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Structural Analysis of an Electronic Module Incorporating Hybrid
Microcircuits in Power Distribution Package of Satellites
Abhiram B Aithal#1, Anirudh G Deshpande#2, Chetan A Pai#3 Naveen
Kumar M#4 and Rajeev R Badagandi*5 #Department of Mechanical
EngineeringM. S. Ramaiah Institute of TechnologyBangalore,
Karnataka - 560054 INDIA
[email protected]@gmail
[email protected]@gmail.com
*Scientific and Remote Sensing Integration Division (SIG),ISRO
Satellite Centre
Bangalore – 560 017, Karnataka, INDIA [email protected]
AbstractElectronic equipment can be subjected to a wide range
of
vibratory loads which is nowhere more evident than in the ones
employed in satellites. The mechanical enclosures and the sensitive
electronic sub-assemblies have to be designed to survive the launch
loads with high reliability and to endure the harsh space
environment in orbit throughout the intended mission life of a
satellite. The design and analysis of such a sensitve sub-assembly,
the shunt switch module incorporating Hybrid Micro Circuits - HMCs
used in power distribution package of satellites, by finite element
method is presented. The modeling and numerical simulations are
carried out using UG NX 7.5 to evaluate the design. The natural
frequency of card (640.1 Hz) and assembly (452.0 Hz) comply with
general stiffness. The stress values under static and random
loading are nominal for PCB and base module. There is a very good
margin of safety (MOS) over allowable strength of PCB and base
module material. The results of static, modal and random analyses
validate the adequacy of design.
1. IntroductionFew human ventures are as audacious and
indispensable
as the artificial satellites launched into orbit around the
Earth. These satellites are used for numerous applications ranging
from communication, weather prediction, disaster warnings to
reconnaissance and much more. In a satellite, electronic units form
a major part of the spacecraft bus mass budget and, generally, up
to a quarter of the total mass of the equipment is made by their
enclosures [1]. These complex electronic systems permit them to
perform the above mentioned diverse functions seamlessly. Analogous
to other products, satellites and the electronic subassemblies go
through the phases of design, fabrication, testing and shipment.
However, far greater complexities are encountered in each of these
stages of development of satellites and subassemblies, especially
during the shipment to their destination, than other products
[2].
Unlike their terrestrial counterparts, the electronic
subassemblies in satellites are subjected to far more treacherous
mechanical, thermal and electromagnetic environments. During
ascent, the payloads should be able to withstand low frequency
dynamic loads due to motor ignition and shut-offs; acoustic noise
due to flight in the transonic regime and reverberation of engine;
and shock
loads due to separation events such as spacecraft separation and
staging [3]. When once satellites are delivered to desired orbit or
trajectory, they have to cope with the severe space environment.
The space environment is characterised by a very hard vacuum; very
low gravitational accelerations; ionizing radiation; extremes of
thermal radiation source and sink temperatures; severe thermal
gradients; micro-meteoroids and orbital debris [4]. For the
mechanical enclosures and the sensitive electronic sub-assemblies,
launch survival is the primary design driver. Also, these
components have to be designed to endure the harsh space
environment in orbit throughout the intended mission life of
satellites.
In the present work, an optimized and reliable configuration for
an on board electronic module that safeguards crucial electronic
components from damages caused by vibrations and shock loads during
launch is developed.
Fig. 1. Assembly of HMC shunt switch module
The design and analysis of shunt switch module used in power
distribution incorporating hybrid microcircuits or HMC’s using
finite element method is presented in the current work. The cuurent
work aims at analysis and improvement of the preliminary design of
shunt switch module incorporating Hybrid Micro Circuits - HMCs,
used in power distribution package of satellites by finite element
method. The HMC, developed indigenously at the Indian Space
Research Organization – ISRO, in order to reduce size and weight,
executes the crucial task of shunting the excess power generated.
Consequently, the existing design of the module has to be modified
to accommodate the miniaturized HMC shunt switches. The HMC shunt
switch module, shown
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in figure 1, is a part of the satellite power distribution
package. It consists of a base module housing structure or the
chassis. The chassis supports the printed circuit board (PCB) to
which four Hybrid Micro Circuits (HMC’s) are connected. The shunt
switches are used for bus regulation. The shunt switch control
decides whether the solar array should be included or excluded.
