This document describes various analysis methods for modeling active and passive damping in structures using NX I-deas and NX Nastran software. It discusses modeling constrained layer damping, piezoelectric fibers, and viscoelastic damping materials to increase structural damping. Examples are provided of applying these methods to design damping treatments for a spacecraft and liquid rocket engine. The key methods allow identifying important vibration modes, estimating modal damping contributions of candidate materials, and predicting changes to modal damping and forced response with added damping treatments.

1. See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/220677947
Analysis methods to support design for damping
Article in Engineering with Computers · March 2007
DOI: 10.1007/s00366-006-0022-1 · Source: DBLP
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2. ORIGINAL ARTICLE
Mary Baker
Analysis methods to support design for damping
Received: 9 December 2005 / Accepted: 29 March 2006
Ó Springer-Verlag London Limited 2006
Abstract Methods are documented for active and passive
damping studies with capabilities within NX I-deas and
NX Nastran (http://www.ugs.com/products/nx/). The
focus is on the methods that can be applied to a wide
variety of products and design goals. Project examples
are used to illustrate the methods and indicate the level
of success obtained from real applications. Specific
examples include passive damping for a liquid rocket
engine, actuators for spacecraft interface that can sup-
press spacecraft response to launch vehicle vibration,
active ceramic-fiber vibration suppression, constrained
and free layer damping as well as the use of a secondary
mode to increase effective damping or improve settling
time of a manipulator arm.
Keywords Design for damping Æ Spacecraft vibration
suppression Æ Finite element modeling Æ NX Nastran Æ
I-deas response analysis
1 Introduction and background
The goal for designing structures that meet some
damping target is to maintain the dynamic response of a
structure in a known environment to specified or toler-
able limits. When the design driving loads are sine dwell
and acoustic, damping becomes a critical issue. The
structure must be able to dissipate some of the energy to
which it is exposed to avoid large dynamic amplification.
This could mean including materials that have signifi-
cant loss factors or adding discrete energy absorbing
elements such as shock absorbers. The process of
designing energy dissipation into a structure generally
involves the following steps: identify the modes that
dominate the response to be controlled; determine the
strain energy distribution in the basic structural concept
and the important modes; determine potential strain
energy in the candidate active or passive energy
absorption treatment; add elements to model the
damping material or treatment and predict the damping
by mode and possibly the effect on the forced response.
This approach is based on the understanding [1, 2] that
the contribution of each materials or region of material
to the loss factor for a structure is proportional to the
strain energy in the structure carried by that material
region.
For example, in Fig. 1, the results of a forced re-
sponse analysis of a satellite antenna system (a simplified
system has been used for paper figures to protect pro-
prietary information) shows the peak strain energy dis-
tribution due to launch loads. The strain energy is
concentrated in the connection of the booster to the
satellite electronics as highlighted in the figure.
The frequency response functions (FRF) for stress
and acceleration, shown in Fig. 2, were obtained by
applying a unit input force uniform for all frequencies to
show the structural characteristics. In particular this
FRF identifies the fifth mode, at 9.7 Hz, as the impor-
tant mode for the response of interest and the input
direction selected. The strain energy distribution in this
mode is shown in Fig. 3. Those peak strain energy areas
are candidate locations for added damping treatment to
control the response.
Table 1 provides another way to determine the
locations most effective for damping treatment applica-
tion. Regions of the structure are organized into groups;
I-deas outputs spreadsheet text files with the percent of
total strain energy defined by group in each mode. For
the fifth mode this table shows that the strain energy is
concentrated in the local attachment between the sa-
tellite and the booster.
From both approaches, it is clear that this is the
location where we should put damping materials to
control the response. In order to design the distribution
and type of damping, we need to quantify the modal
damping contribution of candidate damping treatments.
