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 本文根據von Karman 幾何大變形理論，推導一54 個自由度高精確度的高階三角形板元素，用來分析與討論複合層板在承受溫度場改變的熱挫屈後之自由振動行為。當溫度高於臨界挫屈溫度時，可將層板之位移分為靜態位移與動態位移。靜態位移為熱挫屈後層板之變形量，利用Newton-Raphson 疊代法可求得後挫屈的靜態位移。在動態分析部分，則利用Hamilton 定理推導出動態平衡方程式後，並且帶入後挫屈靜態位移，便可在頻率域中求得自然頻率與振動模態，文中考慮兩種熱膨脹係數不同的材料，並探討其對自然頻率與振動模態所造成的影響。結果顯示對於正交性複合層板而言，因熱膨脹係數的影響，T300/5208 層板較早發生挫屈，並產生變形，使得層板之自由頻率逐漸高於AS4/3501-6 層板。另外在後挫屈範圍內，當展弦比越高，基礎振動模態越會被高階振動模態所取代。對於角交性複合層板而言，纖維角度影響著層板之彎曲勁度與x、y 方向的熱膨脹量，間接地造成自然頻率的改變，結果顯示當挫屈模態發生轉移時，會造成層板之勁度急速的改變，因此振動模態會劇烈變化。如果層板是受到非均勻溫度變化的影響，則層板的變形越大時，會改變模態排列順序，而且在挫曲模態轉移時，振動模態的改變較緩慢，且沒有振動模態的頻率會降至零。
 Base on the von karman large deflection plate theory, a 54 degree-of-freedom high precision higher order triangular plate element is developed for free vibration of thermally buckled composite laminated plate. For buckled plate, the total response of the plate is assumed to be the sum of displacement due to the buckled static deformation and that due to small dynamic deformation. The static deflection of the buckled plate is solved by using Newton Raphson iteration method. The natural frquency and free vibration mode of the plate can then be obtained in frequency domain after applying the static thermal postbuckling deflections into the equation of motion. Two different laminates are considered due to their distinct thermal expansionproperty. Results show that T300/5208 cross-ply laminate will be buckled earlier than the AS4/3501-6 laminate that makes the T300/5208 laminate stiffer and in term gives higher natural frequencies. The higher vibration mode of the cross-ply laminates will become the fundamental mode when the aspect ratio of plate goes higher. For the angle-ply laminates, a buckle pattern　change may occur in the post-buckling region and the natural frequencies of the laminates will also be changes abruptly. If the laminate is subjected to temperature gradient through the thickness, the plate becomes more stiffer and none of the natural frequencies will drop to zero as the temperatureincreases. Also, the vibration mode shift induced by buckle pattern change will occur slowly.
 目錄中文摘要………………………………………I英文摘要………………………………………Ш誌謝……………………………………………V目錄……………………………………………VI表目錄…………………………………………VIII圖目錄…………………………………………IX符號說明………………………………………XII第一章緒論……………………………………11.1 研究動機…………………………………11.2 文獻回顧…………………………………11.4 研究架構…………………………………5第二章公式推導………………………………72.1 複合層板基本公式………………………72.2 應變能與動能……………………………92.3 有限元素推導……………………………102.4 動態方程式………………………………152.5 求解流程…………………………………16第三章複合層板熱挫屈後之自由振動………183.1 程式驗證…………………………………183.2複合層板之熱挫曲自由振動行為………………………………………………………19 3.2.1 Cross-ply 正交對稱複合層板…………………………………………………19 3.2.2 Angle-ply 角交對稱複合層板…………………………………………………243.3 溫度梯度效應……………………………………………………………………………28第四章　　結論………………………………………………………………………………31參考文獻……………………………………………………………33附錄…………………………………………………………………37表……………………………………………………………………39圖……………………………………………………………………41自述…………………………………………………………………68著作權聲明………………………………………………………69
