Recently, National Aeronautics and Space Administration's (NASA's) White Sands Test Facility (WSTF) has tested rocket engines with high pulse frequencies. This has resulted in the use of some of WSTF's existing thrust stands, which were designed for static loading, in tests with large dynamic forces. In order to ensure that the thrust stands can withstand the dynamic loading of high pulse frequency engines while still accurately reporting the test data, their vibrational modes must be characterized. If it is found that they have vibrational modes with frequencies near the pulsing frequency of the test, then they must be modified to withstand the dynamic forces from the pulsing rocket engines. To make this determination the Mobile Modal Testing Unit (MMTU), a system capable of determining the resonant frequencies and mode shapes of a structure, was used on the test stands at WSTF. Once the resonant frequency has been determined for a test stand, it can be compared to the pulse frequency of a test engine to determine whether or not that stand can avoid resonance and reliably test that engine. After analysis of test stand 406 at White Sands Test Facility, it was determined that natural frequencies for the structure are located around 75, 125, and 240 Hz, and thus should be avoided during testing

Wilder, Andrew J.

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Modal Analysis with the Mobile Modal Testing Unit 
 
A.J. Wilder 
NASA White Sands Test Facility, Las Cruces, NM 88012, USA 
 
Abstract 
Recently, National Aeronautics and Space Administration’s (NASA’s) White Sands Test 
Facility (WSTF) has tested rocket engines with high pulse frequencies. This has resulted in the 
use of some of WSTF’s existing thrust stands, which were designed for static loading, in tests 
with large dynamic forces. In order to ensure that the thrust stands can withstand the dynamic 
loading of high pulse frequency engines while still accurately reporting the test data, their 
vibrational modes must be characterized. If it is found that they have vibrational modes with 
frequencies near the pulsing frequency of the test, then they must be modified to withstand the 
dynamic forces from the pulsing rocket engines. To make this determination the Mobile Modal 
Testing Unit (MMTU), a system capable of determining the resonant frequencies and mode 
shapes of a structure, was used on the test stands at WSTF. Once the resonant frequency has 
been determined for a test stand, it can be compared to the pulse frequency of a test engine to 
determine whether or not that stand can avoid resonance and reliably test that engine. After 
analysis of test stand 406 at White Sands Test Facility, it was determined that natural 
frequencies for the structure are located around 75, 125, and 240 Hz, and thus should be 
avoided during testing. 
 
Nomenclature 
௦݂  =   Sampling frequency 
௖݂  =   Highest frequency within a signal 
 
I.  Introduction 
NASA’s White Sands Test Facility is a branch of NASA’s Johnson Space Center whose primary 
function is testing. One of WSTF’s core capabilities is the testing of a wide range of propulsion 
systems. In certain scenarios variable thrust levels are required by a rocket engine to 
accomplish various mission objectives such as controlling the attitude of a space craft.  
However, in some instances, a rocket engine is limited in its ability to control thrust by throttling 
the engine valves to control the flow of propellant into the system. In these instances rapid 
pulsation of the engine can be performed to control thrust instead. This high frequency pulsing 
is used in hypergolic engines, where fuel and an oxidizer combust on contact, eliminating the 
need for an ignition source. As such, WSTF needs to be able to reliably test engines with this 
type of mission duty cycle. In rocket engine testing, WSTF uses test stands to hold engines and 
measure their thrust. These test stands must therefore be able to withstand rapid pulsation from 
the engines. Some of the stands being used for this testing were designed for sustained bursts 
or relatively low pulse frequencies, and thus their dynamic response must be characterized to 
determine how they will handle higher frequencies. The primary issue arises in finding the 
resonant, or natural, frequencies of the test stands. The natural frequency of a structure is a 
frequency at which the structure tends to oscillate with greater amplitude. While testing, if one of 
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Figure 1 Accelerometer Placement on a Test Stand 
(Accelerometers denoted by points on model) 
the test stands is oscillating at its natural frequency the strong vibrations can obscure the thrust 
data that WSTF provides to its customers, or worse, cause damage to the stand or test article. 
To capture the natural frequency of a test stand, a physical modal analysis was conducted 
on the test stand structure using the Mobile Modal Test Unit (MMTU). The MMTU uses 
accelerometers placed on a structure to measure vibrations when the structure is excited with 
an impact hammer. This system will provide experimental results for the natural frequencies of a 
given test stand. 
If any of these natural frequencies are within expected testing frequencies, the structure 
must be altered, or tuned, to shift the natural frequency away from the testing frequency. The 
MMTU software is capable of modeling and animating the mode shapes of specific vibrational 
modes. This tool can be applied to vibration modes found within the testing range, and used in 
the tuning process to strategically add and/or remove material and supports. 
 