The proposed base module or chassis of the electronic unit
should protect the PCB from the vibratory and shock loads
encountered during launch and also offer radiation shielding during
operation. The chassis consists of four pockets to house the HMC’s.
It consists of a pair of criss-crossing ribs to increase its
stiffness and support the PCB. It has six supports or lugs which
are mounted to the satellite. It also provides a provision to add
four 50-pin connectors for electrical connectivity. The lugs of the
chassis provide all the support needed for the entire assembled
module and thus are given special consideration while
designing.
2. Design of HMC Shunt Switch Power ModuleThe HMC shunt switch
module is a part of the satellite
power distribution package. It consists of a base module housing
structure or the chassis. The chassis supports the printed circuit
board (PCB) to which four Hybrid Micro Circuits (HMC’s) are
connected. Each HMC consists of four shunt switches. The shunt
switches are used for bus regulation. The shunt switch control
decides whether the solar array should be included or excluded.
The HMC is a miniaturized electronic circuit constructed of
active components, such as transistors and diodes, and passive
components, such as resistors, inductors, transformers, and
capacitors, fused to a substrate. PCBs are very sensitive to
environmental conditions. Depending on the device type in which a
PCB is utilized, different requirements come into existence such as
mechanical integrity of a system, durability against thermal
loading and prevention of electromagnetic interference (EMI). In
order to meet such requirements PCBs are mounted onto frames or
into box-like structures.
HMC shunt switch power module is made up of:a. Printed Circuit
Boardb. Base Platec. HMCsd. Chotherme. Connectors
2.1. Printed Circuit BoardA printed circuit board (PCB)
mechanically supports and
electrically connects electronic components using conductive
tracks, pads and other features etched from copper sheets laminated
onto a non-conductive substrate. PCBs can be single sided (one
copper layer), double sided (two copper layers) or multi-layer.
Conductors on different layers are connected with plated-through
holes called vias. Advanced PCBs may contain components -
capacitors, resistors or active devices - embedded in the
substrate.
PCB is used primarily to create a connection between components,
such as resistors, integrated circuits, and connectors. It turns
into an electrical circuit when
components are attached and soldered to it, which then is called
printed circuit board assembly. PCB is constructed using the FR-4
composite, whose properties are listed in table 1. The PCB is fixed
to the chassis at the corners and at the intersection of the ribs.
This provides additional stiffness to the PCB when subjected to
vibrational loads. The PCB supports each of the four HMC’s and four
connectors among other electrical components. The PCB,
228.6mm×198.4mm×2mm in size, is employed in the current module. The
size of PCB is prescribed by considering its applications and the
type of components to be mounted. Several holes are cut into the
PCB as seen in figure 2 for mounting the PCB onto the base module,
HMCs onto it and for the lead wires of HMCs. The different
orthographic views of PCB are depicted in figure 2.
Fig. 2. Initial design of PCB
Fig. 3. Initial Design of Base Module
2.2. Base ModuleFor electronic equipment, generally speaking,
launch
survival is the major mechanical design driver.The base module
or chassis of the electronic unit should protect the PCB from the
vibratory and shock loads encountered during launch and also offer
radiation shielding during operation. The chassis consists of four
pockets to house the Hybrid Micro Circuits. It consists of a pair
of criss-crossing ribs to
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increase its stiffness and support the PCB. It has six supports
or lugs which are mounted to the satellite. It also provides a
provision to add four 50-pin connectors for electrical
connectivity. The chassis is generally made of a metal or an alloy
while PCB is predominantly a composite based component. The lugs of
the chassis provide all the support needed for the entire assembled
module and thus have to be given special consideration while
designing.
The mechanical requirements placed on equipment design are set
by the authority in charge of the overall spacecraft development.
These requirements aim to ensure that the equipment can withstand
without failures the mechanical environment produced at the
equipment location during launch. This environment consists of low
frequency dynamics and steady accelerations, combined with random
vibrations, acoustic loads and shocks.
Another important requirement concerns the lowest natural
frequency of vibration allowed for the equipment, in order to avoid
dynamic coupling with the low frequency modes of spacecraft and
launch vehicle. For equipment weighing up to few kilograms this is
usually 100 Hz [5].
Finally the equipment must be able to withstand the load factors
which are produced during the launch phases. These loads are
usually called Quasistatic Loads (QSL) since they are produced by
relatively low frequency dynamics. An example of QSL specification
for aerospace equipment couldbe 15 g applied simultaneously along
the three axes. Compliance with this requirement is usually
demonstrated with a high amplitude sine sweep test, such as 15 g
[6].