 1. Bisplinghoff, R. L., and Pian, T. H. H., ”On the vibrations of thermally buckled bars and plates,” Proceedings of 9th International Congress for Applied Mechanics, Vol. 7, pp. 307-318, 1957.2. Yang, T. Y., and Han, A. D., ”Buckled plate vibrations and large amplitude vibrations using high-order triangular elements,” AIAA Journal, Vol. 21,No. 5, pp. 758-766, 1983.3. Tang, S., ”Natural vibration of isotropic plates with temperature-dependent properties,” AIAA Journal, Vol. 7, No. 4, pp. 725-727, 1969.4. Bailey, C. D., ”Vibration of thermally stress plates with various boundary conditions,” AIAA Journal, Vol. 11, No. 1, pp. 14-19, 1973.5. Dhotarad, M. S., and Ganesan, N., ”Vibration analysis of rectangular plate subjected to thermal gradient,” Journal of Sound and Vibrations, Vol. 60,No. 4, pp. 481-497, 1978.6. Ganesan N., ”Vibration of heated plates with two opposite edges simply supported,” Journal of Sound and Vibrations, Vol. 66, pp. 99-107, 1979.7. Rajagopal, S. V., Singh, G., and Rao Y. V. K. S., ”Large-deflection and nonlinear vibration of multilayered sandwich plates,” AIAA Journal, Vol.25, No. 1 ,pp. 130-133, 1987.8. Singh, J. P., and Dey, S. S., ”Transverse vibration of rectangular plates subjected toinplane forces by a difference based variational approach,”Int. J. Mech. Science, Vol. 32, No. 7, pp. 591-599, 1990.9. Gray, C. C., and Mei, C., ”Finite element analysis of thermally post-buckling and vibration of thermally buckled composite plates,”AIAA Paper 91-1239, pp. 2296-3004, 1991.10. Zhou, R. C., Xue, D. T., Mei, C., and Gray, C. C., ”Vibration of thermally buckled composite plates with initial deflections using triangularelements,” AIAA Paper 93-1321, pp. 226-235, 1993.11. Bhimaradd, A., and Chandrashekhara, K., ”Nonlinear vibration of heated anti-sysmmetric angle-ply laminate plates,” Journal of Solid Structure, Vol.30, No. 9, pp. 1255-1268, 1993.12. Lee, D.M., and Lee, I., ”Vibration analysis of stiffened laminated plates including thermally postbuckled deflection effect,” Journal of Reinforced Plastics and Composites, Vol. 16, No. 12, pp. 1138-1153, 1997.13. Liu, C. F. and Huang, C. H., ”Free vibration of composite laminated plates subjected to temperature changes,” Computers and Structures, Vol. 60,pp. 95-101, 1996.14. Shiau, L. C., and Wu, T. Y., ”Free vibration of buckled laminate plates by finite element method,” Journal of Vibration and Acoustics, Vol. 119, pp.635-640, 1997.15. Tenek, L., ”Vibration of thermally stressed composite cylinders,” Vol. 37,No. 11, pp. 1520-1521, 1999.16. Park, J. S., Kim J. H. and Moon, S. H., ”Vibration of thermally post-buckled composite plates embedded with shape memory alloy fibers,”Journal of Composite Structures, Vol. 63, pp. 179-188, 2004.17. Yang, T. Y., ”Finite element structural analysis,” Prentice -Hall, 1986.18. Gibson, F., ”Principles of composite material mechanics,”Mcgraw-Hill, pp. 315-321, 1994.19. Tsai ,”Composite design,” Appendix b unit conversions and ply data b2-b3 , 1988.20. Wu, T.Y., “Geometrically nonlinear analysis of laminate plate by finite element method,” Ph.D.Dissertation, IAA., National Cheng KungUniversity, 1995.21. Kuo, S. Y., ”Aerothermoelastic analysis of composite sandwich Plate”,Ph.D.Dissertation, IAA., National Cheng Kung University, 2002.22. Chen, C. Y., ”Thermal buckling analysis of composite laminates,”M.S.Thesis, IAA, National Cheng Kung University, 2003.23. Chuang, J. W., ”Thermal post-buckling analysis of composite laminate plate,” M.S.Thesis, IAA, National Cheng Kung University, 2003.
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