II.  Theory 
The MMTU, along with the ModalView software it uses, is a robust tool allowing its users to 
determine the resonant frequencies of a wide variety of structures. To do this effectively, 
however, it must be used properly. There are several factors to take into consideration while 
testing with the MMTU, many of which will be examined here.  
First, the MMTU has five accelerometers, each able to measure movement along three 
different axes, and an impact 
hammer, which is used to excite 
the structure. The accelerometers 
measure the minute accelerations 
that occur at the various locations 
on the structure when it is excited 
with the hammer.  The ModalView 
software twice differentiates this 
value to determine the 
displacement of the accelerometer 
and the time taken to reach this 
translation. A Fast Fourier 
Transform, a mathematical method 
for transforming a function of time 
into a function of frequency, is then 
applied to the data to determine frequencies at which these displacements occurred. (Nave) 
To optimize the results of a test, the accelerometers must be placed in clusters at several 
different locations throughout the structure, as seen in Figure 1. Placing all five accelerometers 
in a cluster allows them to work together to build a clear picture of the vibrations occurring in 
that portion of the structure. Once one set is completed, all five accelerometers must be moved 
to a different location on the structure. These different locations are very important, as sufficient 
data points must be selected to obtain a clear picture of the mode shapes of the entire structure. 
Depending on the geometry and size of the structure being tested, many locations may need to 
be chosen for accurate results. 
Top
Bottom
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Figure 2   
Accelerometer placement for the top plate of 
the test stand 
Just as important as accelerometer placement is the use of the impact hammer. There are 
various tips available for the impact hammer, ranging from soft rubber to hard metal. A tip must 
be selected which will excite the structure sufficiently to obtain vibrational readings from the 
accelerometers, yet it must not cause excessive excitement, as the noise within the signal will 
make acquiring accurate readings very difficult. This decision can be made by looking at the 
material and design of the structure. In the case of the test stand, a metal tip was selected to 
excite the structure. Also, in order to get consistent readings between sets, the impact hammer 
must strike the same location every time. A location must be preselected which will excite the 
entire structure on impact. The location selected for the test stand is indicated by the star in 
Figure 1. 
Another important aspect to any kind of frequency testing, and therefore important when 
using the MMTU, is the sampling rate at which the data is acquired while testing is occurring. 
The Nyquist Sampling Theorem states that  
“The sampling frequency should be at least twice the highest frequency 
contained in the signal,” (Olshausen) 
or, as shown in equation 1: 
 
௦݂ 	൒ 2 ௖݂																																																																																	ሺ1ሻ 
 
Following this rule prevents data from being misinterpreted due to aliasing. Aliasing occurs 
not enough data is collected to define the peaks and troughs of the signal being measured. To 
insure this does not happen during MMTU testing, a sampling rate of over 1000 Hz was 
selected. Current rocket engine testing frequencies are well below 500 Hz, a 1024 Hz sampling 
frequency is more than enough to capture any natural frequencies in the testing range. 
 
III. Results 
Using the system and guidelines described above a tap test, or modal test, was performed 
with the MMTU on the Test Stand 406 thrust stand at White Sands Test Facility. The test was 
done at a sampling frequency of 1024 Hz to 
ensure accuracy within our desired testing 
range. 
To set up the test, the accelerometers 
were placed in eight sets of five, with three 
readings taken and averaged for each set. 
By averaging three readings for each set, 
the outliers and noise within the data sets 
was reduced. To achieve an optimal 
covering of the structure, two sets were 
placed on the top plate of the test stand, 
two on the bottom, two on the circular front 
band of the structure, and one on each side 
plate. Figure 1 can be referenced for exact 
placement of accelerometers on the test 
stand, and Figure 2 shows how the 
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accelerometers are placed on the stand (they are physically attached using beeswax on the 
contacting surface). Once the accelerometers within a set were placed, the impact hammer was 
used to excite the structure and obtain the desired readings. This process was completed for 
each set. With the testing completed, the results from all of the accelerometers were able to be 
combined into Figure 3, which shows the Frequency Response Function (the amplitude of 
vibrations against the frequency at which they occured) of the accelerometer data once the 
Fourier Transform has been applied. The frequency and amplitude are along the x and y axes, 
respectively.  
The MMTU is also capable of estimating natural frequencies based on the FRF data which 
is provided in Figure 3. The peaks in the graph represent the natural frequencies of the test 
stand. Table 1 shows the natural frequencies estimated for the data set in Figure 3. The 
estimation is only applied between 0 and 500 Hz, as anything above 500 Hz is out of the 
sampling rate frequency 
range. Looking at the graph, 
it is easy to see that several 
of the estimated frequencies 
are very close to each other, 
and are actually located 
within the same large peak. 
This occurs because along 
the graph, there are minute 
peaks within the larger 
peaks where the test has 
recorded small deviations 
within the data, illustrated in 
Figure 3. These deviations 
occur for several reasons. 
Three readings at eight 
locations analyzing three 
directions led to 24 sets of 
vibrational data. This data is 
 