Thermal loads occurring during the active life of the electronic
equipment once on orbit are also extremely important for the
mechanical design. However this work focuses on the vibration
environment during launch and therefore thermal loads are not
considered in this study [7].
Other than these mechanical requirements, the chassis must
fulfil certain configurational requirements. There should be
adequate space for mounting components. The connector and PCB
interfaces should allow for easy electrical connectivity. There
should be enough volume around the PCB for assembly and rework. In
addition to these, the design of the chassis should be such that it
occupies minimum space. With the above design principles, the
following initial design for the base module is proposed as shown
in figure 3. The chassis, 284mm long and 217.6mmwide and 35mm in
height, is composed of Aluminium 6061 alloy and weighs 0.548kg. The
properties of Al-6061 are depicted in table 1.
2.3. HMC Shunt SwitchIn spacecraft, solar array is used for
energy generation
and battery for energy storage and support during payload
operation. The power from solar array is distributed into several
solar array strings. The number of solar array strings depends on
the class of satellite. The shunt switch and associated circuitry
is a major component of power electronics. The shunt switches are
used for bus regulation. The shunt switch control decides whether
the solar array strings should be included or excluded. The shunt
switches consists of MOSFET, a diode and monitoring and drive
resistors. The monitoring resistors provide information
regarding status. The required drive is provided by drive
resistors. There is also a protection for the drive signal. In
order to reduce the size and weight of these shunt switches,
hybridised versions of the same are currently being developed
indigenously by ISRO. Four number of electrically isolated shunt
switches are accommodated in a single HMC package of twenty pins
(input, output, ground, monitoring and control).
The HMC shunts switch basically dissipates the excess amount of
power from the power distribution package in the form of heat. The
HMC shunt switch is made of a kovar ring frame, copper cored alloy
based leads and eyelets and the power package base made up of
molybdenum. A chotherm is placed between the contact surfaces of
the pockets in the chassis and the HMC shunt switches.
3. Overall Analysis StrategyFirstly, the material properties of
the components are
experimentally measured. The static load analysis with
quasistatic loads as inputs (25g in normal direction and 15g in
lateral direction to the mounting plane) is then performed. Next,
an eigenvalue analysis (SEMODES 103) is carried out. Finally,
random response analysis (SEMODES 103 Response Simulation) is
performed.
The modelling and numerical simulations are carried out using UG
NX 7.5 [8] to evaluate the design. The reliability of finite
element analysis is improved by accurately modeling the individual
HMC’s. The points where HMC’s are fixed to PCB are not entirely
free to deform. Therefore, two corresponding points where HMC’s are
mounted are connected with RBE2 elements. This increases the local
stiffness and depicts a more realistic behavior of the PCB. RBE2
element provides a rigid connection between the two nodes with no
relative displacement between them. RBE2 element is thus created at
all places where two or more components are clamped together. The
properties of mesh are given in tables 2 – 3.
The emphasis is placed on random response of the electronic
components. The random load on spacecraft encompasses acoustic
excitation due to rocket, engine noise and acoustic noise due to
flight in transonic regime [9]. The PSD input for random response
analysis is depicted in table 5. This input PSD of acceleration is
applied in the directionnormal to the mounting plane of the module
by means of the enforced motion boundary condition.
The failure criteria for PCB and the electronic module are
largely based on the displacement and stiffness constraints which
are in turn dependent on the natural frequency. The natural
frequency of the PCB and assembly should be greater than 300Hz and
125Hz respectively. The other important failure criteria are Grms
and transmissibility values obtained under random load. The Grms
value should not exceed 110G and transmissibility should be around
50 –60. Also, the maximum stresses induced must be less thanthe
yield stress of the material under consideration.
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3.1. Mesh GenerationThe thickness of surfaces of base module and
PCB of the
electronic unit is negligible compared to other dimensions,
namely length and width. The maximum thickness is only 12 mm while
the average length and width are 250 mm and 200 mm respectively.
Thus, plane stress condition is assumed and the entire 3D model can
be reduced to 2D. This is achieved by generating mid-surfaces of
all faces of the base module and PCB.
The next step of analysis is assigning of material properties to
each individual component. The material assigned to base module is
Al - 6061 the properties of which are given in table 2.