M. Baker
ATA Engineering Inc., San Diego, CA, USA
E-mail: mary.baker@ata-e.com
Tel.: +1-858-4802054
Fax: +1-858-7928932
Engineering with Computers (2006)
DOI 10.1007/s00366-006-0022-1

3. Energy loss in a dynamic system can be modeled as a
force term in the equation of motion. The damping force
is always out of phase with the displacement. This force
term can be a viscous term where the force is propor-
tional to velocity as shown in (1) for a single degree of
freedom system (or a mode of a system with any number
of degrees of freedom expressed as modes),
m€
x þ c_
x þ kx ¼ f ðtÞ ; ð1Þ
or it can be a stiffness term which is proportional to the
material loss factor (structural or hysteretic damping)
where the resisting force is proportional to displacement
as shown in (2)
m€
x þ ik g
|{z}
loss coeff:
x þ kx ¼ f ðtÞ ;
m€
x þ kðig þ 1Þ
|fflfflfflfflffl{zfflfflfflfflffl}
complex stiffness
x ¼ f ðtÞ :
ð2Þ
With the following definitions for f and xn,
f
c
2
ffiffiffiffiffiffi
km
p ;
xn
ffiffiffiffi
k
m
r
:
Fig. 2 Stress and acceleration response shows mode at 9.7 Hz is an
important mode excitation in a selected direction
Fig. 1 Strain energy distribution at time of peak response during
boost phase
Fig. 3 Strain energy distribution in important mode

4. Equation (1) becomes
€
x þ 21xn _
x þ x2
nx ¼ 0 :
In these equations, m is the mass, k is the stiffness, c is
the viscous damping coefficient, g is the material loss
factor, f is the critical damping ratio, x is the single
degree of freedom and f(t) is the forcing function.
Two types of loss modeled by these equations involve
different physics but have the same peak amplitude at
resonance when the following relationship holds:
g ¼ 2f :
Any finite element program assembles a mass matrix and
a stiffness matrix from the element definitions and the
material properties. If the material properties include the
material loss factor or discrete viscous damping elements
connecting nodal degrees of freedom, I-deas and NX
Nastran will also assemble a physical damping matrix,
[C]. The mass and stiffness matrices are used in an eigen-
solution to obtain the undamped natural frequencies
and mode shape vectors, [w]. Using the following triple
matrix product, an estimate of the modal damping is
provided by I-deas.
c
½
|fflfflfflfflffl{zfflfflfflfflffl}
Modaldamping
c
½ ¼ w
½ T
C
½
|{z}
physical
damping
matrix
w
½ : ð3Þ
Although the modal damping matrix, [c] is not in general
diagonal, the diagonal terms provide a modal damping
estimate that is listed and can be directly applied for
forced response. For light damping, which is mostly
material damping, the off-diagonal terms tend to be
small compared to the diagonal terms, indicating that
this estimate of mode by mode damping is reasonable.
I-deas (the internal solver called Model Solution) cal-
culates modal damping twice: once to calculate hyster-
etic damping (structural damping) and a second time to
calculate viscous damping (damper elements). The vis-
cous modal damping values are converted to modal
damping factors by dividing by the critical damping
value for each mode. (This capability is standard in
I-deas but currently requires DMAP implementation in
any version of Nastran including NX Nastran).
The off-diagonal terms are used only to provide
confidence factors for the diagonal damping values. A
confidence factor of 1.0 indicates that the sum of the off-
diagonal terms is zero. A confidence factor of 0.5 indi-
cates that the sum of the off-diagonal terms equals the
value of the diagonal element.
Thus once the locations of structure with high strain
energy in the forced response or the important modes
have been identified, the design can start to include loss
mechanisms at these locations. What is important is to
design the materials with high loss factors into the
structure such that they are forced to undergo significant
strain. These materials are never stiff compared to the
structural materials that carry most of the load. Thus the
design must include materials with loss in such a way
that stiff parts of the structure force deformation and
strain in the materials with high loss. Some candidate
treatments are discussed here along with modeling ap-
proaches.
One of the most effective damping treatments is to
constrain a high loss material between two stiff layers of
structural material such that the damping material must
deform significantly. The damping material is forced to
undergo shear deformation as it is forced to follow the
contours of the stiff layers on either side. Thus strain is
forced into the damping material which can be much less
stiff than the constraining material layers. This con-
strained layer damping can be modeled with the above
methods. As an example two strips of aluminum were
modeled with solid elements with a layer of damping
material [3M Visco-elastic Damping Polymer: loss factor
0.9, shear modulus 1 MPa, (145 psi)] between these
layers. Four layers of parabolic solid elements through
the thickness were used for each of the aluminum layers
and for the damping material layer. This model was
obtained by first building the elements with the thickness
much greater and then using the I-deas automatic
updating to shrink the thicknesses to the correct values.
Although the damping layer elements do not have a
good aspect ratio, a successively finer mesh was tried
until confidence in the adequacy of the aspect ratio was
achieved.