Figure 3 Frequency Response Function results of the test done on Test Stand 406 
 Frequency (Hz) 
68.886 
84.135 
118.385 
123.991 
124.015 
129.596 
154.559 
231.901 
232.207 
236.378 
302.360 
341.654 
466.493 
467.649 
 
Table 1 
Natural Frequencies Estimated 
by MMTU Software 
 
 
Figure 4 
Zoomed in View of the 
Peak at 125 Hz 
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condensed into the graph in Figure 3. With this large amount of data, some variation is to be 
expected as testing conditions do not remain the exact same for every test set. There may also 
be a small error associated with the newly calibrated accelerometers used in 
the testing process. Regardless of the reasons for the 
deviations, however, the estimation software is looking for 
peaks. Rather than picking one large peak it will select all 
of the high amplitude peaks. Combining this knowledge 
with the graph in Figure 3, Table 1 can be narrowed down 
to a list of three major natural frequency estimations that 
are shown by the major peaks in the graph. Table 2 shows 
these major natural frequencies, which are the frequencies 
which must be taken into consideration while performing 
rocket engine tests on this particular test stand. 
 
IV. Discussion 
With the analysis of the test results completed, it can be seen that there is a natural 
frequency within this test stand in the range of 240 Hz. This is a frequency that must be avoided 
when testing rocket engines on this stand. There are other natural frequencies located around 
125 and 75 Hz whose amplitudes are not as extreme as the one located at 240 Hz, however 
these should be avoided as well when testing. The reason for having several of these natural 
frequencies at relatively low frequency lies in the design of the structure itself. The test stand is 
a very thin structure – only 1/8 of an inch thick- that is essentially a hollow cylinder with large 
sections cut out. The thinner a structure is, the more susceptible it is to low frequency vibrations. 
Thin structures oscillate much more freely with much lower forces required. The test stand, 
therefore, begins to oscillate at its natural frequencies very easily once dynamic forces are 
applied to the structure. In order to test at the natural frequencies listed above on this stand, the 
test stand must be altered in such a way to adjust these natural frequencies. This can be 
accomplished by adding mass to the test stand. Adding mass to a structure can serve to stiffen 
the structure. This will raise the frequency at which resonance occurs. To determine how to 
place the mass on the structure, knowing the mode shape for the natural frequency is required. 
The mode shape is how the structure vibrates at that natural frequency. If it is known, then mass 
can be placed in such a way to suppress the vibration and thus alter the frequency that it occurs 
at. Initially, mode shape analysis was a part of this project, however at the time this paper was 
written technical difficulties with the ModalView software prevented the mode shapes from being 
obtained. That is the next step that will be required in order for WSTF to make modifications to 
the test stand. 
 
V. Conclusion 
After analysis of test stand 406, it was determined that natural frequencies for the structure 
are approximately 75, 125, and 240 Hz. Because natural frequencies can lead to inaccurate 
data or even damage to the test stand or test article during testing, these frequencies must be 
avoided when testing high pulse frequency rocket engines on this test stand. If a customer 
requires a rocket engine to be tested at these frequencies on this stand, then further analysis 
must be performed to determine the mode shape. The mode shape will allow the structure to be 
Frequency 
(Hz) 
75 
125 
240 
 
Table 2 
Refined Natural Frequency List 
 
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strategically altered in order to shift the natural frequencies of the structure. Doing so will allow 
testing to be performed at the desired frequencies. 
 
Acknowledgements 
A.J. Wilder thanks Jeremy Bruggemann for his outstanding mentorship on this, along with 
other, projects in the propulsion area. The project would not have been able to be completed if 
not for his patience, knowledge, and willingness to teach. A.J. Wilder also thanks Ryan Maurer 
for assistance in familiarization with the MMTU and ModalView system, along with assisting with 
the modal testing of Test Stand 406. Finally, A.J. Wilder would like to convey his thanks and 
gratitude to the entire propulsion area staff, facilities engineering staff, and management at 
White Sands Test Facility for the opportunity provided and the openness with which they 
received him. 
 
Resources 
1Bruggeman, Jeremy, NASA White Sands Test Facility, private communication, November 
2013. 
2Nave, C.R., Fast Fourier Transforms [online database] URL: http://hyperphysics.phy-
astr.gsu.edu/hbase/math/fft.html [cited November 27, 2013] 
3Olshausen, Bruno A. Aliasing, URL: http://redwood.berkeley.edu/bruno/npb261/aliasing.pdf 
[cited November 25, 2013]. 


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