Dynamic Structural Response Estimation of a Printed Circuit Board Installed on a Microsatellite Due to a Half-Sine Impact/Shock Loading *

Transcription

1 Journal of Aeronautics, Astronautics and Aviation, Series A, Vol.43, No.4 pp (2011) 279 Dynamic Structural Response Estimation of a Printed Circuit Board Installed on a Microsatellite Due to a Half-Sine Impact/Shock Loading * Shao-Tai Lu 1, Syh-Tsang Jenq **,1, Chieh Kung 3, Jyh-Ching Juang 2, and Jiun-Jih Miau 1 1 Department of Aeronautics & Astronautics 2 Department of Electrical Engineering No.1, University Road, Tainan City 701, Taiwan, R.O.C. 3 Department of Computer Application Engineering Far East University, Hsin-Shih, Tainan, Taiwan, R.O.C. ABSTRACT The goal of this work is to assess the structural dynamic response of a printed circuit board (PCB) installed on the NCKU self-developed micro-satellite subjected to prescribed shock/impulsive loading environment using the vibration response spectrum method. The commercial finite element method (FEM) code ANSYS was adopted to simulate the dynamic structural response of the electronic printed circuit board (PCB) structure installed in micro-satellite due to specified loading. A drop tower impact tester was used to generate the specific shock/impact loading environment. The purpose of this drop impact test is to generate the prescribed shock/impulsive loading to the PCB structure made of glass fiber reinforced plastic (GFRP) for the acceleration signal determination at specific locations on the PCB structure in question. An evaluation of the satellite structure component s integrity at these locations can be performed using the predicted dynamic structural response by means of vibration response spectrum method. Keywords: NCKU self-developed micro-satellite, Half-sine shock loading, Impulsive loading, Drop impact, Electronic PCB structure, CKUTEX, LEAP I. INTRODUCTION National Cheng Kung University (NCKU) in Taiwan has been developing microsatellites for over a decade and has constructed two self-reliant micro-satellites which are LEAP (Low-frequency EArthquake Precursor) and CKUTEX (Cheng Kung University Technology EXperimental). The mission of LEAP is to detect the ULF emission in space to confirm postulations on the correlation between the presence of ELF/ULF (Extremely Low Frequency/Ultra Low Frequency) signals and earthquake activities, paving a way for earthquake detection and mitigation. Taiwan is in the earthquake hotspot region and has previously encountered several major earthquakes including the Chi-Chi (M=7.5) earthquake in September An illustration of the deployed LEAP spacecraft is shown in Fig. 1. In addition, the scope of the CKUTEX includes the design, analysis, manufacturing, assembly, integration, and test of the CKUTEX with the goal of delivery of a flight model for in-space validation. To realize this mission, the CKUTEX satellite will carry self-developed space-borne GPS receiver (GPSR) and digital sun sensor (DSS) as main payloads. The design and fabrication of the satellite subsystems and payloads will emphasize on the establishment of capability in meeting a high-quality and space-qualified standard. Fig. 2 shows a 3D illustration of the CKUTEX spacecraft. * Manuscript received, Oct. 27, 2011, final revision, Dec. 26, 2011 ** To whom correspondence should be addressed, stjenq@mail.ncku.edu.tw

2 280 Shao-Tai Lu Syh-Tsang Jenq Chieh Kung Figure 1 An illustration of the deployed LEAP spacecraft Figure 2 A 3D illustration of the deployed CKUTEX spacecraft NCKU self-developed micro-satellite includes the satellite bus and the payload. The satellite bus consists of six subsystems: power (EPS), structure (SMS), telecommunication (TT&C), onboard computer (C&DH), thermal control (TCS), and attitude control (ADCS). Fig. 3 and Fig.4 respectively show the internal view of the LEAP and CKUTEX. Details on the mission, design, and status of the LEAP microsatellite can be found in [1, 2, 3] and the CKUTEX microsatellite in [4]. The design of each subsystem is briefly described in the following. The SMS of LEAP is an aluminum box of size 20 cm x 20 cm x 30 cm (height) and the overall mass is 24 kg. The cross-shaped ULF payload box is positioned on top of the satellite body. The TCS adopts an NCKU self-fabricated MEMS-based temperature sensors for temperature monitoring. These sensors are mounted on appropriate