w d r -  ci d o 6 / c f g - , /  
STRUCTURAL DYNAMICS TEST SIMULATION AND OPTIMIZATION 

FOR AEROSPACE COMPONENTS 

S. E. Klenke and T. J. Baca 
Experimental Structural Dynamics Department 

Sandia National Laboratories 
Albuquerque, New Mexico 87185-0557 

ABSTRACT: 
This paper initially describes an innovative approach to 
product realization called Knowledge Based Testing 
(KBT). This research program integrates test 
simulation and optimization software, rapid fabrication 
techniques and computational model validation to 
support a new experimentally-based design concept. 
This design concept implements well defined tests 
earlier in the design cycle enabling the realization of 

simulation and optimization software environment 
provides engineers with an essential tool needed to 
support this KBT approach. 

This software environment, called the Virtual 
Environment for Test Optimization (VETO), integrates 
analysis and test based models to support optimal 
structural dynamic test design. A goal in developing 
this software tool is to provide test and analysis 
engineers with a capability of mathematically 
simulating the complete structural dynamics test 
environment within a computer. A developed 
computational model of an aerospace component can 
be combined with analytical and/or experimentally 
derived models of typical structural dynamic test 
instrumentation within the VETO to determine an 
optimal test design. The VETO provides the user with 
a unique analysis and visualization environment to 
evaluate new and existing test methods in addition to 
simuIating specific experiments designed to maximize 
test based information needed to validate 
computational models. The results of both a modal and 
a vibration test design are presented for a reentry 
vehicle and a space truss structure. 

INTRODUCTION: 
This paper presents the Knowledge Based Testing 
(KBT) concept which incorporates aspects of design, 
analysis, and test with rapid prototyping to optimize 
test based product information from an experiment. 
The purpose of developing a KBT program is to utilize 
testing earlier in the design cycle. There are a number 

% 
?- 

. <  highly reliable aerospace components. A test i 

of research activities that will be discussed in this 
paper that help modify the conventional testing 
paradigm that normally tests a product at the end of 
development. 
One of these research areas being developed is the 

Virtual Environment for Test Optimization, VETO'. 
This innovative tesdanalysis tool reduces test 
instrumentation iterations, producing better tests 
through optimal test design. Communication between 
test and analysis engineers is enhanced early in the 
design cycle. Traditionally, the role of testing in the 
product realization process is limited to the end of the 
design cycle, after hardware manufacturing decisions 
have been made. As a result, data analysis and test 
requirements for a component are only considered 
when the hardware is scheduled for testing. Thus, the 
full benefit of the analysis in guiding the test is not 
realized. A goal in developing this software tool is to 
provide test and analysis organizations with a 
capability of mathematically simulating the complete 
test environment within a computer. Derived models of 
test equipment, instrumentation and hardware, called 
virtual instruments, can be combined within VETO to 
provide the user with a unique analysis and 
visualization capability to evaluate new and existing 
test methods. By providing engineers with a tool that 
allows them to optimize an experimental design within 
a computer environment, pre-test analysis can be 
performed using analytical models to rapidly evaluate 
components before manufacturing has occurred. The 
benefits of using this type of experimental design tool 
can be very extensive. The user can evaluate the use of 
different types of test instrumentation and equipment 
as well as investigating new testing techniques for 
system identification used to experimentally validate 
analytical models. 
A second research activity has focused on using the 
recently developed stereolithography to 
reduce the time between concept and product 
realization by evaluating plastic models to predict the 
structural behavior of actual metal parts. This 

TER 
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DISCLAIMER 

This report was prepared as an account of work sponsored by an agency of the 
United States Government. Neither the United States Government nor any agency 
thereof, nor any of their employees, makes any warranty, express or implied, or 
assumes any legal liability or responsibility for the accuracy, completeness, or use- 
fulness of any information, apparatus, product, or process disclosed, or represents 
that its use would not infringe privately owned rights. Reference herein to any spe- 
cific commercial product, process, or service by trade name, trademark, manufac- 
turer, or otherwise does not necessarily constitute or imply its endorsement, recom- 
mendation. or favoring by the United States Government or any agency thereof. 
The views and opinions of authors expressed herein do not necessarily state or 
reflect those of the United States Government or any agency thereof. 



