臺灣博碩士論文加值系統

摘要
電子元件常被裝設於暴露在嚴荷振動及衝擊環境下的印刷電路板。因此如何保護其上設計元件並提升印刷電路板的可靠度巳變成研究領域一件相當重要的工作。
本論文主要在研究移動點或邊界支撐之印刷電路板的隨機振動，文中將引用疊加法來處理具不同約束邊界之印刷電路板的固有值問題(Eigenvalue Problem)，同時也提出一遞迴演算法來計算印刷電路板在白噪音及非白噪音穩態過程加速度激振下板的橫向位移均方值。本數值結果與蒙地卡羅模擬法之模擬值也做了比較，結果顯示相當吻合。由此我們可以發現，對點支撐印刷電板而言，支撐點最好不要位在低頻模態的節線上，反之板上的質量則最好放在此節線上，對匯流槽夾持或楔形夾持而言，夾持剛度增加可提高印刷電路板的自然頻率並降低板的位移均方值。

ABSTRACT
The electronic devices are often mounted on the Printed-Circuit-Boards (PCBs), which may be exposed to severe vibration and shock environment. Therefore, how to protect the devices and how to increase the reliability of the PCBs have become an important task in the research.
The random vibration of PCBs with moving point or edge supports is studied in this thesis. The superposition method will be introduced to deal with the eigenvalue problems of PCBs constrained by different edge conditions. The mean square value of the relative transverse displacement of plate element is evaluated for the white and non-white stationary random process acceleration excitations by using the proposed recursive algorithm. Furthermore, the numerical results are also compared with those using the Monte Carlo simulation approximations, and the excellent agreement between the two results is obtained. It is found that the constraint point had better not be located on the nodal line of low mode for the case of point supported PCBs; on the other hand the attached mass had better be put on it. It is further found that for the case of plug-in connector supported PCBs or wedge retainer supported PCBs, the increment of connector or retainer stiffness will promote the natural frequencies and lower the mean square value of displacement of PCBs.

目錄
摘要I
ABSTRACTII
誌謝III
目錄IV
圖表索引VI
符號表XII
第一章1
1.1前言1
1.2 文獻回顧2
1.3本文目的與架構5
第二章 矩形平板疊加原理7
2.1 自由振動矩形平板之運動方程式7
2.2 疊加法(Superposition Method)12
第三章 印刷電路板的模態分析22
3.1 四點支撐印刷電路板模態分析22
3.2安插於匯流槽之印刷電路板模態分析31
3.3楔形夾持印刷電路板模態分析36
3.4 印刷電路板上電子元件之模擬40
第四章 印刷電路板統計響應43
4.1移動支撐矩形平板運動的運動方程式43
4.2 印刷電路板在隨機激振下之位移均方值45
4.3 響應關聯方程式(Correlation Equation)47
4.4 遞迴法49
4.5數位模擬56
第五章 數值範例58
5.1 印刷電路板模自然頻率及自然模態58
5.1.1範例一：點支撐印刷電路板60
5.1.2 範例二：匯流槽印刷電路板66
5.1.3範例三：楔形夾持之印刷電路板72
5.2 印刷電路板位移均方值78
5.2.1 範例四：印刷電路板在穩態白噪音過程激振下的位移均方值78
5.2.2 範例五：印刷電路板在穩態非白噪音過程激振下的位移均方值85
第六章 結論與未來展望91
參考文獻93
作者簡介97