positions to measure the temperature. In addition, patch heaters are used as active thermal control devices. The micro-satellite is 3-axis stabilized. The ADCS provides active (magnetic coils) and passive control (gravity gradient boom) to stabilize the satellite. The gravity gradient boom is comprised of 16 tubular elements with total deployed length 2.96 m. The spacecraft pointing accuracy is in the range of < 5º. The EPS is comprised of surface-mounted solar cells, batteries (Li-ion) and the DRU (Distribution and Regulation Unit). An average on-orbit power of 19.8 W is being provided. The C&DH employs COTS (Commercial Jyh-Ching Juang Jiun-Jih Miau Figure 3 An explosion view of the LEAP microsatellite Figure 4 An explosion microsatellite view of the CKUTEX off the shelf) devices consisting of CPU, DIO (Digital Input Output), ADC (Analog Digital Converter), and DAC (Digital Analog Converter). About 1.4 MByte of data are being generated per orbit. The LEAP payload includes a ULF payload for earthquake precursor research, a GPS payload experiment, a DSS (Digital Sun Sensor) payload for attitude control usage and an ECP (Experiment of Communication Payload) for the high frequency communication experiment. Furthermore, the CKUTEX dimension is 36.5 cm x 26.0 cm x 39.9 cm. The Aluminum Alloy 6061 T651 is selected as the satellite bus and frame material. The design of the CKUTEX structure must account for the interface between the payloads and the body panels. On the surface of the panel, the sun sensor, DSS payload and GPS antennas are mounted on the Y and Y panels. Two TT&C antennas are extended along the X and X directions. On the Z direction, the magnetometer is positioned. The body five direction are mounted with solar cells on the Z, X, +X, Y, and +Y faces. There are torque rods positioned on the X and Z faces. On the bottom of the satellite, there are two battery modules. Thirty two pieces of batteries are classified two modules. Via arranging the battery modules position, it is helpful to modify and improve the weight arrangement of satellite

3 Dynamic Structural Response Estimation of a Printed Circuit Board Installed on a Microsatellite Due to a Half-Sine Impact/Shock Loading 281 on the bottom panel. There are five circuit modules, EPS & TT&C, C&DH, ADCS, and GPSR modules inside the CKUTEX body. The EPS & TT&C module is fixed with +Z and Z panels. On the +Y direction, ADCS module and GPSR module are equipped on the face of EPS & TT&C module. In the opposite direction, C&DH module and GPS connector are equipped on the face of EPS & TT&C module. The CKUTEX satellite takes advantage of socket structure to increase the stiffness of circuit module. To verify and validate the design of the SMS, it is imperative to analyze and test the vibration response of the satellite during ground handling, launch, and in space. The approach and results of the vibration and impact analysis and test of the NCKU self-developed micro-satellite printed circuit boards used in LEAP and CKUTEX microsatellites are discussed in the following sections. Notice that the PCB boards invested in the present work are used in the subsystem circuit boards for the LEAP microsatellite, as shown in Fig. 3. In addition, the power (EPS), telecommunication (TT&C), onboard computer (C&DH), GPS receiver (GPSR), and attitude control (ADCS) subsystems for CKUTEX microsatellite also adopt the current studied PCB boards, as shown in Fig. 4. II. VIBRATION RESPONSE SPECTRAL ANALYSIS In this study, a vibration response spectral analysis was adopted to characterize the dynamic response of a printed circuit board (PCB) mounted in the core module of the LEAP and CKUTEX micro-satellites subjected to the prescribed impact/shock loadings during rocket launching and satellite separation process. The PCB plate structure was modeled to be a multi-degree-of-freedom system and the ground excitation loads were applied in terms of the prescribed acceleration power spectral density (PSD) curves. Theoretical basis of the vibration response spectral analysis can be found in [5] and some important equations are described in the following sections. Consider a single-degree-of-freedom system subjected to a base excitation in which m, c, and k, respectively, stand for the mass, viscous damping coefficient, and stiffness. In addition, variables x and y represent for the absolute displacement