The reduction of 3D model of the base module to 2D planar
surfaces facilitates the generation of thin shell elements on them.
Several physical properties should have to be assigned to them such
as thickness and non-structural mass. Non-structural mass
corresponds to any distributed mass that has to be smeared onto the
surfaces of the 2D model. Since the thickness is different at
different sections, each surface is assigned with individual
physical properties.
The next step is creating a thin shell mesh collector for the 2D
model. Mesh collector stores all the information pertaining to the
mesh such as physical properties, material properties etc. Each
unique set of physical properties is assigned to a corresponding
mesh collector.
The final step is to discretize the 2D surfaces of model to
generate the requisite QUAD – 4 elements and nodes. The mesh is
generated by selecting the surface and assigning the respective
mesh collector to it. A mesh refinement study is also carried out
to determine the optimum element size and the level of convergence
is aimed at at least 3%. It is seen that the mesh with element size
of 1mm is sufficiently refined. Therefore, QUAD – 4 elements of
element size 1mm are used for finite element analysis. The
properties of finite elements used in the analysis are given in
table 2.
The same procedure is repeated for mesh generation of PCB and
HMCs by assigning appropriate materials, whose properties are
depicted in table 3.
The layout of different electrical components on the PCB are not
known, the total mass of these components are smeared onto the
surface of PCB as non-structural mass. The non-structural mass
distributed on PCB is 100 grams. The mass of both connectors is 50
grams and point masses of 25 grams are applied on the eight
mounting holes. Thus the total mass of the HMC shunt switch power
module is 1.144kg.
3.2. Boundary Conditions for Static AnalysisMesh generation is
followed by application of proper
boundary conditions and finding the solutions. The boundary
conditions could be constraints posed on the degrees of freedom of
certain regions of the domain or loads applied on the body. In
static analysis, the quasistatic forces are applied as gravity
loads. The fixed constraint is applied to the screw holes used to
clamp the housing to the satellite body. The effects of sinusoidal
loads acting on the package are also studied in the static analysis
[10]. This is due to the fact that the frequency of the sinusoidal
transient loads acting on the package during the launch is less
than 100Hz and the natural
frequencies of both PCB and base module are greater than 100Hz.
Thus, these loads do not excite the resonant modes of vibration of
either PCB or base module and the transient effect of these loads
can be ignored. From the data compiled from previous launches, it
is found that the package should be able to survive a load of 25 g
in the axial direction and 15 g in the lateral direction.
Table I. Material properties of base module, PCB and HMC used in
FE analysis
Property
Base
Module –
Al 6061
PCB –
FR4
HMC Base –
Molybdenum
HMC Ring
Frame –
Kovar
Young’s
Modulus68.98GPa 20GPa 329GPa 159GPa
Poisson’s
Ratio0.33 0.18 0.31 0.317
Density
(kgm-3)2711 1900 10280 8000
Allowable
Stress248MPa 310MPa 620MPa 270MPa
Table II. Properties of finite elements used
Property PCB Base ModuleComponents
on PCBType of Element
QUAD – 4 QUAD – 4
Distributed mass of 100g
Element Property
Thin Shell Thin Shell
Material Used FR4 Al6061
Total Number of Elements
47790 115555
Mass 0.196 kg 0.548 kg
Table III. Properties of finite elements usedProperty Bolt Joint
Connectors HMCs
Type of Element
Rod 0 – D QUAD – 4
Element Property
RBE2 Point Mass Thin Shell
Material Used ----- -----Molybdenum Base;
Kovar RingTotal Number of Elements
386 8 14232
Mass ----- 0.100 kg 0.200 kg
Table IV. Quasistatic loads on the package
Load (Acceleration in Terms of Gravity) Direction
25 g Normal to mounting plane (z)
15 g Lateral to mounting plane (y)
3.3. Boundary Conditions for Modal AnalysisThe modal analysis is
performed to study the free modes
of vibration of PCB, base module and the coupled modes of
vibration of their assembly. The fixed constraint is applied to
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the screw holes used to clamp the housing to the satellite body.
Since free vibration analysis is performed, no loads are applied to
the package.