Table 1 Strain energy per mode by structural group
Mode/load number 1 2 3 4 5 6 7 8 9 10
Frequency (Hz) 1.5 1.5 6 6.1 9.7 14 16.3 17.2 23.7 26.3
Model region by group
Reflector base 0.16 0.16 2.9 2.79 0.03 7.72 0.2 0.08 0.2 17.3
Reflector dish 0.41 0.42 8.27 8.55 0.11 0.99 88.9 94.2 0.79 58.1
Springs 4.79 4.79 4.71 4.7 9.47 87.4 – – 8.87 5.31
Booster 0.51 0.51 0.28 0.28 0.25 2.61 – – 0.04 0.23
Satellite body 39.4 39.4 34.5 34.4 55.5 0.57 – – 55.7 7.49
Sat booster attach 47.5 47.5 7.08 7.05 30.2 0.42 – – 4.66 0.09
Sat antenna attach 7.21 7.19 41.4 41.4 4.44 0.25 – – 29.6 5.56
Reflector beams 0.04 0.04 0.86 0.86 0.02 – 10.9 5.68 0.13 5.94
Total percent energy 100 100 100 100 100 100 100 100 100 100

5. The first three bending modes are shown in Fig. 4
along with the structural damping ratio predicted for
each. Experiments with these strips indicated that the
bending modes die out in just a few cycles which are
consistent with these damping estimates.
In the next section these methods will be illustrated
using application examples from projects.
2 Damping treatment examples
ATA Engineering has performed a number of projects in
which increased damping was the design goal. NX I-deas
and NX Nastran provided strong capabilities for these
studies. The following project design goals are described.
1. Application of constrained layer damping and semi-
active ceramic fibers to spacecraft motion and
pointing accuracy.
2. Application of damping treatment to the exterior (not
constrained layer) of a spacecraft after the design was
complete with the intension of having the material
weight burned off in flight.
3. Use of a secondary mode to reduce settling time due
to a step or shock excitation.
2.1 Controlling spacecraft pointing accuracy
For the satellite system shown in Fig. 1, the FRF for the
rotation of the antenna, shown in Fig. 5, indicates that
the important modes for this response is mode 5.
For this FRF, baseline damping by mode was ob-
tained by using structural damping of 2% (1% equiva-
lent viscous) for the aluminum and antenna composite
material and the springs connecting the three major
components; thus the modal damping for this baseline
was 2% structural in each mode.
The strain energy table (Table 1) and plot (Fig. 1)
show that damping would be effective in the satellite
body as well as the connectors in the shell elements and
the springs on the satellite at the interface with the
booster and antenna. The maximum-principal-stress
plot, Fig. 6, for the satellite body at the booster end of
the satellite suggests load paths for this structural region
in this mode.
Piezoelectric fibers were considered for this region.
When these fibers are stretched, they generate electrical
energy which can be stored in capacitors and then used
to cause the fibers to create a restoring force. A micro-
processor can be used to cause a time delay which rep-
resents a shift in phase. This phase shift will be different
for each mode. In this case, we have identified a single
important mode which makes it feasible to use this ap-
proach. This effect creates a force much like the struc-
tural damping force in (2) above. This type of
piezoelectric fiber composite has been used successfully
in skis and tennis rackets [3]. It may also be possible to
use these fibers as passive dampers [4]. When used pas-
sively the electrical energy generated by the fibers is
dissipated through resistors and not used for active
control.
For the design process, these treatment fibers were
included in the finite element model. The fibers were
modeled as beams using cross-sectional and material
properties from one supplier of these fibers [3]. Figure 7
shows the fibers on the satellite surface next to the
booster.
The fibers were given a structural damping factor of
0.5 to represent the best possible efficiency. The resultant
modal damping for the first ten modes is provided in
Table 2, which shows we have more than doubled the
effective structural damping in the important mode 5
from 2 to 5.9%.
As an alternative approach the top and bottom of the
satellite were replaced with aluminum of approximately
the same thickness but with a constrained layer of visco-
elastic damping polymer. As a first estimate of this
Fig. 4 Constrained layer
damping modeled in I-deas

6. effect, the sample problem shown above was used to
estimate the material damping. Taking the conservative
value of damping found in the first bending mode of 0.16
loss factor (16%), the shells on the top and bottom of
the satellite used a material with this structure damping
loss factor. Table 2 shows that this results in much
higher modal damping in the first five modes with 11.6%
in the fifth mode.