of the mass and the absolute displacement of the base, respectively. The governing equation of motion of the based excited system is mz + cz + kz = my, (1) where variable z is equivalent to the relative motion of the mass as (x y). One may take the Fourier transform of Eq. (1) and then integrate it by parts to get ω Z( ω) + j2 ξωω Z( ω) + ω Z( ω) = Y ( ω), (2) 2 2 n n A where the undamped natural frequency and damping ratio are respectively represented by ω n = k/ m and ξ = c/(2 mω n ). The functions Z(ω) and Y(ω) are the frequency functions describing the relative displacement of the mass and the absolute displacement of the base, respectively. The relation of the response of the relative displacement to the absolute displacement of the base can be written as Z( ω) = Y ( ω ) A 2 2 [( ωn ω ) + j2 ξωωn]. (3) 2 Knowing that Z ( ) ( ) A ω = ω Z ω and let the subscript A denote the acceleration, eqn. (3) can be further expressed as 2 ω Z ( ω) = Y ( ω). (4) A 2 2 A [( ωn ω ) + j2 ξωωn] The acceleration relation between the absolute motions X and Y (i.e., X A( ω ) and YA ( ω )) can be expressed as [5, 6] 2 ( ωn + j2 ξωωn) 2 2 n + j n X A( ω) = YA( ω). (5) [( ω ω ) 2 ξωω ] Multiply each side by its complex conjugate and note that * the Fourier transform pairs X A( ω) X A( ω ) and * YA( ω) YA( ω ) can be converted into power spectral densities (PSD). Therefore, the relationship of power spectral densities of the absolute motions function X ( ω ) and the base motion function Y( ω ) can be subsequently expressed as 2 [1 + (2 ξλ) ] Xˆ ( ) ˆ APSD f = YAPSD ( f), (6) [(1 λ ) + (2 ξλ) ] where f is frequency and the normalized parameter λ is equal to f / f n. Noted that f n is the natural frequency. The root mean square acceleration response x GRMS can be furthermore obtained by integrating X ˆ APSD ( f ) across the frequency spectrum and then taking the square root of the integrated area. From the point view of random vibration analysis, the root mean square value of the acceleration of absolute motion in response to a stationary input excitation is one sigma or one standard deviation values with zero mean value [7]. The result follows a Gaussian distribution and its interpretation is that the response will be less than the standard deviation value in 68.3% of the time. In this study, the one standard deviation value of the acceleration of the absolute motion is used as an indicator to characterize the dynamic response of the PCB to the based input excitation.

4 282 Shao-Tai Lu Syh-Tsang Jenq Chieh Kung Jyh-Ching Juang Jiun-Jih Miau III. IMPULSIVE LOADING ENVIRONMENT CONSTRUCTION IV. PRINTED CIRCUIT BOARD (PCB) DROP IMPACT TEST DESCRIPTION In the present study, the half-sine impulsive loading conditions was adopted as the input base excitation as shown in Fig. 5. The half-sine impulse with a peak acceleration of 1,500G and duration of 0.5 ms complies that required in the JEDEC standard JESD22-B111 Condition B [8]. Another type of impulsive loading that follows the MIL-STD-202G requirement which acquires a pulse in a terminal-peak-sawtooth (TPS) shape was also conducted but is to be reported in a separate paper. Time expression of the impact loads was numerically converted through Fourier transformation in a frequency format. Then, the power spectral density is obtained based on Eq. (6). Fig. 6 shows the acceleration power spectral density of the half-sine impact with a peak acceleration of 1500 G and 0.5 ms duration. This study employs a PC-104 printed circuit board (PCB) controller for dynamic structural response investigation. The PC-104 PCB controller is a core device mounted on the LEAP and CKUTEX micro-satellites and is considered to be the most vulnerable component subjected to the impact environment. The board level drop test method of components for handheld electronic products, i.e. the JESD22-B111 standard [8], is referenced to conduct the current drop impact tests. A detailed description of the drop impact test setup and the related data acquisition equipment used in tests is referred to ref. [9]. While most of the loading conditions follow what JEDEC regulates, the bare PC-104 PCB board is used as the test board and was mounted vertically instead of horizontally on a supporter. Fig. 7 shows that the micro-satellite PCB controller board was screwed at its four corners to the copper standoffs. The copper standoffs are