stereolithography process has provided the means of 
economically generating very exact plastic prototype 
parts from three dimensional solid models. This 
process rapidly produces prototype plastic parts with 
astounding accuracy including bolt holes, countersinks, 
fillets, cutouts, etc. These stereolithography plastic 
prototypes include all the detail and are nearly perfect 
replicas of the actual parts. They afford detail that 
cannot be included in finite element models without 
extremely expensive high order meshes of very small 
features which may be important to the structural 
performance of the design. 
These prototypes are currently used primarily to verify 
geometries, for interference checks, and for product 
visualization. The ability to perform mechanical tests 
on these plastic prototypes and infer actual metal part 
structural performance could significantly reduce 
design cycle times. Mechanical tests of interest include 
static loading, modal testing and vibration testing. 
These rapid prototype test results could also be used to 
validate analytical models early in the design process 
to provide predictive models for effective design 
iterations and tradeoff studies. These very exact plastic 
prototypes offer a new realm of opportunity for the use 
of plastic models to predict the structural performance 
of actual metal parts. 
A third area of ongoing research related to the KBT 
program is in computational model validation4. 
Improved finite element modeling techniques and the 
ever decreasing cost of computing have been a major 
contributor to the increased capability of 
computationally-based engineering simulations. The 
current trend toward increased reliance on simulations 
for design and performance evaluation is pervasive 
throughout the industry. However, within the KBT 
program it is also recognized that there is a need for 
increasingly sophisticated testing and physical 
simulation that is essential to the development and 
validation of engineering models. Thus, by combining 
the use of the VETO, to optimally design an 
experiment, with the use of rapid prototyping 
techniques for generating component parts, the 
processes of model updating and validation becomes 
much more efficient. These tools are critical to 
providing test based information needed to produce 
confidence in the predictive capabilities of 
computational models of aerospace components. 

KNOWLEDGE BASED TESTING (KBT) 
OVERVIEW: 
As was mentioned in the previous section, the goal of 
the KBT program is to position testing earlier in the 

design cycle. This new vision or role for testing is 
partly motivated by increased modeling capabilities as 
well as the recent increase in computational power. In 
this vision, the definition of testing will not simply 
mean to provide the "admiral's tests" but will be used 
as an underlying tool that is essential to model 
development and validation. A view of the KBT 
concept is shown in Figure 1 .  This bubble chart depicts 

Rapid Product 
Realization 

Figure 1. Knowledge Based Testing Chart 
the important interactions between design (starting 
with requirements and specifications), analysis and test 
used to support rapid product realization. 

The initial step in the KBT program is the generation 
of a computer aided design model which represents the 
geometry of the component or component housing to 
be tested. This model is generally driven by certain 
requirements and specifications. This geometric model 
is then used to assist component visualization, to 
generate a computational model used for dynamic 
analysis, and to produce a rapid prototype component 
through a stereolithography or "fastcast" process* '. 
The developed computational model of the component 
is then combined with analytical andor experimentally 
derived models of the test instrumentation within the 
VETO software to determine an optimal test design. 
The VETO is then used to simulate the structural 
dynamics experiment in order to maximize the test 
based information gathered from the experiment. The 
next step in the KBT process is the performance of the 
experimental test or characterization test using the 
rapid prototype component given the VETO test 
design. The results of this experiment are then used to 
update and validate the computational model. 
This systematic approach to rapid prototype evaluation 
integrated with optimal test design software is an 

+Fastcast uses a stereolithography or laser sintered part as 
a mold for an automatic metal casting system. 

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important part of the KBT concept that helps bridge the 
gap between the old testing paradigm and this new 
testing vision. Design and analysis methods are 
integrated to support test simulations. These 
computationally-based simulations provide predictions 
of component or system response to testing 
environments and the results of these simulations are 
then used to guide an actual characterization test. By 
completing the test design within the virtual 
environment, the user can effectively evaluate what 
test information is needed from the experiment to 
update and validate the computational model. After 
this validation process is complete and some level of 
confidence is established in the computational model, 
further optimization and simulation studies can be 
performed using the model before any manufacturing 
or building of the component is done. It should be 
noted that the KBT concept also includes aspects of 
testing necessary for product verification. The KBT 
definition of product verification includes certification 
testing, design margin testing6 and failure mode/ 
mechanism identification testing. Lon g term 
monitoring of component performance is the final type 
of KJ3T which involves health monitoring7. 

