本文之研究主旨在利用單自由度系統衝擊響應頻譜之預測方法，預測結構體於外在衝擊環境所造成基底衝擊負載之響應，論文中推導無阻尼單自由度結構系統承受五種常用衝擊波(方波、半正弦波、後緣鋸齒波、遞減三角波、對稱三角波)之暫態結構反應解析解，並由最大響應描繪出衝擊響應頻譜，探討此數種衝擊波施於印刷電路板之反應。接著利用商業有限元素軟體ANSYS與Ls-Dyna對印刷電路板結構作衝擊負載之數值模擬，探討暫態分析與頻譜分析對於衝擊結果之預測，並利用自由落體式衝擊試驗機對電路板試片產生相同之衝擊環境，擷取其加速度響應與數值模擬結果作比對，以驗證數值模擬方法在衝擊的環境負載下之準確性。
暫態分析是利用加速度邊界條件輸入法來對電路板固定支撐點施予加速度負載，模擬時僅需建立電路板，而不需考慮電路板掉落過程之導向桿以及碰撞面性質等因素。在頻譜分析則是結合衝擊響應頻譜以預測結構之最大響應，且頻譜分析常用於無法用時域訊號描述之環境(如爆炸、地震、火箭升空等)。
最後應用頻譜分析方法於成大自製衛星CKUTEX之整顆衛星結構分析，探討飛行環境中之衝擊振動對於控制核心電路板的影響，檢視結果之合理性以提供未來衛星分析與設計改良之參考，期望能夠提高衛星結構與酬載在發射升空過程中的存活率，減少因為結構的不良設計所造成的次系統與酬載折損。

The main goal of this thesis is using shock response spectrum method that is expanded from the single-degree-of-freedom structural system to predict the response under the base shock excitation induced by external shock environment. The closed-form solutions for the transient structural response of an undamped structural system with SDOF sustain the impact acceleration pulse from five types of waveform(half sine, rectangular, decay triangular, sawtooth, symmetrical triangular) are derived. The largest response describes the shock response spectrum. After that, confer the effect of different drop impact test conditions on the transient structural response of the printed circuit board. And then with using FEM simulation software “ANSYS” and “Ls-Dyna” to simulate the dynamic response of a PCB structure under shock load, and then the response will compared with the transient analysis and the spectrum analysis. Moreover, use free-falling impact tester to generate the same shock environment on PCB structure. We can verify the accuracy of shock response spectrum method under the shock vibration environment.
The transient analysis was using Input-G-method which the acceleration can be directly input to the support screw of PCB assembly as boundary condition and requires building the model of the test vehicle only whereas does not have to consider friction of the guide rod for the drop table and the strike material. The spectrum analysis combine the shock response spectrum to predict the largest response of structure, and the analysis method can be used in Pyroshock, Seismic Shock and launcher flying.
Subsequently, with the application of the aforesaid method, the structural analysis of CKUTEX satellite which made by NCKU can show the effect of main payload and control PCB in satellite system under launcher shock vibration environment. For the sake of reference of future analysis, design and improvement of satellite, Herewith the survival rate of satellite and payload can be raised during the launching. Besides, the subsystem and payload damage caused by the improper design of structure can be reduced accordingly.

1.OPS, “Minotaur IV User’s Guide Release 1.1”, Orbital Sciences Corporation, 2006
2.ARIANESPACE, “ARIANE-5 Users Manual Issue 5”, ARIANE Space Agency ,2008
3.ARIANESPACE, “Soyuz CSG User’s Manual Issue 1”, ARIANE Space Agency ,2006
4.JEDEC Solid State Technology Association, JESD22-B110: Subassembly Mechanical Shock, 2001.
5.Department of Defense USA，Test Method Standard Electronic And Electrical Component Parts of Product MIL-STD-202G, Military Standard,1989
6.IEC Standard IEC 68-2-27, "Basic environmental testing procedures Part 2: Tests Ea and guidance: Shock," International Electrotechnical Commission (IEC), 1987.
7.Steinberg D.S., Vibration Analysis for Electronic Equipment, John Wiley &. Sons, 2000
8.Tee, T. Y., Luan, J. E., Pek, E., Lim, C. T., and Zhong, Z. W., “Novel numerical and experimental analysis of dynamic responses under board level drop test,” Proc. EuroSime2004. Conf., pp. 133-140 (2004).
9.Tee, T. Y., Luan, J. E., “Novel board level drop test simulation using implicit transient analysis with Input-G method,” Proc. 6th EPTC. Conf., pp. 671-677 (2004).
10.Luan, J. E. and Tee, T. Y., “ Analysis of PCB subassembly dynamic responses using integrated analytical ,numerical and experimental techniques,” Proc. 6th EPTC. Conf., pp. 133-140, 2005
11.Tee, T. Y., Luan, J. E., Hun Shen Ng, “Development and Application of Innovational Drop Impact Modeling Techniques,” Proc. 7th EPTC. Conf., pp. 504-512 (2005).
12.C. L. Yeh, Y. S. Lai, “Support excitation scheme for transient analysis of JEDEC board-level drop test”, Microelectr. Reliabi.; Vol.46, No2-4, pp.626-636, 2006.