screwed into a steel supporter which then is secured on the steel heavy drop table. The signals were acquired through two accelerometers after impact. Accelerometer #1 was mounted on an L-bracket connected to the PCB test board so that the accelerometer #1 could pick up signal in the direction of the drop impact. Notice that the PCB board structures are designed to be located vertically so that less bending load may be introduced during launching/separation processes. Accelerometer #2 was mounted on top of the rigid steel drop table in order to pick up the current impulsive signal after impact initiated. This impulsive signal can be used as the input to the support of the PCB test board (i.e. the standoffs). During the drop impact test, drop table falls along the guide rods and then hits the rigid strike surface. The impact contact acceleration signals were picked up by two Kistler made accelerometers as shown in Fig. 7. Current study can provide us with a proper numerical model which may represent the test model more closely when the PCB structure is subjected to a specific half-sine shock loading. Figure 5 A half-sine pulse loading waveform based on the JEDEC standard JESD22-B111, condition B [8] Figure 6 The acceleration power spectral density of the half-sine input impulsive loading (with a peak of 1,500 G and 0.5 ms pulse duration). Figure 7 The mounting layout of the instrumented PC-104 PCB test board

5 Dynamic Structural Response Estimation of a Printed Circuit Board Installed on a Microsatellite Due to a Half-Sine Impact/Shock Loading 283 V. FINITE ELEMENT MODEL & NUMERICAL SIMULATIONS In order to investigate the dynamic response of the PCB test board subjected to impact loading, a numerical model was created using the commercial ANSYS finite element code. The model contains the bare PC-104 PCB test board connected with the standoffs. The board lies in x-y plane with y-axis parallel with the drop impact direction. To facilitate numerical simulation, the bare PCB test board was modeled with the 2nd order shell elements, i.e. the SHELL 93 in ANSYS element library. The element has six degrees of freedom at each node: translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z-axes. The material properties of the PCB test board are shown in Table 1. The standoffs made of copper were modeled with beam elements, i.e. the BEAM 189 in ANSYS element library [10,11]. The material properties of the copper standoffs are tabulated in Table 2. The reason for adopting shell 93 element is that it has six degrees of nodal freedom, large deflection, plasticity, etc. capabilities and the element can be defined by the effective orthotropic material properties, such as EX, EY, EZ, etc. The effective orthotropic elastic properties for the bare PC-104 PCB structure were obtained as shown in Table 1 and then applied to the numerical model. Notice that the accelerometer no. 2 installed on the rigid base plate of drop table was used to sense the test acceleration profile. In doing so, the impact contact simulation problem that involves the entire drop impact system as depicted in Fig. 7 could be simplified. Since the base drop table is assumed to behave as a rigid material, the accelerometer-measured profile could be used as the input to the PCB finite element model with elastic standoff rods considered. Certainly, due to complex wave propagation in the device, the pulse shape may vary a lot at different positions and time. Note that this concept is similar to the input-g method used by S. T. Jenq, et al. [9] and Luan and Tee [12]. The input pulse shape is presented in Fig. 5 with a half-sine pulse loading of 1,500 G and 0.5 ms as specified in the JEDEC standard JESD22-B111, condition B. Current simulated vibration response is also found to be almost the same as that found numerically using the ANSYS shell 99 element. Notice that the shell 99 element adopted the composite laminated theory to compute the bending, extension and coupling stiffness matrices for laminates. We do not account for the layer information when using the commercial PC-104 PCB test boards in our microsatellite system. Fig. 8 shows the finite element model of the PC-104 PCB test board mounted on the standoffs. The model contains 1,422 elements. It should be noted that the model is shown with /ESHAPE toggled on; that is, the model does not suggest there is only one meshed