ROLE OF STRUCTURAL DYNAMIC TEST 
SIMULATION AND OPTIMIZATION IN KBT: 
The VETO software environment currently integrates 
analysis and test based models to support optimal 
structural dynamic test design. The structural dynamics 
testing environment was selected as the initial VETO 
environment for investigation into areas of design/ 
analysis/test interfaces, visualization, versatility and 
repeatability. This initial VETO effort has focused on 
assisting engineers to maximize the value and 
information gathered from these tests. 
A major objective of the VETO software development 
effort is flexibility. Because the virtual environment is 
a prototype software system, a primary concern for its 
design is that the code be easy to develop. To minimize 
this effort, existing software tools are used wherever 
possible, provided that the necessary functionality and 
flexibility are available. Another significant design 
objective is to provide a final software system that can 
be used by a variety of individuals who have not been 
involved in its development. As is described below, 
VETO integrates several commercial tools to meet 
these objectives. 

Currently, the VETO software tool has been developed 
to support a modal virtual test environment while 
development of a vibration virtual environment is 
under development. Many of the tools needed to 

- 

support simulations of these two structural dynamic 
test capabilities are similar, however, because of the 
various differences in these technologies, two distinct 
simulation approaches have been developed. The first 
approach, which was formulated to support modal test 
optimization, provided the user with an environment 
where numerical integration is performed on a system 
of state space models which described the modal test 
configuration. This method served very well in the 
support of simulations which did not include closed 
loop control. However, in our second approach an 
effort is being made to address simulations that do 
include control aspects, namely vibration tests. The 
vibration virtual environment will include hardware-in- 
the-loop (both control and data acquisition elements) in 
addition to instrument and equipment models to 
support the simulation. Further details on these 
approaches are described below. 
For both of the structural dynamic testing 
environments, the database, integration, utility and user 
interface functions are performed in the Vetomain 
module, Figure 2. This main interface provides the 

Figure 2. Vetomain Graphical Interface 
communication links between the two commercial 
software packages: AVS which is used for 
visualization and MATLAB which is used to perform 
modeling and time integration. The "File" option of the 
vetomain menu bar allows users to load finite element 
(FE) models and previously defined virtual test files 
into the VETO software. The setup for the test 
simulation is performed using Vetomain to construct 
parametric models of the instruments, and to formulate 
interconnections between the models. The user is able 
to interact with the virtual instrument to provide and 
view information on the devices needed in the 
simulation. This user interaction includes the selection 
of the number of desired response locations, the 
location of input excitation and the type of instruments 
needed to support the simulation. This interface 
module also provides numerous tools to assist the 
engineer in setting up and understanding how the 
various virtual instruments interact together to support 
a specific structural dynamic test simulation. These 
tools will help guide the engineer in the design of tests 
that will accurately identify all the desired modes of 
the structure, select the appropriate test instrumentation 
as well as identify the proper excitation levels for the 
test. 

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MODAL TEST SIMULATIONS AND 
OPTIMIZATION: 
The SIMULINK Dynamic System Simulation 
Software provided by MATLAB is used as the 
environment to assemble and ultimately integrate 

. mathematical models of the modal test system. This 
same software controls the simulation processing. 
Dynamic response equations are integrated by 
SIMULINK to provide system output time histories. 
Within the VETO software, inputs such as type of 
device and interconnection of instrumentation models 
are combined to facilitate the rapid connection of 
various models (including models of test 
instrumentation, equipment and hardware) which 
comprise a given modal testing process. In order to 
achieve rapid set up of this virtual environment, 
models representing the instrumentation and test 
equipment need to be developed. These models consist 
of mathematical descriptions of the dynamic response 
of the instruments derived either theoretically or 
experimentally. Most of the instruments modeled to 
date have been modeled in the discrete state space 
domain. A number of system identification tools were 
used in MATLAB to generate the mathematical 
models. Development was based on an experimental 
frequency response function of the instrument or 
equipment. 

The models of the different types of instruments and 
equipment (transducers, ampwiers, filters, etc.) needed 
to represent a complete modal testing environment are 
located in a SIMULINK Virtual Test Equipment 
Library (VTELib). When preparing for a test 
simulation, the selection of the desired test 
instrumentation from the Vetomain is performed with 
the assistance of a MATLAB code which searches the 
VTELib for available instrument models. Optimal 
experimental design and simulation of the complete 
test environment is further facilitated by the VETO'S 
ability to include models of external inputs and 
electronic instrumentation noise. In addition, complex 
instrumentation models, such as the data acquisition 
system (Front End), are constructed by combining 
multiple submodels to simulate the dynamic response 
behavior of the hardware. 