13.T. Y. Tsai, C. L. Yeh, Y. S. Lai, R. S. Chen, “Response Spectra Analysis for Undamped Structural Systems Subjected to Half-sine Impact Acceleration Pulses”, Microelectronics Reliability; 47; pp1239-45, 2007.
14.Yeh, T.-Y. Tsai, Y.-S. Lai, “Transient Analysis of Drop Responses of Board-Level Electronic Packages using Response Spectra Incorporated with Modal Superposition,” Microelectronics Reliability, Vol. 47, No. 12, 2007, pp. 2188-2196.
15.Tsai, T. Y., Yeh, C. L., Lai, Y. S., Chen, R. S., 2007, "Incorpating Response Spectra and Modal Superposition in Analzing Transient Responses of Structural Systems Subjected to half-sine Impact Acceleration Pulse" Proc. 57th ECTC. Conf., Reno, NV, USA, pp.543-547.
16.Clough RW, Penzien J. Dynamics of structures. 2nd ed. New York: McGraw-Hill; 1993.
17.Paz, M., Structural Dynamics: Theory and Computation, Third Edition, Van Nostrand Reinhold, New York, 1991.
18.W. Thomson, Theory of Vibration with Applications, Second Edition, Prentice-Hall, New Jersey, 1981.
19.J. L. Humar, Dynamics of Structure, Second Edition, A.A. Balkema, Canada,2002
20.ANIL K. Chopra, Editor; Dynamics of Structure : Theory and Applications to Earthquake Engineering, Prentice Hall, New Jersey, 1995.
21.J. M. Biggs, Introduction to Structural Dynamics, McGraw-Hill Book Co., Inc., New York, NY, 1964, pg. 262, article 6.4.
22.Demeter G. Fertis, “Dynamics and vibration of structures” , by John Wiley＆Sons. Inc., 1973
23.Craig ROY R., Fundamentals of Structural Dynamics, Second Edition, Baker & Tayl, 2006
24.Cyril Harris, Editor; Shock and Vibration Handbook, Fourth Edition, MCGraw-Hill, New York, 1996.
25.T. Irvine, “Response of A Single-degree-of freedom System Subjected to a Classical Pulse Bace Excitation”, August 18, 1999
26.T. Irvine, “An Introduction to the Shock response Spectrum”, May 19, 2009
27.L. Meirovitch, Analytical Methods in Vibration, Macmillan, New York, 1967.
28.Ahlin, Magnevall, Josefsson: Simulation of Forced Response in Linear and Nonlinear Mechanical Systems Using Digital Filters. ISMA 2006, September 2006, Leuven, Belgium.
29.Smallwood, David: “An Improved Recursive Formula for Calculating Shock Response Spectra” 51st Shock and Vibration Bulletin, 1980.
30.Kelly, R.D. and Richman, G., Principals and Techniques of Shock Analysis, SVM-5, Sec. 6.7, Shock and Vibration Information Center. 1969.
31.R. Dorf, Modern Control Systems, Addison-Wesley, Reading, Massachusetts, 1980.
32.蒙以正, 數位信號處理應用MATLAB, 旗標出版股份有限公司, 2004
33.Jiří TŮMA and Petr Kočí, CALCULATION OF SHOCK RESPONSE SPECTRUM, Colloquium Dynamics of Machines 2009, Prague,2009
34.B.J. Shi, D.W. Shu, S. Wang, J. Luo, Q. Ng and J.H.T. Lau et al., Shock response and power spectrum analysis of a head actuator assembly, Transactions on Engineering Sciences (United Kingdom), Vol. 49, pp 470 - 479.
35.Dhakal R.P. and Pan T.C. Response characteristics of structures subjected to blasting induced ground motion. International Journal of Impact Engineering. 28(8). 813-828, 2003
36.G. Parzianelloa, A. Francesconib and D. Pavarinb,An estimation method for the Shock Response Spectrum propagating into plates subjected to hypervelocity impact ,Journal of the International Measurement Confederation ,Volume 43, Issue 1, January 2010, Pages 92-102
37.Chehab AG, Hesham M, Naggar EI. Response of block foundations to impact loads. Journal of Sound and Vibration 2004;276:293–310.
38.許宏旭, “印刷電路板之低速衝擊研究”, 國立成功大學航空太空工程研究所碩士論文, 2004.
39.呂紹台, “應用振動響應頻譜預測方法於微衛星結構之衝擊環境分析與驗證”, 國立成功大學航空太空工程研究所碩士論文, 2008.
40.Wijker, J. Spacecraft Structures. Springer. Berlin, Germany, 2008.
41.Department of Defense USA, Metallic Materials and Elements for Aerospace Vehicle Structures, MIL-HDBK-5J, Military Standard,2003
42.Wilfried Ley, Klaus Wittmann, Willi Hallmann, Handbook of Space Technology (Aerospace Series (PEP)), Wiley, 2009
43.P. N. DeSouza et al., “Structural Design of the Brazilian Scientific Applications Satellite (SACI-1) ”, 10th Annual AIAA/USU Conference on Small Satellite, Sept 16-19, 1996.
44.J. Zhang, Y. Chen, Z. Y. Zhang and H. X. Hua, “Research on the Random Vibration Test of the Satellite ”, Mechanical Strength; 28:pp.16-19, 2006.
45.Gupta, Ajaka Kumar, Response Spectrum Method in Seismic Analysis and Design of Structures, Baker & Taylor Books,1992