Research Article
Design and experiment of a passive
damping device for the multi-panel
solar array
Advances in Mechanical Engineering
2017, Vol. 9(2) 1–10
Ó The Author(s) 2017
DOI: 10.1177/1687814016687965
journals.sagepub.com/home/ade
Yongfang Kong and Hai Huang
Abstract
With the space technology development, large flexible space deployable structures have been used widely. Studying on
the vibration control for large flexible space deployable structures becomes very important. In this study, a novel passive
vibration damping device is developed for the multi-panel sun-orientated deployable solar array. Its upper strut contains
a viscous damper while the lower strut is rigid. The device is lockable and located near the solar array root hinge to
increase the structural damping without reducing the fundamental frequency. This design will not influence the original
functions of the solar array, such as folding, deploying, and sun tracking. The corresponding finite element models are
established, and the properties of the damping device are investigated by modal analysis and transient response analysis.
The damping mechanism design for a certain type of solar array is presented. The associated modal tests based on a
solar array test sample verify the effectiveness of the device. Conclusions are drawn to help define design guidance for
future damping device implementations.
Keywords
Deployable solar arrays, vibration control, viscous damper, finite element analysis, mechanical design, modal test
Date received: 8 July 2016; accepted: 13 December 2016
Academic Editor: Fakher Chaari
Introduction
With the space technology development, large flexible
space deployable structures, such as large-scale solar
arrays, antennas, and space manipulators, have been
used widely. These components have structural features
like large scales, high flexibility, low stiffness, and low
damping. Therefore, large vibration is easily induced
when the flexible components are disturbed, which may
seriously affect the system performances. However, many
on-orbit interference factors are inevitable, such as the
disturbance generated by the spacecraft attitude adjustment, orbit transfer, space debris impact, and thermal
shock. In order to improve the life of large flexible space
deployable structures and the system’s running accuracy,
the structural vibration must be effectively controlled.
On vibration control for large flexible space deployable structures, various ways have been explored.
These ways can be divided into two different categories,
passive and active. One passive method is to transfer
the host structural vibration energy. An adaptive passive damping system using tuned mass dampers
(TMDs) was developed for the low-order modes of
spacecraft large solar arrays.1 Another common passive
method is to increase the structural damping. For
example, a damper consisting of a titanium flexure and
viscoelastic damping material was designed for the rigid
Hubble Space Telescope (HST) solar array, SA-3. It
was mounted in the base of the mast to achieve the
School of Astronautics, Beihang University, Beijing, P.R. China
Corresponding author:
Hai Huang, School of Astronautics, Beihang University, 37 Xueyuan Road,
Haidian District, Beijing 100191, P.R. China.
Email: hhuang@buaa.edu.cn
Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 3.0 License
(http://www.creativecommons.org/licenses/by/3.0/) which permits any use, reproduction and distribution of the work without
further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/
open-access-at-sage).
2
improvement in the overall structural damping level
and suppress structural vibration induced by the control system.2 A mast damping system was developed
for the Shuttle Radar Topography Mission’s 60-m-long
deployable mast which served to deploy an outboard
antenna.3 The mast damping elements were located at
the canister attachment truss aft bipod and the vertical
strut to control the mast’s first two orthogonal bending
modes and first torsional mode, respectively.4 The
other passive way is to improve the structural stiffness.
This is normally implemented by a new design, such as
a novel design of the composite structural lattice frame
for the spacecraft solar arrays,5 and a tape spring hinge
designed by an optimization method for the deployment of solar arrays.6 For active vibration control, considerable modes have also been studied, like positive
position feedback,7 autonomous decentralized intelligent control,8 and proportional-derivative (PD) control.9 Actually, active vibration control methods can
achieve excellent results. However, all of these active
methods require additional energy devices and have
difficulties in the controller design. The methods for
improving part of the structure have higher requirements on the design with only limit increase in the stiffness. On the contrary, increasing the structural
damping with passive methods, especially only attaching a damping system to the host structure, is easier to
implement. Additionally, it has the advantages of high
reliability and good economic benefits. Moreover, A
Rittweger et al.10 researched four different damping
principles for the corresponding damper device predesign. These principles were based on the following
physical effects: hydrodynamic concept, hydraulic concept, coulomb friction, and viscoelastic bushings. For
good accuracy and high stability, dampers designed
according to the first concept, especially viscous dampers, are adopted most in engineering projects. Thus,
passive damping method based on the viscous damper
is advisable for space structural vibration control.