參考文獻
﹝1﹞Steinberg, D.S., 1988, Vibration Analysis for Electronic Equipment, John Wily & Son, New York.
﹝2﹞Michael, 1991, Handbook of Electronic Package Design, Marcel Dekker , New York.
﹝3﹞S.J. Ham and S.B. Lee “Experimental Study for Reliability of Electronic Packaging under Vibration”, Experiment Mechanic, Vol. 36, No. 4, December 1996, pp.339-344.
﹝4﹞Sidharth and D.B. Barber “Vibration Induced Fatigue Life Estimation of Corner Leads of Peripheral Leaded Components”, ASME Journal of Electronic Packaging, Vol. 118, December 1996, pp. 244-249
﹝5﹞John Lau, Laura M. Powers-Meloney, James R. Baker, Don Rice and Bob Shaw, “Solder Joint Reliability of Finite Pitch Surface Mount Technology Assembilies”, IEEE Transactions on CHMT, Vol. 13, 1990, pp. 534-544.
﹝6﹞A.W. Leissa 1969 NASA SP-160. Vibration of Plates.
﹝7﹞J.M. Pitarresi, A.A. Primavera, “Comparison of Modeling Techniques for the Vibration Analysis of Printed Circuit Cards”, ASME Journal of Electronic Packaging, Vol. 114, December 1992, pp.378-383.
﹝8﹞G.H. Lim, J.H. Ong, and J.E.T. Penny, “Effect of edge and Internal Point Support of a Printed Circuit Board under Vibration”, ASME Journal of Electronic Packaging, Vol 121, June 1999, pp. 250-257.
﹝9﹞Arturo O. Cifuentes, “Estimating the Dynamic Behavior of Printed Circuit Boards”, IEEE Trans on Components, Packaging, And Manufacturing Technology, Vol. 17 No. 1, February 1994, pp. 69-75.
﹝10﹞光灼華, 林淑芬, “印刷電路板之振動分析”, 中國工程學會第十四屆全國學術研討會, 1997, pp. 221-228.
﹝11﹞D.J. Gorman and R.K. Sharma, “A Comprehensive Approach to the Free Vibration Analysis of Rectangular Plates by Use the Method of Superposition”, Journal of Sound and Vibration, 47, 1976, pp. 126-128.
﹝12﹞D.J. Gorman, “Free Vibration of Rectangular Plates with Symmetrically Distributed Point Supports Along the Edges”, Journal of Sound and Vibration, 73, 1980, pp. 563-574.
﹝13﹞D.J. Gorman, “Free Vibration Analysis of the Completely Free Rectangular Plate by the Method of Superposition”, Journal of Sound and Vibration, 57, 1978, pp. 437-447.
﹝14﹞D.J. Gorman, “An Analytical Solution for The Free Vibration Analysis of Rectangular Plates Resting on Symmetrically Distributed Point Supports”, Journal of Sound and Vibration, 79, 1981, pp. 561-574.
﹝15﹞D.J. Gorman, “Free Vibration Analysis of Cantilever Plates by the Method of Superposition”, Journal of Sound and Vibration, 49, 1976, pp. 453-467.
﹝16﹞D.J. Gorman and R.K. Singal, “Analytical and Experimental Study of Vibrating Rectangular Plates on Rigid Point Supports”, AIAA Journal, Vol. 29, No. 5, 1991, pp. 838-844.
﹝17﹞D.J. Gorman, “A General Solution for the Free Vibration of Rectangular Plates Resting on Uniform Elastic Edge Supports”, Journal of Sound and Vibration, 139, 1990, pp. 325-335.
﹝18﹞D.J. Gorman 1999, Vibration Analysis of Plates by the Superposition Method, World Scientific.
﹝19﹞C.Y. Tang 1986, Random vibration of structures, Wiley, New York.
﹝20﹞D.E. Newland 1993, An Introduction to Random Vibration and Spectral Analysis, Longman.
﹝21﹞Y.K. LIN, Probabilistic Theory of Structural Dynamics, McGraw-Hill, New York, 1976.
﹝22﹞T.T. Song and Mircea Grigoriu 1993, Random Vibration of Mechanical and Structural System, Prentice-hall, New York.
﹝23﹞R.A. Ibrahim, Parametric Random Vibration, John Wiley and Sons, Hertfordshire, England, 1985.
﹝24﹞W.D. Iwan and P.-T. Spanos, “Response Envelope Statistics for Nonlinear Oscillators With Random Excitation”, ASME Journal of Applied Mechanics, Vol. 45, March, 1978, pp. 170-174.
﹝25﹞C.W.S. To, “An Implicit Direct Integrator for Random Response of Multi-Degree-of-Freedom Systems”, Computers & Structures, Vol. 33. No.1, 1989, pp. 73-77.
﹝26﹞M. Shinozuka, “Simulation of Stochastic Process by Spectral Representation”, Appl. Mech. Rev. Vol. 44, No. 4, April 1991, pp. 191-203.
﹝27﹞J.-N. Tang, ”On the Normality and Accuracy of Simulated Random Processes”, Journal of Sound and Vibration, 26, 1973, pp. 417-428.
﹝28﹞M. Shinozuka and C.-M. Jan, “Digital Simulation of Random Processes and Its Applications”, Journal of Sound and Vibration, 25, 1972, pp. 111-128.
﹝29﹞J.C. Roberts and D.M. Stillo, “Random Vibration Analysis of a Printed Wring Board with Electronic Component”, J. IES, vol. 35, no. 1, 1991, pp.25-31.
﹝30﹞Wei Huang, Dimitri B. Kececioglu and John L. Prince, “A Simplified Random Vibration Analysis on Portable Electronic Products”, IEEE Transaction on Components and Packaging Technology, vol.23, no. 3, 2000, pp.505-515.
﹝31﹞A.W. Leissa, “The Free Vibration of Rectangular Plates”, Journal of Sound and Vibration, 31, 1973, pp. 257-277.
﹝32﹞D.J. Johns and R. Nataraja, “Vibration of Sqare Plate Symmetrically Supported at Four Points”, Journal of Sound and Vibration, 25, 1972, pp.75-82.
﹝33﹞A.W. Leissa, “Recent Research in Plate Vibrations: Classical Theory”, Shock Vib. Dig., 9(10), 1977, pp. 13-14.
﹝34﹞A.W. Leissa, “Plate Vibration Research, 1976-1980: Classical Theory”, Shock Vib. Dig., 13(9), 1981, pp. 11-22.
﹝35﹞呂理宏, 呂森林, “平板於非白噪音空氣動力壓力下振動之研究”, 中國工程學會第十四屆全國學術研討會, 1997, pp. 199-205.