3.4. Boundary Conditions for Random Vibration Analysis
Random vibration is vibration that can be described only in a
statistical sense. The instantaneous magnitude is not known at any
given time; rather, the magnitude is expressed in terms of its
statistical properties (such as mean value, standard deviation, and
probability of exceeding a certain value). The random load on
spacecraft encompasses acoustic excitation due to rocket, engine
noise and acoustic noise due to flight in transonic regime. These
random excitations are usually described in terms of a power
spectral density (PSD) function. The PSD input for random response
analysis is depicted in figure 4.This input PSD, prescribed by the
authority in charge of overall spacecraft development, is based on
data from previous launches. This input PSD of acceleration is
applied in the direction normal to the mounting plane of the module
by means of the enforced motion boundary condition [11].
NX Nastran performs random response analysis as a
post-processing step after frequency response analysis. The
frequency response analysis is used to generate the transfer
function, which is the ratio of the output to the input. The input
PSD multiplies the transfer function to form a response PSD. The
input PSD can be in the form of auto- or cross-spectral densities.
Random response output consists of the response PSD,
autocorrelation functions, number of zero crossings with positive
slope per unit time, and RMS (root-mean-square) values of
response.
Table V. Frequency – PSD input normal to base moduleFrequency
(Hz) PSD Qualification Level (G2/Hz)
20 – 100 +3dB/oct100 – 700 0.15
700 – 2000 -6dB/octOverall RMS acceleration 12.8 g
3.5. Unpredictability involved in Finite Element AnalysisThe FEM
analysis is not completely free from
uncertainties. To begin with, the material properties of PCB are
different in different directions as it is a composite material
whereas we assume it as an isotropic material while carrying out
the analysis. Also, the values of several other material properties
are not fully reliable as they are obtained from different
manufacturers.
Depending on vibration modes of a PCB, the location of component
may affect the dynamics of the PCB. Since, it is difficult and time
consuming to model all the components present on the PCB, the total
mass of the components is distributed uniformly on the PCB as
non-structural mass. This adds to the inaccuracy in the final
result.
One of the most important issues in finite element modeling of
printed circuit boards is defining boundary conditions. The PCB is
connected to the base module by an RBE2 element which arrests all
degrees of freedom which is not correct as a finite rotational
stiffness actually exists in the real scenario. Damping coefficient
value has to be obtained
from the past experimental results. This may not be the true
damping value but only a close approximation.
Fig. 4. Input PSD curve
4. Results and Discussions
4.1. Static AnalysisThe robustness of initial design against
quasistatic loads
encountered during launch is tested. Gravity loads of 25 g
normal to mounting plane and 15 g lateral to mounting plane are
applied. The maximum von Mises stress developed underthese loads is
22.20 MPa, while the yield stress of Al-6061used in base module is
248 MPa and thus the assembly would survive the quasistatic
loads.
4.2. Modal AnalysisModal analysis is performed for PCB and base
module as
well as the assembly. The natural frequency of PCB calculated
when nine
points are fixed does not entirely encompass the behavior of PCB
since the points where HMCs are fixed to PCB are not entirely free
to deform. Therefore, a case is also run where the two
corresponding points where HMC’s are mounted are connected with
RBE-2 elements. This increased the local stiffness and thus
depicted a more realistic behavior of the PCB.
It is observed that the natural frequencies of PCB and base
module are not separated by one octave (fpcb/fmod =1.155 < 2).
This would result in severe coupling of modes of vibration of PCB
and base module as is seen in the results of random vibration
analysis below.
4.3. Random AnalysisGrms value is computed at the node where
displacement in
free vibration condition at the significant mode of vibration is
maximum. The design is based on the Grms at that node and its value
should be within the permissible limits. The Grms and RMS value of
von Mises stresses under the action of input PSD. The value of
116.9 G is extremely high and much above the upper limit of 110 G.
Therefore, the design in its present form does not conform to the
specified standards. Extensive changes have to be made to the
existing design to reduce the value of Grms.
4.3. Modifications of the initial designThe natural frequencies
of PCB and base module are
close to one another. Very high acceleration levels in PCB are
thus obtained. In order to avoid this, the natural
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frequencies of the base module and PCB must be well separated,
at least by an octave [11]. The number of mounting points of PCB is
increased from nine to fifteen and the thickness of PCB is
increased from 2mm to 2.3mm as shown in the figure 5. The first
natural frequency of vibration is found to be 640.1Hz. It is not
feasible to further increase the number of supports for the PCB
since the space available to mount components decreases. Thus
further modifications have to be made to the design of base module.