element in the out-of-plane direction. For each drop impact loading, the numerical simulation begins with a modal analysis followed by a spectral analysis. During the analysis, the finite element model was fixed at its four standoffs where acceleration power spectral was inputted. Table 1 Material properties of the printed circuit board (PCB) made of glass fiber reinforced plastic (GFRP) modulus of elasticity, E x 16.2 Gpa modulus of elasticity, E y 16.2 Gpa modulus of elasticity, E z 7.4 Gpa shear modulus of elasticity, G xy Gpa shear modulus of elasticity, G yz Gpa shear modulus of elasticity, G zx Gpa Poisson s ratio, ν xy 0.36 Poisson s ratio, ν yz 0.11 Poisson s ratio, ν zx 0.11 Density, ρ 1,900 kg/m 3 Table 2 Material properties of the copper standoffs Modulus of Elasticity, E x 110 Gpa Poisson s ratio, ν 0.33 Density, ρ 8900 kg/m 3 Figure 8 The meshed finite element model of the PCB test board and the stand-off rod structures VI. RESULTS & DISCUSSION Impact Pulse Transmission Fig. 9 shows the measured time domain acceleration response at the base and the PCB test board due to the half-sine impulsive loading of approximately 1,500 G peak acceleration amplitude for 0.5 ms. The dynamic response measured at the base shown in Fig. 9 reveals that the half-sine base input signal is well constructed using the current test apparatus. It is noticed that the structure dynamic response measured at PCB test board site shows an oscillatory response with peak amplitude slightly higher than the input base acceleration and the phase lagging is also observed due to flexibility of the PCB test board with an accelerometer mounted. Since the PCB board structure is flexible, the output response may vary with the base oscillatory input signal. The mass of the accelerometers used is about 4 gram and the mass of the bare PC-104 PCB test board is about 50 gm. A limited mass effect of the accelerometer on the measured signal may exist. The real time signal picked up at accelerometer #2 installed at the rigid drop table as shown in Fig. 7, was transformed to an acceleration

6 284 Shao-Tai Lu Syh-Tsang Jenq Chieh Kung Jyh-Ching Juang Jiun-Jih Miau power spectral density (PSD) function as shown in Fig. 10. Notice that the base input acceleration PSD function is to be used as the input for subsequent numerical study. Fig. 10 also reveals that two major peaks are observed in the test determined PSD function plot for the PCB test board in question. The first peak at a frequency of approximately 1,800 Hz corresponds to the external loading frequency of the input half-sine impact pulse with a duration of approximately 0.5 ms as shown in Fig. 9, while the second peak of approximately 4,200 Hz indicates the characteristic frequency of the PCB test board studied here Modal Analysis of the PCB Test Board The numerical model describe in Sec. 5 was created to perform modal analysis. For the numerical modal analysis, the PCB test board is bonded with the copper standoffs and the other end of the standoff rods are modeled to be fixed at their roots. The PCB test board has a mass density of 1,900 kg/m 3 made of glass reinforced plastic (i.e. GFRP) and the constitutive relationship of the PCB test board is assumed to behave transversely isotropically. The in-plane (x-y plane) and out-of-plane elastic modulus are 16.2 GPa and 7.4 Gpa, respectively, and its in-plane and out-of-plane shear moduli are GPa and Gpa, respectively. (See Table 1) The copper standoffs are assumed to behave isotropically with an elastic modulus of 110 Gpa, Poisson s ratio of 0.33, and density of 8,900 kg/m 3. After performing the modal analysis, the mode shapes and corresponding modal frequencies of the PCB test board were obtained but not presented here. Among these analyzed eigenmodes, the 18 th mode (approximately 4,200 Hz) is the most significant one and it has the largest modal coefficient suggesting that the 18 th eigenmode dominants dynamic structural response. The modal shape of the 18 th mode is shown in Fig. 11. Note that the 18 th modal frequency is close to the resonant frequency of the PCB test board based on the simulated frequency response spectrum using the ANSYS harmonic analysis with the prescribed half-sine impulsive loading applied. The vibration modal shape shown in Fig. 11 is a high order coupled structural mode. If the external loading peak amplitude is further