Today, the multi-panel sun-orientated deployable
solar array is commonly utilized to provide spacecraft
power generation. Most deployable solar arrays employ
rigid honeycomb panels. In order to satisfy the requirements of spacecraft such as cost, mass, and power
growth capability, honeycomb panels become larger
and are even replaced by tensioned flexible blanket systems for some missions.11 Large solar arrays probably
easily bring low-frequency and longtime bending modal
responses, threatening the safety of the spacecraft structures. Hence, vibration damping for large solar arrays
is necessary. The HST vibration suppression is a successful example of passive control applications.2
However, its damper was in a series damping mode and
had a trade-off between the damper stiffness and damping performance. The final damper made the SA-3
Advances in Mechanical Engineering
fundamental bending frequency decreased, which had a
negative impact on the HST jitter performance.
In this study, a novel passive vibration damping
device is developed for the multi-panel sun-orientated
deployable solar array. Its upper strut contains a viscous damper while the lower strut is rigid. This device
has the following features. First, this is a fluid viscous
damper with no stiffness. Second, the oblique strut
damper is attached to the solar array root hinge in a
parallel damping mode, increasing the structural damping without reducing the fundamental frequency. Third,
the damping device can be folded at launch, deployed
along with the solar array deployment and then be
locked. Furthermore, the device will not influence the
sun-orientated function.
The rest of the article is organized as follows: in section ‘‘Solar array damping device,’’ the proposed
damping device is introduced. In section ‘‘Finite element modeling and analysis,’’ the corresponding finite
element models are established and the properties of
the damping device are investigated. Section ‘‘Damping
mechanism design’’ provides the damping mechanism
design. Experimental results are presented in section
‘‘Experiments.’’ And the last section draws the
conclusions.
Solar array damping device
The multi-panel solar array on-orbit works in the
deployed state, which belongs to the typical cantilever
beam pattern. Generally, its first mode is the bending
vibration mode and the corresponding frequency is
much lower than other vibration modes, so the bending
vibration is most likely to be aroused. Adding an oblique member near the solar array root hinge to improve
the structural stiffness or damping was considered as
the vibration suppression method. Early in the project
design phase, the corresponding finite element models
were created. The models were employed to analyze the
control effect of different methods. Simulation results
indicated that the improvement in structural stiffness
and vibration suppression was poor by only adding a
rigid rod to the root. Practically, most modal strain of
the deployed solar array’s first vibration mode is concentrated at the root. Therefore, attaching damping element to the root can well damp the structure.
Moreover, the linear viscous damping approach was
selected based on good accuracy, high stability, simple
design concept, and amenability to existing analysis
tools.4 Considering the viscous damper has no stiffness,
a parallel damping concept was employed to develop
the solar array damping device. The purpose of such
damping device design is to increase the structural
damping without reducing the fundamental frequency.
As mentioned before, for the general multi-panel solar
Kong and Huang
3
(a)
C
(b)
Lockable
A
hinge
A
D
C
B
D
B
Figure 2. (a) Stowed state and (b) developed state.
1
x ðt Þ
d = ln
,
n
xðt + nTd Þ
Figure 1. Schematic of the solar array damping device.
array, the out-of-plane bending vibration is its main
vibration mode. Consequently, we developed a damping device to especially achieve a substantial increase
for the modal damping ratio in the first bending mode.
Figure 1 presents a schematic of the proposed solar
array damping device. The upper strut (1) is a viscous
damper while the lower strut (2) is a rigid rod. They are
connected by a hinge which can be locked after deployment to improve the reliability of the mechanism. A
beam (3) attached to the yoke is used to connect with
the rigid rod. The viscous damper is supported by a
vertical beam (4) added between the solar array drive
assembly (SADA) and the root hinge flange.
With the lockable hinge, the upper and the lower
strut can be folded at launch (see Figure 2(a)) and combined into one strut after deployment (see Figure 2(b)).
The device is installed between the root hinge flange
and the yoke, which will not affect the sun-orientated
rotation. Thus, this design will not influence the original system functions.
To assess the damping performance in vibration suppression for the deployed solar array and optimize its
design, the analytical models are needed. The passive
damping performance is usually evaluated by the system equivalent modal damping ratios. For an underdamped linear system, one of its modal damping ratios
can be drawn by analyzing the free vibration response
in that modal frequency.