As these models are added to the new simulation 
system, interconnecting lines are placed between the 
block models within SIMULINK. These lines represent 
the flow of signals in the actual modal test system and 
are specified using the "wire" instrument in Vetomain. 
Using these interconnecting lines, the input signals 
from the actuator devices (e.g. impact hammers) are 

fed to both the device under test (D JT) model or 
simulation of system excitation and to the "Front End" 
device for simulation of data acquisition. This DUT 
model is directly generated using the FE modal data 
given the user desired input and sensor locations for 
the simulation. The "Front End" device also receives 
the signals from the sensors that have been attached to 
the DUT to simulate structural system response to the 
actuator input. Both the simulated actuator and sensor 
signals are linked through amplifier and filtering 
blocks to represent preconditioning of the signals. 
The process of simulation begins when the user selects 
"Run" from the "Simulate" option on Vetomain. The 
data files which define the dynamics of the desired 
instrumentation are loaded into the test simulation 
system and the "Simulation Monitor" is created and 
displayed. This monitor allows the user to observe the 
estimated system response based on the numerical 
integration. The Simulation Monitor represents the data 
acquisition environment commonly used to gather data 
in a physical test and is a graphical interface through 
which the user interacts with the modal test simulation 
system. After collecting the desired amount of 
simulated data, the user can activate a window 
providing an interface to analysis routines for 
computing measures such .as frequency response 
functions, power spectral densities and coherence 
based on the simulated data. 

MODAL TEST APPLICATION: 
An aerospace component was selected as a test case for 
application in the VETO environment. The VETO 
software simulation tool was used to design an optimal 
experiment for this mock reentry vehicle, Figure 3. The 

Figure 3. Mock Re-entry Vehicle Model 

goal of performing this test design optimization was to 
observe the vibration modes of interest and to study the 
interaction of the support flanges with the reentry 
vehicle housing. The initial steps in the test design 

, 

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American Institute of Aeronautics and Astronautics 



were to select an appropriate set of instrumentation 
(including sensors and actuators) needed to perform a 
modal experiment within the VETO environment and 
to simulate responses on the aerospace component. A 
symmetric finite element model of the structure was 
loaded into the VETO environment for use in the 
modal test simulation. The test design was performed 
over a frequency band, up to 250 Hz, which included 
fifteen vibration modes of the reentry vehicle. 

The outcome of the VETO test design "Setup" was to 
excite the structure using an impact hammer and to 
measure acceleration responses on the reentry vehicle 
at 40 different locations in order to characterize the 
dynamic behavior of the component. Approximately 
half of the response locations were automatically 
selected using an analysis code to optimize the sensor 
locations. Some care was taken in utilizing this code to 
ensure that redundant or closely spaced response 
locations on the structure were not used in the 
simulation. Other instrumentation such as the signal 
conditioning amplifiers and the data acquisition system 
were also set up with the use of Vetomain in 
preparation for the test simulation. Data acquisition 
parameters for sampling, averaging and acquiring the 
desired analysis measurements were also selected for 
use in the post-simulation analysis. 
A number of "Pre-simulation" tools were used to 
determine the completeness of the test design. First, the 
effects of mass loading the component were calculated 
given the test design sensor set. Small accelerometers, 
Endevco 2250s, were selected in the test design in 
order to minimize the mass loading effects that might 
occur during the experimentation. This analysis 
predicted that very small changes in the frequencies of 
vibration (approximately 0.1 %) would be experienced 
if an experimental test was conducted based on the 
selection of small accelerometers in the test design. 
Second, a normal mode indicator function and a 
driving point frequency response function were viewed 
before conducting the test simulation in order to assess 
whether the selected sensor and actuator (selected 
impact location) set would accurately identify all the 
desired modes of interest on the aerospace component, 
Figures 4 and 5 .  By using the normal mode indicator 
function, it was determined that a single input location 
at the nose of the reentry vehicle would not excite a1 of 
the modes of the structure. Therefore, additional 
excitation locations would need to be included in the 
test setup so that all the modes of vibration of the 
reentry vehicle could be observed. Finally, the Modal 
Assurance Criterion (MAC) was calculated for the test 
design to determine if the modes of vibration of the 
structure could easily be distinguished from one 