increased and/or the duration of the pulse is shorten, the induced acceleration power spectral density may increase. It may result in damaging the PCB test board. In the present study, the PCB test board remains intact after the prescribed half-sine shock loading (with a peak of 1,500 G and 0.5 ms pulse duration) is applied Vibration Response Spectral Analysis The vibration spectrum analysis with prescribed random vibration loading type was used to analyze the dynamic response of the present PC-104 PCB controller circuit board. The PSD excitation is applied at the roots of the copper standoffs mentioned above. The displacement response is evaluated at selected nodes on the model. The selected nodes are those points on the PCB where the accelerometers were mounted. The curves shown in Fig. 12 compare between the experimental and Figure 9 Measured acceleration response at the base of drop table and the PCB test board subjected to a half-sine pulse loading of 1,500 G and 0.5 ms Figure 10 The acceleration power spectral density (PSD) functions for the half-sine impulsive pulse transformed from the test determined acceleration signal presented in Fig. 9 Figure 11 The modal shape of 18 th mode for the PC-104 PCB test board

7 Dynamic Structural Response Estimation of a Printed Circuit Board Installed on a Microsatellite Due to a Half-Sine Impact/Shock Loading 285 Figure 12 Comparison of the test determined and code simulated acceleration power spectral density function due to the half-sine impulsive loading. The solid line was presented in Fig. 10 and the dashed line is the ANSYS simulated result numerical acceleration power spectral density functions due to the half-sine impact load with a 1,500 G peak acceleration amplitude and 0.5 ms duration. The experimental power density function is derived using the Fourier transform based on the data picked up by the accelerometer located on the PCB test board and it is location was shown in Fig. 7. The corresponding numerical simulated power spectral density functions is also obtained through the FEM code. From Fig. 12 that as the two simulated dominant frequencies are closed to the two experimental ones, it may suggest that the finite element model is feasible for the present vibration response analysis with the half-sine impulsive loading specified. The experimental and numerical power spectral density function curves due to the Terminal peak sawtooth (TPS) pulse type impulsive loading with a 40 G acceleration and 11 ms duration were also obtained but not presented here. It is reported that close relationship between the numerical simulated result and test finding was found, and therefore, it is suggested that the current finite element model is also feasible for subsequent dynamical response analysis for the TPS type impulsive loading environment Vibration Response Analysis Fig. 13 shows the acceleration root mean square value (i.e., GRMS) of the PCB test board in response to a half-sine pulse excitation according to the JEDEC Standard No. 22-B111 Condition B. The solid line curve shown in Fig. 13 forms an envelope of the GRMS of any single-degree-of-freedom system subjected to the mentioned half-sine impulse with a peak acceleration of 1,500 G and 0.5 ms pulse duration. The solid line curves shown in Figs. 14(a) to (d) are similarly obtained when a half-sine impulse with the same peak acceleration of 1,500 G but pulse duration varies from 0.05 to 0.8 ms. Notice that any acceleration value on the envelope line Figure 13 The G RMS value of the PCB due to the half-sine pulse impact (with a peak of 1,500 G and 0.5 ms pulse duration) curve at the specific frequency shown in the figures implies a possibility of 68.3% that the structural peak acceleration amplitude may achieve for the specific mode of structure in question based on the general approach theoretical prediction. Notice that the Mile s equation is a special case of the general approach. The circles represent the GRMS values of each mode of the PCB in response to the impact simulated using the ANSYS code. It can be seen that the greatest GRMS value exists in accompany with the 18th mode and is about 3,000 G as shown in Fig. 13, and this result suggests that the PCB test board may subject to an acceleration of 3,000 G in the probabilistic sense when loaded by a 1,500 G peak half-sine acceleration with a 0.5 ms pulse duration. Effect