The free vibration displacement response of the system under a single mode can be expressed as
xðtÞ = Aejvn t sinðvd t + u0 Þ
ð1Þ
where A and u0 are parameters defined by the initial
conditions, j is the modal damping ratio, vn is the
undamped
natural
frequency of the system, and
pffiffiffiffiffiffiffiffiffiffiffiffi
ffi
vd = 1 j2 vn is the damped natural frequency.
For j 1, the equivalent modal damping ratio can
be analyzed by the free decay method
j’
d
2p
ð2Þ
where d is the logarithmic decrement and n is the number of selected amplitude interval period.
Therefore, transient response analysis and modal test,
which can obtain free vibration response, are utilized to
analyze the equivalent modal damping ratios in the finite
element models and the testing system, respectively.
Finite element modeling and analysis
Modeling and analysis for the deployed original solar
array and the solar array with damping device have been
performed using MSC/PATRAN. The solar array studied here contains a yoke, three solar panels, a root hinge,
and three pairs of hinges between the plates. In modeling, the plate is located in the XY plane of the global
coordinate frame, and the long side is along the X axis.
The beam element has been employed to model the
yoke, while the laminate shell element has been applied
to model the solar panel. And the bush element has been
employed to model the hinge, while the linear viscous
damper element has been used to model the damping
device. The damping law is F = CV, where F is the
damping force, C is the damping coefficient, and V is
the relative velocity between the ends of the damper.
The solar panel is honeycomb sandwich structure
with length 3 width 3 thickness of 2258 mm 3
1826 mm 3 30 mm for every piece. Both the upper and
the lower panel have three layers with thickness of
0.3 mm. They are made of M40 carbon fiber/epoxy
composite.
The core is regular hexagon aluminum honeycomb,
with wall thickness of t = 0.04 mm and side length of
l = 4 mm. It can be equivalent to orthotropic continuous structure as the following formulas12
4 t 3
2 t
E11 = E22 = pffiffiffi
Es , E33 = pffiffiffi Es ,
3 l
3l
pffiffiffi 3
3g t
G12 =
Es
2 l
pffiffiffi
ð3Þ
3g t
g t
Gs ,
G31 = pffiffiffi Gs , G23 =
2 l
3l
8 t
r = pffiffiffi rs , m12 = ms
3 3l
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Advances in Mechanical Engineering
Table 1. The performance parameters of honeycomb core
equivalent material.
Parameters
Value
E11 (MPa)
E22 (MPa)
E33 (MPa)
G12 (MPa)
G23 (MPa)
G31 (MPa)
r (kg/m3)
m
0.165584
0.165584
827.9
0.031047
77.94
116.9
42.158
0.33
Figure 3. The finite element model of the deployed original
solar array.
Table 2. The equivalent six-direction stiffness of hinges.
Directions
Root hinge
Hinge between the plates
X (N/m)
Y (N/m)
Z (N/m)
RX (N/m/rad)
RY (N/m/rad)
RZ (N/m/rad)
3,240,000
266,000
357,000
1680
5558
58,600
7,428,000
993,600
517,200
1104
792
54,840
where g is generally chosen between 0.4 and 0.6 in
practice. Here, it is chosen to be 0.5. Es, Gs, rs, and ms
are Young’s modulus, shear modulus, density, and
Poisson ratio for the core wall material, respectively.
These parameters are assigned as Es = 71.7 GPa,
Gs = 26.95 GPa, rs = 2740 kg/m3, and ms = 0.33. After
calculating, the honeycomb core equivalent material
parameters needed to define three-dimensional orthotropic material in MSC/PATRAN, are shown in
Table 1.
Every hinge is modeled as bush element with length
of 80 mm. Their equivalent six-direction stiffness is
listed in Table 2.
Figure 3 illustrates the finite element model of the
deployed original solar array. Based on it, a linear viscous damper element and a steel solid beam element
are attached to the solar array root hinge, as shown in
Figure 4. They are used to model the parallel damping
device.
Figure 4. The finite element model of the solar array with
damping device.
Table 3. First four order frequencies of the original solar
arrays (Hz).
Order
Frequency
1
2
3
4
0.17278
0.59229
1.0897
2.5252
For the solar array with damper, all degrees of freedom of its left end points are also fixed to make modal
analysis. No matter what value the damping coefficient
of the damper is, its frequencies are nearly unchanged.