:::: 0.1 50 100 150 2w 250 30( 
Frequency 

Figure 4. Normal Mode Indicator Function 
another given the selected sensor set. Small values on 
the off-diagonal terms of this MAC matrix, Figure 6, 

Actuator uui-:i. 

l0"t 
1 0' 1 02 10' 

Frequency 

Figure 5 .  Drivin Point Frequency 
Response % unction 

Mod3 Assurance Criteria 

Mode# '' Mode # 
Figure 6 .  Modal Assurance Criterion 

indicate the relative independence of the modes of 
vibration, thus facilitating correlation with analysis. 
With the complete test design within the VETO 
environment, a SIMULINK block model of the test 
environment is automatically generated to support the 
simulation of the modal test. Figure 7 shows a partial 

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American Institute of Aeronautics and Astronautics 



Figure 7. Modal Test Simulation Block Model 

block model of the SIMULINK environment. 

The next step in the modal test simulation is the 
numerical integration of the mathematical models 
within SIMULINK to estimate the system responses. 
Using the Simulation Monitor, these responses are 
observed for each set or frame of data to be collected, 
Figure 8. Once the data are gathered to support the 
desired measurement set, the test simulation within 
SIMULINK is concluded. A window which provides 

Figure 8. Simulation Monitor 
an interface to the post-simulation analysis routines is 
then used to download the data for measurement 
analysis. A number of analysis routines for computing 
desired measures such as frequency response functions, 
power spectral densities and coherences are available. 
The simulated data, which are based on the FE 
dynamic analysis, were used to generate frequency 
response functions, Figure 9. 

VIBRATION TEST SIMULATION AND 
OPTIMIZATION: 

As was mentioned earlier, the vibration virtual 
environment is currently under development. Some of 
the issues that must be addressed in this particular 

50 100 150 200 2YJ 300 
10-2 

Frequsncy (Hz) 

Figure 9. Measured FRF using Simulated Data 
simulation environment that are not included in the 
modal virtual environment are: closed loop vibration 
control, detailed shakedamplifier models and shaker/ 
fixture/component interaction. Because of these issues 
as well as others, it was determined that a new 
simulation approach would be developed using some 
of the existing hardware that directly support vibration 
tests. These simulations, called hardware-in-the-loop 
simulations, would provide the user with the ability to 
combine actual vibration test hardware (such as 
vibration control and data acquisition systems) with 
instrumentation models to support vibration test 
design. Models of the external load (the shaker/ 
amplifier, interface block, fixturing, device under test, 
accelerometers and signal conditioning elements) will 
be combined into a single state space model using 
MATLAJ3 routines and then downloaded onto a real- 
time control processor. With the simulation model of 
the external load residing on the processor, the physical 
hardware is then connected to the processor for 
performing the vibration test simulation. The particular 
processor used in our simulation environment was 
developed in-house and has the capability of handling 
16 inputs and 16 outputs with a total of 128 states. The 
sampling rate of the processor is based on the size or 
number of states of the model. Figure 10 shows a 
simple representation of this hardware-in-the-loop 
simulation environment. 
The virtual vibration environment will allow the user 
to evaluate the overall testability of a component or 
system. The test engineer will be able to observe the 
effects that different control parameters might have on 
the DUT without putting the physical hardware 
through an actual vibration test. An advantage of this 
environment is that it can help limit unnecessary 
vibration inputs to flight hardware. New and existing 
fixture designs can also be studied through the 
development of analytical models that can be 
integrated into this simulation environment. Testing 

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American Institute of Aeronautics and Astronautics 



r .  

I(eal-l'ime 
Codrol Processor 

Sun Workstation 
d MATLAB &FtT(P 

VibrationControl 
Conplter 

Figure 10. Vibration VETO Concept 
methodologies such as the number of control 
transducers, the location of control transducers and the 
control strategy or method can also be investigated 
within the vibration environment. These developments 
will help assist analysis, design and test engineers in 
maximizing the value of each vibration test. 

VIBRATION TEST APPLICATION: 
A large gamma truss structure was selected as the test 
case for the vibration test simulation environment*. 
Figure 11 shows a uicture of the actual truss hardware 

Figure 1 1. Gamma Truss 
that was used to demonstrate the hardware-in-the-loop 
simulation concept. It should be noted that due to the 
ongoing development of the vibration virtual 
environment, not all of the instrumentation models 
(namely the shakerhnplifier model) were included in 
this demonstration of the vibration simulation 

capability. Our goal at this point is simply to show the 
hardware-in-the-loop simulation process. 