Another approach is to use viscous dampers (shock
absorber) with 30% critical viscous damping in the
spring elements that are used to connect the compo-
nents. These results are also shown in Table 2. The
equivalent viscous damping percentage is twice as
effective as structural damping at resonance. The dis-
crete shock absorber approach is also more effective for
mode 5.
Thus three design approaches for controlling the first
five modes have been demonstrated. Selection of the
solution of choice might come from using these ap-
proaches in a forced response for transient, random, or
sinusoidal excitation. The damping values for all modes
computed in this way are automatically provided to the
forced response module in I-deas; here, that module was
used to predict the transient, random and sinusoidal
response of angular displacement at the base of the an-
tenna before and after damping treatment. Figure 8
shows the FRF comparisons which should be the right
relative response for sinusoidal loads.
Figure 9 compares the responses for a launch tran-
sient for three types of damping and the baseline. Con-
strained layer damping treatment provides the best
settling time of this response, but the ceramic fiber ap-
proach shows the lowest peak value. The input transient
is shown in Fig. 10.
For vertical random vibration applied at the booster,
the power spectral density (PSD) response at the base of
the antenna was computed for each type of damping
treatment; responses are shown in Fig. 11. For com-
parison, the PSD vibration input is shown as a dotted
line in this figure. The plot has been zoomed to the range
2–50 Hz where the response is the greatest. For this
environment, the most dramatic decrease in RMS value
is provided by the constrained layer.
In the responses computed above we focused pri-
marily on modes 1 through 6. Modes 7, 8 and 10 are
primarily antenna modes. In order to reduce vibration
response here, a treatment that could be applied to the
composite material is needed. The following discussion
about free layer damping may be of interest for these
modes and this part of the structure.
2.2 Free layer damping
Free layer damping is sometimes attractive because it
can be added after the structure is already built without
greatly affecting the design and can be more easily re-
moved. The disadvantage of free layer damping is that it
is hard to get a significant amount of strain energy into
the damping materials. Most materials with a high loss
factor, such as visco-elastic materials, have low stiffness
relative to the structural materials. For constrained layer
damping, the visco-elastic material is forced to undergo
large shear deformation by the constraining layers of
structural material. For free layer damping, the defor-
mation comes from bending or stretching of the outer
fibers of structural material on which the material is
fastened. Thus free layer damping depends on the
damping layer having a stiffness that is not trivial in
comparison to the base material in order to undergo
enough strain to contribute the desired loss factors.
Because of the challenge of getting strain energy into the
damping material, the analytical prediction of the
effective damping becomes even more important. This is
so to ensure that the structural concept has a reasonable
Fig. 5 Frequency response functions (FRF) for rotation of
antenna due to vibration at the base of the spacecraft
Fig. 6 Location of maximum principal stress at location control-
ling mode 5

7. chance of achieving the desired damping before the de-
sign is taken too far or too much detailed modeling is
done.
For free layer damping, just as for constrained layer,
finite element approaches can be used. For example,
Fig. 12 shows a carbon–carbon cone, which is similar to
a segment of a nozzle of a launch vehicle design project
completed by ATA [5, 6]. At one stage in this launch
vehicle project, the nozzle was believed to be over-
stressed due to sinusoidal and acoustic loading envi-
ronments and the very light damping of the baseline
carbon–carbon material. The model shown is not the
real structure but has similar structural characteristics.
Two layers of solid parabolic orthotropic elements are
used for the base material; for the damping material, two
Table 2 Effective structural and
viscous damping by mode for
ceramic fibers, constrained layer
and connector shock absorbers
Mode Frequency Ceramic fibers %
(structural)
Constrained layer %
(structural)
Connector shock
absorbers %
Structural Viscous
1 1.5 7.20 13.9 2.00 0.00
2 1.5 7.20 13.9 2.00 0.00
3 6.0 3.20 12.6 2.00 0.20
4 6.1 3.20 12.6 2.00 0.20
5 9.7 5.90 11.6 2.00 2.70
6 14.0 2.00 2.01 2.00 3.80
7 16.3 2.00 2.00 2.00 0.00
8 17.2 2.00 2.00 2.00 0.00
9 23.7 2.90 11.5 2.00 6.70
10 26.3 2.00 3.03 2.00 3.80
Fig. 8 FRF response provides comparison of three types of
damping treatment to baseline
Fig. 10 Input acceleration at the base used to obtain forced
angular displacements in Fig. 9
Fig. 7 Ceramic fibers shown as strips on the base of the satellite
near the booster attachment
Fig. 9 Transient response to launch loads compares three types of
damping treatment to the baseline

8. layers through the thickness of the free layer damping
material are used. This damping material was selected
such that it would burn off in flight when the nozzle
segment becomes hot and when the weight of the nozzle
was critical.