The first order frequency remains to be
f1 = 0.17278 Hz. This verifies that the passive parallel
damping method does not reduce the fundamental
frequency.
Transient response analysis
Modal analysis
The original solar array modal analysis is carried out in
cantilever state with all degrees of freedom of the root
hinge end points fixed. Its first four order frequencies
are listed in Table 3.
The first four modal shapes of the original solar
array are presented in Figure 5. The results indicate
that the first mode of the general multi-panel solar
array is out-of-plane bending mode.
According to the modal analysis results, a vertical sinusoidal excitation whose frequency is close to the first
order modal frequency is exerted at the middle point of
the model free end for 5 s. The force is given by
f ðtÞ = sinð0:4ptÞ
ð4Þ
The direct method is used to do transient response
analysis. The original overall structural damping ratio
is set to 0.5% based on empirical knowledge. Many
Kong and Huang
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Figure 5. Modal shapes of the original solar array: (a) first, (b) second, (c) third, and (d) fourth.
Figure 6. The displacement response curves of the solar array
with damper.
Figure 7. Result with the model structural damping ratio of 1%.
researches also assume a damping ratio value around
0.5% of critical in the baseline model, such as HST
solar array damper research.2 For the solar array with
damping device, the displacement response curves of
the same point under different damping coefficients are
shown in Figure 6. At the first 5 s, the response is
forced vibration response. After that, the result
becomes free vibration response. It can be seen that the
amplitude decay rates are not the same. At first, the
decay rate is accelerated with the increase in the damping coefficient. When the damping coefficient increases
to a certain value, the decay rate reaches the fastest.
Then, as the damping coefficient becomes larger again,
the decay rate will slow down. Thus, there is an optimum damping coefficient. As shown in Figure 6, the
amplitude attenuates the most quickly at the coefficient
of 3e5 N s/m. After analysis, the optimum damping
coefficient of the damper element in such size for this
solar array is about 3e5 N s/m.
According to equation (2), the solar array modal
damping ratio in the first bending vibration mode is
calculated to be about 2.1% with damper of the optimum damping coefficient. In this situation, more than
four times the original is achieved, which is a substantial increase.
Dynamic response analysis for structural damping
variation
In order to further understand the effect of the original
overall structural damping ratio on this passive vibration control, the original damping ratio value is changed in the transient response analysis. Other parameter
values and the motivate settings still remain the same
as the above. The damping coefficient is selected to be
3e5 N s/m. Figure 7 shows the transient response result
with the model structural damping ratio of 1%. It can
be calculated that the modal damping ratio in the first
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Advances in Mechanical Engineering
Figure 9. The finite element model of the certain type of solar
array with damper.
Figure 8. The final configuration design of the solar array
damping mechanism.
bending vibration mode is equivalent to 2.5%, in this
case, 2.5 times the original. Combined with the result
above, it is clear that when the original structural
damping ratio is relatively small, after attaching the
parallel damping, the damping ratio is improved more
markedly compared to the bigger one.
Note that when the solar array is deploying, the
angular velocity of the yoke becomes faster and faster,
and until about fully deployed it comes up to 30 deg/s,
which means that the damper may be pulled at a velocity of 0.1 m/s. However, the damper velocity at work
is on the order of 1e–4 m/s, which is quite low. At low
speed, the equivalent linear damping coefficient should
meet the value of 3e5 N s/m to achieve an excellent
vibration damping effect. If the coefficient keeps the
same, then the damping force at high speed will be too
large to damage the structure. Hence, the damper was
designed as nonlinear. The damping law is as follows13
F = CV N
Damping mechanism design
This parallel damping passive control design is applied
to a certain type of satellite solar array.
In order to minimize the changes in the original
solar array yoke and root hinge, simultaneously considering the requirement of eliminating interference
between the rods, the final configuration design is
shown in Figure 8.
The anticipated stowed state is that the lower strut
can be folded within the yoke. During the deployment,
the viscous damper should be pulled out a few millimeters to ensure the solar array hinges can be locked.
However, this distance does not require too long. Here,
it was set to about 5 mm.
Viscous damper design
According to the above requirements and the dimensional characteristics of the actual deployable solar
array, the mechanism dimensions were determined.
The viscous damper dimensions were also identified.
Figure 9 illustrates the corresponding finite element
model of this deployed solar array with damper established in MSC/PATRAN.