The truss structure was designed with integrated 
sensors and actuators to provide a testbed for studying 
structural controls applications. Through numerous 
control studies, experimental data had been gathered in 
the form of input/output models for the truss. For use 
in the vibration test simulation, an eight inpuueight 
output experimental model was selected as the model 
that would represent the truss in the simulation. This 
state space model of the truss was combined with 
models of the sensors (accelerometers) and signal 
conditioning elements to form a single state space 
model of the vibration external load. This combined 
state space model was then downloaded onto the real- 
time control processor in order to support running the 
test simulation. An actual vibration test control and 
data acquisition system was then connected to the real- 
time processor for the simulation study. 

A single vibration drive signal was generated from an 
arbitrary shaped random spectrum (up to 200 Hz) and 
then used in the simulation to excite the external load 
model on the processor. The first output or response 
channel from the processor was feed back into the 
vibration control computer as the control channel. The 
drive signal was updated in order to match this shaped 
random spectrum for the chosen control channel. This 
drive signal was notching at 4 4  Hz due to a lightly 
damped mode at that frequency. Figure 12 shows the 
drive spectrum for this vibration simulation. By 
utilizing this vibration test simulation environment, the 
engineer is able to select desired control parameters 
such as control Degrees of Freedom, frequency 
resolution and time constants to successfully control a 
specified vibration test, Figure 13. This simulation 
example shows the strong advantage of having an 
environment to setup and customize vibration tests. 

im 

Figure 12. Vibration Drive Spectrum 

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Using this tool, test engineers can easily change 
parameters within the simulation to optimize vibration 
tests. 

CONCLUSIONS: 
An important goal in developing the KBT program is 
to provide an environment in which designers and 
analysts are given earlier access to test based 
information in order to make intelligent design 
decisions. There are a number of significant research 
activities ongoing that directly support this new testing 
vision. A test simulation and optimization software 
tool called VETO is one of these activities that helps 
position testing earlier in the design cycle. Using this 
simulation software and rapid prototype parts, 
characterization tests can be performed in order to 
generate test data needed to update and validate 
computational models. 

Within the VETO software environment, engineers are 
able to investigate the testing of aerospace 
components, using computational models, prior to the 
existence of any hardware. A goal in developing this 
software tool is to provide test and analysis 
organizations with a capability of mathematically 
simulating the complete test environment within a 
computer. Applications of this test simulation 
environment have been shown for both modal and 
vibration capabilities essential to the development of 
aerospace components. 

ACKNOWLEDGEMENT: 
This work was supported by the United States 
Department of Energy under Contract DE-AC04- 
94AL85000. 

REFERENCES: 
[ l ]  Klenke, S., Reese, G., Schoof, L. and Shierling, C., 
"Modal Test Optimization Using VETO (Virtual 
Environment for Test Optimization)", Sandia Report 
SAND95259 1, January 1996. 
[2] Gregory, D. and Hansche, B., "Rapid Prototype and 
Test", Sandia Report, 1996. 

[3] Jacobs, P., "Rapid Prototyping & Manufacturing 
Fundamentals of Stereolithography", McGraw, 1992. 
[4] Dalton, E., Chambers, B., Bishnoi, K., Bateman, 
V., and Baca, T., "Test Validation of MANTA: A Code 
for the Practical Simulation of Shock in Complex 
Structures", Proceedings of the 65th Shock and 
Vibration Symposium, Vol. 1, San Diego, CA, October 

[5] Zanner, F., and Maguire, M., "FASTCAST, A 
Program to Remove Uncertainty from Investment 
Casting", Modem Casting, 8/93. 

1994, pp. 66-75. 

[6] Baca, T., Bell, R., and Robbins, S., "Conservatism 
Implications of Shock Test Tailoring for Multiple 
Design Environments", Proceedings of the 58th Shock 
and Vibration Symposium, Vol. 1, October 1987, 

[7] James 111, G., "Development of Structural Health 
Monitoring Techniques Using Dynamic Testing", 
Sandia Report SAND96-0810, April 1996. 

[8] Lauffer, J., Allen, J., and Peterson, L., "Structural 
Dynamics Considerations for Structural Control", 
Proceedings of the 7th International Modal Analysis 
Conference, Vol 11, February 1989, pp. 1079-1086. 

pp.29-47. 

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