of the pulse duration of the half-sine peak 1,500G amplitude impulsive loading on the dynamic structural response of the present PCB test board is also studied. The simulated results are shown in Figs. 14(a) through (d). From these figures, the PCB test board may subject to acceleration of as high as 7,000 G when the duration of the half sine impulse is 0.2 ms even if the peak acceleration value is 1,500 G. Therefore, one may conclude that as the impulse duration becomes shorter (say shorter than 0.5 ms), the root mean square acceleration GRMS value of the PCB test board at the locations of interest becomes amplified. It may produce failure of the satellite components and result in the unwanted collision and/or interference of the micro-satellite components. VII. CONCLUSION The structural dynamic response of a printed circuit board (PCB) installed on the NCKU self-developed micro-satellite using the vibration response spectrum method is reported. Both experimental and numerical of the PCB test board subjected to the half-sine impulse with a peak acceleration of 1,500G and duration of 0.5 ms complies that required in the JEDEC standard JESD22-B111 Condition B were performed. The ANSYS finite element code was used to perform the harmonic vibration analysis and vibration spectrum analysis with

8 286 Shao-Tai Lu Syh-Tsang Jenq Chieh Kung Jyh-Ching Juang Jiun-Jih Miau (a) pulse duration : 0.8 ms (b) pulse duration : 0.5 ms (c) pulse duration : 0.2 ms (d) pulse duration : 0.05 ms Figure 14 The G RMS value of the PCB corresponding to the half sine impact. (with 1,500G acceleration and various input pulse durations) prescribed vibration loading in the PSD format. Comparison between the experimental and numerical power spectral density functions due to the half-sine impact load with a 1,500 G peak acceleration amplitude and 0.5 ms duration is reported. Effect of the pulse duration of the half-sine peak 1,500G amplitude impulsive loading on the dynamic structural response of the present PCB test board is also reported. In the present study, the PCB test board remains intact after the prescribed half-sine shock loading (with a peak of 1,500 G and 0.5 ms pulse duration) is applied. ACKNOWLEDGEMENT The authors would like to thank the support by grants NSPO-CNT-0619 from National Space Organization (NSPO) of Taiwan and NSC E from National Science Council (NSC) of Taiwan. REFERENCES [1] Juang, J. C., Miau, J. J., Liu, Y. Y., and Chen, B. C., Earthquake Research from Space: LEAP Microsatellite Design in Taiwan, Proceedings of the Asian Space Conference, Singapore, [2] Kramer, Herbert J. Observation of the Earth and Its Environment: Survey of Missions and Sensors - LEAP (Low-frequency Earthquake Precursor) microsatellite, announce.php? an_id= [3] Juang, J. C., Tsai, Y. F., and Miau, J. J., Status Update of the LEAP Micro-Satellite, Proceedings of the Asian Space Conference, Taipei, [4] Juang, J. C., Tsai, Y. F., Tsai, C. T., Jenq, S. T., Tsai, J. R., and Pan, H. P., CKUTEX An Experimental Microsatellite by NCKU, Proceedings of the AASRC conference, Taoyuan, [5] Clarence W. de Silva, Ed., Vibration & Shock Handbook, 2005, CRC Press, Taylor & Francis Group, LLC, Boca Raton FL, USA. [6] Singiresu S. Rao, Mechanical Vibrations, 3rd ed., 1995, Addison-Wesley Pub. Co., Reading, MA, USA. [7] Lu, S. T., Analysis & verification of microsatellite structure subjected to shock environmental loading using vibration response spectrum method, M.S. thesis, National Cheng Kung University, Taiwan, [8] Board level drop test method of components for handheld electronic products, JESD22-B111,

9 Dynamic Structural Response Estimation of a Printed Circuit Board Installed on a Microsatellite Due to a Half-Sine Impact/Shock Loading 287 JEDEC, Arlington, VA, USA. [9] Jenq, S. T., Sheu, H. S., Yeh, C. L., Lai, Y. S., and Wu, J. D., High G drop-impact response and failure analysis of a chip packaged printed circuit board, Int. J. Impact Engineering, Vol. 34, No. 10, 2007, pp [10] ANSYS User s Manual, 2002, Swanson Analysis Systems, Inc., Houston, PA, USA. [11] ANSYS Structural Analysis Guide, 2002, Swanson Analysis Systems, Inc., Houston, PA, USA. [12] Luan, J. E. and Tee, T. Y., Novel board level drop test simulation using implicit transient analysis with input-g method, In: Proceedings of the sixth electronics packaging technology conference, Singapore, 2004, pp