The optimum damping coefficient of the additional
damper element under this size was analyzed to be
about 3e5 N s/m. When the original overall structural
damping ratio is 0.5%, after attaching such damper,
the modal damping ratio in the first bending vibration
mode is equivalent to about 5%, 10 times the original.
ð5Þ
where N is an exponent. It is determined by the damper
internal structure and usually designed to range from
0.3 to 1 for structural dampers.
The double-rod viscous damper was selected. And its
cylinder was filled with silicone fluid. The dimensions
of the final produced damper are shown in Figure 10.
Viscous damper performance test was conducted.
The experimental data on the damper velocity and
damping force are shown in Table 4.
Fitting the experimental data in equation (5), the
damper damping force–velocity relation is calculated to
be
F = 5:52 3 V 0:484
ð6Þ
where the damping force unit is kN and the velocity
unit is m/s.
The damping force–velocity fitting curve is shown in
Figure 11.
From the experimental data, it can be analyzed that
when the velocity is 0.1 m/s, the damping force is less
than 2000 N, which ensures the structural safety. On the
other hand, at working velocity from 1e–4 to 6e–4 m/s,
its equivalent linear damping coefficient is between 5e5
and 2e5 N s/m. The corresponding transient response
analyses were done after changing the damping
coefficient in the finite element model to be 5e5 and
2e5 N s/m, respectively. The analytical results in Figure
12 verify that this damper enables the model equivalent
modal damping ratio to be more than 4.5%, nine times
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Figure 10. The dimensions of the final produced damper (mm).
Table 4. Velocity and damping force of the produced damper.
Velocity (m/s)
Damping force (kN)
Velocity (m/s)
Damping force (kN)
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0008
0.001
0.047
0.067
0.087
0.0995
0.115
0.1275
0.149
0.1695
0.002
0.003
0.004
0.02
0.04
0.06
0.08
0.1
0.2445
0.302
0.347
0.93
1.26
1.44
1.6
1.74
Figure 11. The velocity–damping force fitting curve.
the original, which is also substantial. Thus, the actual
viscous damper meets the expected requirements.
The lower strut and locking mechanism design
During the launch phase, the upper strut and the lower
strut should be folded. Consequently, the lower strut
was designed into two separate rods which were linked
via a screw and a connecting bar. Then, the viscous
damper could be folded between the two rods. After
deployment, the two struts should be combined into
one strut, becoming an axial force element. Hence, the
Figure 12. Results of the solar array with damper under
different damping coefficients.
hinge connecting the two struts was designed to be lockable. A common lockable spring-pin design concept
was implemented. The spherical rod end bearing of the
piston rod was replaced by a self-designed connector
having a pin-hole (see Figure 13(a)). It has a M8 thread
with the length of 24 mm, which can be screwed into the
piston rod. Except the vicinity of the central hole and
the pin-hole, the connector is hollowed out to reduce
weight. There is one pin on each side of the lower strut
to improve the locking reliability. The compression
spring for locking is placed in the locking cover and
pressed by the adjusting bolt. The design result of the
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Advances in Mechanical Engineering
Figure 15. Schematic diagram of the experimental setup.
Figure 13. (a) The self-designed connector and (b) the lower
strut.
Figure 14. The locking process: (a) stowed configuration
(unlocked) and (b) locked state.
lower strut is shown in Figure 13(b), where the two separate parts are symmetrical.
The material for the lower strut, the connecting bar,
and the locking covers is aluminum alloy to make additional weight as light as possible. However, the stiffness
in the locking portion should be ensured, so the material for the self-designed connector and pins is steel.
Furthermore, a steel sleeve for each pin is embedded in
the lower strut.
The locking process is as follows. When the solar
array is stowed, the pins on both sides are pressed
against the surface of the connector, as shown in
Figure 14(a). With the deployment of the solar array,
the pins slide along the surface. When the angle
between the damper and the lower strut reaches 180°,
the two pins are pressed into the pin-hole by the springs
at the same time, successfully locked as shown in
Figure 14(b).
Experiments
The modal parameters of a linear vibration system,
including the system modal frequencies and damping
ratios, can be obtained by modal test. Therefore, the
associated modal tests of a solar array test sample have
been performed to verify the effectiveness of the damping device. The main concerned mode is the solar
array’s first bending vibration mode, so the method of
exciting the first vibration mode is applied for the tests.