The thickness of certain surfaces of the base module is decreased
to decrease its natural frequency as shown in figure 6.
Upon these modifications, Grms is found to be 88.57 G and the
maximum RMS value of von Mises stress in base module is 65.32MPa.
The maximum RMS value of von Mises stress in PCB is 20.55MPa. The
peak values of von Mises stress at base module and PCB are
195.96MPa and 61.65MPa respectively and the maximum value of
transmissibility being Q = 45.31. It is noteworthy to mention that
the ratio of natural frequencies of modified PCB and base module,
(fpcb/fmod = 1.611), is closer to one octave than for the previous
iterations. The results of analysis are given for critical axis,
that is, z – axis, perpendicular to the mounting plane of PCB in
tables 6 – 7.
Table VI. Results of static load analysis
Component Dimension(mm)
Global Natural Frequency (Hz)
Max von Mises stress under static loads (MPa)
Max displacement under static loads (mm)
PCB 228×200×2.3 640.1 8.19 0.04004Base Module 284×217×30 397.3
28.4 0.04010
Assembly -- 452.0 28.4 0.04010
Table VII. Results of random load analysis
Component
Max RMS von Mises stress under random loading
Grms
Peak von Mises stress under random loading
Allowable stress
MOS
PCB 20.55 MPa
88.57G
61.65 MPa 310 MPa 5.03
Base Module 65.32 MPa 195.96 MPa 248 MPa 1.265
Assembly 65.32 MPa 195.96 MPa -- --
5. ConclusionsA preliminary design of the HMC power
distribution
module was analyzed and improved such that all the failure
criteria are met. Natural frequency of PCB (640.1 Hz) and assembly
(452.0Hz) comply with general stiffness guidelines of 300Hz for PCB
and 125Hz for assembly. The acceleration levels of 88.57G are also
benign and conform to the guidelines. The stress values under
static and random loading are nominal for PCB and base module.
There is a very good margin of safety (MOS) over allowable strength
of PCB and base module material. The results of static, modal,
random and shock analyses validate the adequacy of design.
Fig. 5. Mesh for modal analysis of PCB when fifteen points are
fixed
Fig. 6. Modifications of initial design of base module
References1. G.S. Aglietti, and C. Schwingshackl, 2007,
“Analysis of
Enclosures and Anti Vibration Devices for ElectronicEquipment
for Space Applications” , School of EngineeringSciences,
Aeronautics and Astronautics, University ofSouthampton, UK.
2. Conor D. Johnson and Paul S. Wilke, 2003,
“ProtectingSatellites from the Dynamics of the Launch
Environment”,American Institute of Aeronautics and
Astronautics.
3. Adriano Calvi, “Spacecraft Load Analysis”, PhD
thesissubmitted to ESA / ESTEC, Noordwijk, The Netherlands.
4. P.J. Zulueta, “Electronics Packaging Considerations for
SpaceApplications”, 2001, Jet Propulsion Laboratory,
CaliforniaInstitute of Technology.
5. G. S. Aglietti, C. Schwingshackl, Analysis of Enclosures
andAnti Vibration Devices for Electronic Equipment for
SpaceApplications, Proceedings of the 6th International
Conferenceon Dynamics and Control of Systems and Structures in
Space2004.
6. McKeown, Mechanical Analysis of Electronic PackagingSystems,
Marcel Dekker, Inc., 1999.
7. M. XIE, D. Huang, T. Zhang, L. Lu, Dynamic Analysis ofCircuit
Boards in ANSYS, Proceedings of the IEEE,International Conference
on Mechatronics and Automation,20069. Jung, Park, Seo, Han, Kim,
Structural Vibration Analysis of Electronic Equipment for Satellite
under Launch Environment, Key Engineering Materials Vols. 270-273
(2004) pp.1440-144
8. NX Nastran Release Guide, Siemens, 2013.9. Jung, Park, Seo,
Han, Kim, Structural Vibration Analysis of
Electronic Equipment for Satellite under Launch Environment,Key
Engineering Materials Vols. 270-273 (2004) pp.1440-144.
10. Spacecraft mechanical loads analysis handbook by
EuropeanCooperation for Space Standardization.
11. D. S. Steinberg, Vibration Analysis for Electronic
Equipment,John Wiley & Sons, Inc., 2000.
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