Figure 13 shows the loss factors as percent hysteretic
damping due to the damping material as a function of
frequency for each mode. The base material was given
zero damping such that the effect of the damping
treatment could be identified. An equivalent viscous
damping between 0.2 and 0.5% was later shown to be
appropriate for the base material. Thus the added
damping due to the damping treatment of 0.5–1.2%
represented a doubling of the damping although it was
still relatively lightly damped.
Modeling the damping layer explicitly with solid
elements can lead to large models that may be imprac-
tical for design studies. Modeling damping using shell
models is very difficult to accomplish because of the need
to have a layer of structural material next to a layer of
damping material with shear transfer across the inter-
face. Very detailed offset shell models are more time
consuming and of questionable accuracy compared to
the solid element approach described here. Thus a solid
model with today’s computing power is perhaps the best
way to perform detailed modeling. However, one alter-
native approach is to determine from a breakout model
such as the cone, the damping that can be expected from
the detailed multiple layer solids model and then use this
loss factor in the simpler representation of the structural
component in a global spacecraft model.
For example, in the actual project the nozzle was
represented by a single layer of shells representing the
carbon–carbon. Two damping layers of shells were ad-
ded, one with the correct loss factor for membrane and
one for the correct loss factor for bending. In consid-
ering how to simulate the effect of damping treatment in
these shells, it is important to recognize that the effect of
the damping layer changes as the deformation in the
shells varies between mainly bending to mainly mem-
brane behavior. There is no single-shell material loss
factor that can correctly represent the modal damping in
a single layer of shells as the shells undergo different
types of deformation.
The dependency of loss factor on deformed shapes
can be better understood and accounted for by looking
at the loss factors predicted by classical solutions which
show differences for membrane and bending behavior.
In particular, the loss factor in bending, gb, can be
determined by the following expression:
gb ¼ gD
n
1 þ sn
3 þ 6n þ 4n2
þ 2sn3
þ s2
n4
1 þ 2snð2 þ 3n þ 2sn2Þ þ s2n4
; ð4Þ
from Overst and Frankenfeld [7, 8], where
h plate thickness
hD damping layer thickness
n hD/h; non-dimensional thickness
E elastic modulus of the base material
ED real part of the complex modulus of
the damping material
s ED/E; non-dimensional stiffness
gD damping material loss factor
ED(1+igD) complex modulus
For membrane waves, Cremer and Heckle [7, 9] derived
the following expression for loss factor, gm,
gm ¼ gD
sn
1 þ sn
ð5Þ
and warned that it is much harder to damp longitudinal
waves than bending waves. Note that loss factors from
these formulas are not explicit functions of frequency.
The damping can depend on frequency if the loss factor,
gD, or the modulus, ED, for the damping layer varies
with frequency. There almost surely is some dependence
on frequency and temperature for these damping mate-
Fig. 12 Carbon–carbon cone with free layer damping modeled by
two solid elements through the thickness of both the base cone and
damping layer
Fig. 11 Power spectral density (PSD) response compares three
types of damping treatment to baseline with input shown as dotted
line

9. rial properties; as a result, selecting the damping mate-
rial and performing the analysis may require some
knowledge of the important frequency and certainly the
expected temperatures.
To illustrate the difference in damping achievable for
bending versus membrane deformation, Fig. 14 depicts
the expressions (3) and (4) for loss factor plotted for a
range of ratios, s, for elastic moduli and ratios, n, for
thickness of damping layer to thickness of base material
layer. Note how much lower the effective damping is in
membrane deformation.
The modeling approach using layers of solids for the
damping and base materials should correctly show this
behavior which represents how the damping layer
properties ED, gD, combine with the base materials for
different deformations to achieve the effective damping
in each type of deformation. Every mode is some com-
bination of bending (out-of-plane) and membrane (in-
plane) behavior.