Figure 15 illustrates the schematic diagram of the
experimental setup for the solar array sample attached
with damping device. In the experiments, one end of
the sample was bolted to a rigid fixture. The excitation
and measurement point was in the middle of the free
end. At this point, the first bending mode has the largest amplitude. The solar array’s free vibration at the
first mode was easily obtained by impacting the excitation point or giving the solar array initial displacement
manually in the direction perpendicular to the plate.
And the displacement signal at the same point was
measured by a laser vibrometer.
Take the natural logarithm of both sides of
equation (1)
lnjxðtÞj = jvn t + ln½Ajsinðvd t + u0 Þj
ð7Þ
where vd can be obtained from the collected displacement data using the fast Fourier transform (FFT) algorithm. When the second part takes the same value, the
slope is equal to 2jvn, which is the attenuation
coefficient.
The first bending modal frequency and the modal
damping ratio can be calculated from the frequency
response and the attenuation coefficient.
A hammer test results of the original sample and the
sample with damping device are presented in Figures 16
and 17, respectively.
Compared to Figure 16(a), Figure 17(a) illustrates
that with damper, the vibration displacement response
amplitude decays more rapidly. For the original sample, the damped natural frequency is analyzed to be
about 2.594 Hz and the attenuation coefficient is
20.037275, so its modal damping ratio is about 0.23%.
For the sample with damping device, the damped natural frequency is increased to about 3.319 Hz.
Figure 17(c) shows that the attenuation coefficient has
two distinct values, one is 20.25347, while the other is
20.050972. Therefore, at the initial vibration stage, its
modal damping ratio is equivalent to 1.22% and then
the damping ratio is reduced to 0.24%. The reason for
such phenomenon may be that with large vibration
amplitude, the damper has a great damping effect at
the initial stage, while the vibration decays to a certain
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Figure 16. Hammer test results of the original sample.
Figure 17. Hammer test results of the sample with damping device.
Table 5. Modal test results.
The original sample
Hammer test 1
Hammer test 2
Initial displacement
excitation test
The sample with damping device
The first bending
modal frequency (Hz)
Modal damping
ratio j
The first bending
modal frequency (Hz)
Modal damping ratio j
Initial stage
Later stage
2.594
2.594
2.594
0.23%
0.23%
0.26%
3.319
3.319
3.319
1.22%
1.28%
1.32%
0.24%
0.25%
0.26%
extent, the damper cannot be pulled due to its static
friction force, and almost has no damping effect.
Other hammer tests and initial displacement excitation experiments were also implemented. The test data
were analyzed and their results were quite similar.
Table 5 lists all modal test results.
The experiments reveal that the modal damping
ratio in the first bending vibration mode of the sample
with passive damping device can achieve more than five
times the original when the damper is effective. While
the vibration is quite small, the damper turns to playing
a supporting role to suppress vibration.
Conclusion
A novel passive vibration damping device for the multipanel solar array is presented. The device is lockable
and located near the solar array root hinge to increase
10
the modal damping ratio in the first bending vibration
mode without reducing the fundamental frequency.
Moreover, it ensures that the solar array maintains the
original functions, such as folding, deploying, and sun
tracking.
There is a viscous damper at the upper strut to provide passive damping. Analytical and experimental
results validate the effectiveness of this parallel damping
method. With the finite element models, the properties
of the damping device are investigated. The findings
demonstrate that the damping coefficient has an optimum value and this passive vibration control improves
the modal damping ratio more markedly when the original structural damping ratio is relatively small.
The passive damping device implemented for a certain type of satellite solar array was produced.
Simulation results verify that the actual viscous damper
can meet the requirements and increase the modal
damping ratio substantially. The associated experiments based on a solar array test sample reveal that the
passive damping device has a great damping effect at
large vibration. While the vibration is quite small, the
damper almost has no damping effect; however, it can
play a supporting role to suppress vibration. For future
damping device applications, the viscous damper
design may be further improved, especially minimizing
its static friction force. Additionally, the upcoming
experiments based on the real solar array can help to
obtain more results.
Acknowledgements
The work was carried out at the Key Laboratory of
Spacecraft Design Optimization and Dynamic Simulation
Technologies, Ministry of Education, China, under contract
with Beijing Institute of Control Engineering.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with
respect to the research, authorship, and/or publication of this
article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this
article: This research work was supported by the National
Natural Science Foundation of China (Grant No. 11672016),
which the authors gratefully acknowledge.
Advances in Mechanical Engineering
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