . . . . . . . . . . . . 40
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
4–22 Mode Shape at 548.51 Hz Measured by Accelerometers for Lateral Ex-citation to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4–23 Mode Shape at 680.64 Hz Measured by Accelerometers for Lateral Ex-citation to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4–24 Mode Shape at 858.42 Hz Measured by Accelerometers for Lateral Ex-citation to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
vii
4–25 Mode Shape at 969.66 Hz Measured by Accelerometers for Lateral Ex-citation to MK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4–26 Transfer Functions at Representative Locations . . . . . . . . . . . . . . . 47
4–27 Mode Shape at 86.41 Hz Measured by Laser for Lateral Excitation toMK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4–28 Mode Shape at 135.71 Hz Measured by Laser for Lateral Excitation toMK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4–29 Mode Shape at 189.05 Hz Measured by Laser for Lateral Excitation toMK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4–30 Mode Shape at 239.73 Hz Measured by Laser for Lateral Excitation toMK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4–31 Mode Shape at 239.73 Hz Measured by Laser for Lateral Excitation toMK-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4–32 Mode Shape at 293.35 Hz Measured by Laser for Lateral Excitation toMK-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 GBU-10 . . . . . . . . . . . . . . . . . . 55
5–2 Measurement Points for GVT of GBU-10 . . . . . . . . . . . . . . . . . . 56
5–3 Transfer Functions at Representative Locations . . . . . . . . . . . . . . . 56
5–4 Mode Shape at 35.78 Hz Measured for Lateral Excitation to GBU-10 . . . 58
5–5 Mode Shape at 84.71 Hz Measured for Lateral Excitation to GBU-10 . . . 59
5–6 Mode Shape at 169.71 Hz Measured for Lateral Excitation to GBU-10 . . 59
5–7 Mode Shape at 275.53 Hz Measured for Lateral Excitation to GBU-10 . . 60
5–8 Mode Shape at 288.44 Hz Measured for Lateral Excitation to GBU-10 . . 61
5–9 Mode Shape at 358.7 Hz Measured for Lateral Excitation to GBU-10 . . . 61
5–10 Mode Shape at 535.62 Hz Measured for Lateral Excitation to GBU-10 . . 62
5–11 Mode Shape at 571.56 Hz Measured for Lateral Excitation to GBU-10 . . 63
5–12 Mode Shape at 650.52 Hz Measured for Lateral Excitation to GBU-10 . . 63
viii
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
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
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
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.
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
37
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
38
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
39
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.
0 200 400 600 800 100010
−6
10−4
10−2
100
102
Frequency (Hz)
Mag
nitu
de (
g/lb
f)
bombpylonfin
Figure 4–18: Transfer Functions at Representative Locations
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.
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
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
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
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
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
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 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.
46
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
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
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) 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
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 toMK-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.
49
Figure 4–28: Mode Shape at 135.71 Hz Measured by Laser for Lateral Excitation toMK-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 toMK-84
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.
Figure 4–30: Mode Shape at 239.73 Hz Measured by Laser for Lateral Excitation toMK-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
51
Figure 4–31: Mode Shape at 239.73 Hz Measured by Laser for Lateral Excitation toMK-84
Figure 4–32: Mode Shape at 293.35 Hz Measured by Laser for Lateral Excitation toMK-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
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
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%.
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
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
59
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
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.
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
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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
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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
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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
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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
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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.
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Figure 5–16: Mode Shape at 953.44 Hz Measured for Lateral Excitation to GBU-10
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
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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.
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