Figure 15 shows results for a detailed solids model of
a flat plate made of the same materials that were used in
the conical nozzle and the same thicknesses for damping
and base material and the same frequency range. For the
flat plate, nearly all the modes are mostly bending as
opposed to a mix of bending and membrane deforma-
tion that is expected from the conical shell. Note the
higher damping is predicted for the flat plate.
It is possible to model the nozzle with a single layer of
shells and include different material properties for
bending and membrane deformation. However, for the
prediction of modal damping using the mode shapes,
both NX Nastran and I-deas use the membrane material
loss factor to scale the total element stiffness matrix,
after the bending and membrane stiffnesses have already
been combined, no matter what loss factor is entered for
bending. Because the membrane damping is normally
less, and the lightly damped modes tend to be more
important to the response, it may be appropriate to just
use the membrane material loss factors to estimate the
damping to be expected from free layer damping. An
alternative approach is to use a double layer of shells,
one each for membrane stiffness and loss factor only,
and for bending stiffness and loss factor only.
It is important not to over estimate the damping
achievable from free layer damping in the real structure
by predicting or measuring the damping for a flat plate
with free layer damping treatment. The real structure’s
behavior may exhibit much more membrane behavior
than a small sample of the material with a free layer of
damping. In the actual project involving a launch vehicle
nozzle, the first assessment of damping was done on
small samples that were modal tested. These samples
where excited into bending mode for which the modal
damping was determined before and after adding free
layer damping. In this particular case, damping evalua-
tion was about 5%. It was later learned from modal
Fig. 13 Predicted hysteretic
damping by mode for cone
varies from 0.5 to 1.2%
Fig. 14 Achievable loss factor for structure plotted versus ratio of
their elastic modulus for several different thickness ratios shows
that free layer damping is much more effective for bending than for
membrane deformation

10. testing on the actual nozzle that damping of 0.2–0.5%
was more typical for the important modes.
2.3 Damping for position accuracy
In the previous projects the structure being designed
was subjected to a stationary or periodic vibration or
acoustic environment. If the loading is transient, such
as a shock pulse or a step positioning command,
damping cannot effectively change the peak response,
but it can greatly reduce the time necessary for the
free vibration response to settle to an acceptable po-
sition error. Figure 16 shows the end of a beam-like
structure that is positioned by a step command. The
accuracy of the positioning is diminished by the mode
of the beam ringing. With added damping this ringing
will die out more quickly and achieve the desired
accuracy.
Damping of the structure’s modes proved challeng-
ing: It was difficult to obtain enough damping with free
layer or constrained layer damping. However, by adding
another spring-mass system within the primary struc-
ture, the settling time and thus effective accuracy was
improved. The added spring-mass system provided an
additional modal degree of freedom. This mode brought
improved performance in two ways: the internal mass
tended to move out-of-phase with the primary structural
motion and directly acted to suppress the primary
vibration just as a tuned mass damper does. In this case
the mode of the internal motion did not need to be ex-
actly tuned to the fundamental beam motion, since both
were excited by the step input. The secondary opportu-
Fig. 15 Hysteretic damping
predicted for flat plate varies
from 0.9 to 1.2% with the
typical value closer to 1.2%
Fig. 16 End of a beam-like structure which required very accurate
placement when provided a step position command
Fig. 17 Baseline beam end deflection at a given wait time is greatly
reduced by adding both a mass damper and constrained layer
damping to the beam

11. nity for damping was a discrete damping mechanism in
the internal spring to further dissipate energy.
This system was modeled in I-deas by adding an
additional beam-mass system with springs to maintain
the position of the secondary mass within the primary
structure. The discrete damper within the beam could
also be included in the simulation, along with the
effective material damping from the constrained layer
damping to obtain an overall effective modal damping.
Figure 17 shows the improved settling time when the
incremental spring mass system was added to the already
damped primary structure.
3 Conclusions and recommendations
Analytical methods have been illustrated that support
the design of damping treatment on various structures
such as spacecraft and launch vehicles. These methods
can guide the selection of damping approaches, the
location of damping treatment and the selection of
damping material. The key is the prediction of strain
energy, important modes and the estimate of damping
on a mode-by-mode basis. Simulation methods in-
cluded constrained and free layer damping, active
ceramic fibers and the use of secondary modes. The
difference in bending and membrane behavior defor-
mation of the damping structures was found to be
important for the accurate extrapolation of damping
measured on samples to damping that can be achieved
in an actual structure.
References
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products/nx/
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