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研究生： 孫嘉鴻
Sun, Chia-Hung
論文名稱： 應用微分值積法於三維矩形平板之挫曲及動態分析
Three-Dimensional Buckling and Vibration Analyses of Rectangular Plates by the Differential Quadrature Method
指導教授： 崔兆棠
Choi, Siu-Tong
學位類別： 碩士
Master
系所名稱： 工學院 - 航空太空工程學系
Department of Aeronautics & Astronautics
論文出版年： 2005
畢業學年度： 93
語文別： 中文
論文頁數： 67
中文關鍵詞： 微分值積法 、三維 、挫曲 、振動
外文關鍵詞： vibration, buckling, three-dimensional, differential quadrature method
相關次數： 點閱：81  下載：1 
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    • 　　本論文提出以微分值積法來分析三維矩形平板之挫曲及動態特性。平板的控制方程是以三維彈性理論為基礎，經過無因次化和微分值積法則轉換成代數方程組，從而求出三維矩形平板之挫曲負載或自然頻率。本文的動態分析方面探討了在不同邊界條件、長寬比和厚寬比對三維矩形平板之自然頻率的影響，而挫曲分析方面探討了在單軸或雙軸負載下不同邊界條件、長寬比和厚寬比對平板之挫曲因子的影響。本文所得結果與文獻的正確解或近似解比較皆相當吻合，所以使用微分值積法分析三維矩形平板的問題可以提供準確的結果。

    　This thesis presents an application of the differential quadrature method for three-dimensional buckling and vibration analyses of rectangular plates. The governing equations of rectangular plates are based on the three- dimensional elasticity theory. The formulation of differential quadrature is applied to transform the governing equations into algebraic ones, the eigenvalues of which are buckling loads or natural frequencies of rectangular plates. The influences of aspect ratio and thickness-to-width ratio on natural frequencies of rectangular plates with different boundary conditions are studied. In addition, the buckling factors of rectangular plates with different boundary conditions under uni- and bi-axial loadings are obtained. The present DQ solutions show good agreement when compared with exact or approximate solutions. It is found that the DQM presents accurate result for three-dimensional analyses of rectangular plates.

    摘要..........................................................i 英文摘要.....................................................ii 致謝.........................................................iii 表目錄.......................................................vi 圖目錄......................................................viii 第一章 緒論................................................1 1-1研究動機..............................................1 1-2 文獻回顧..............................................3 1-3 本文研究..............................................8 第二章三維矩型平板之控制方程式............................10 2-1 控制方程式...........................................10 2-2 邊界條件.............................................12 2-3 無因次化.............................................13 第三章 微分值積法.........................................16 3-1 微分值積法原理.......................................16 3-2 取樣點...............................................20 3-3 微分值積法的應用.....................................20 3-4 求解過程.............................................23 第四章 數值結果與討論.....................................24 4-1 收斂性與準確性分析...................................24 4-2 三維矩形平板的振動分析...............................28 4-3 三維矩形平板的挫曲分析...............................29 第五章 結論.................................................30 參考文獻....................................................32 自述........................................................67

    1. Leissa, A. W., The free vibration of rectangular plates, Journal of Sound and Vibration 31, 257-293, 1973.

    2. Kanaka Raju, K. and Hinton, E., Natural frequencies and modes of rhombic Mindlin plates, Earthquake Engineering and Structural Dynamics 8, 55-62, 1980.

    3. Lim, C. W., Liew, K. M. and Kitipornchai, S., Numerical aspects for free vibration of thick plates. Part I: Formulation and verification, Computer Methods in Applied Mechanics and Engineering 156, 15-29, 1998

    4. Lim, C. W., Liew, K. M. and Kitipornchai, S., Numerical aspects for free vibration of thick plates. Part II: Numerical efficiency and vibration frequencies, Computer Methods in Applied Mechanics and Engineering 156, 31-44, 1998.

    5. Liew, K. M., Hung, K. C. and Lim, M. K., A continuum three-dimensional vibration analysis of thick rectangular plates, International Journal of Solids and Structures 30, 3357-3379, 1993.

    6. Srinivas, S., Rao, C. V. and Rao, A. K., An exact analysis for vibration of simply supported homogeneous and laminated thick rectangular plates, Journal of Sound and Vibration 12, 187-199, 1970.

    7. Fromme, J. A. and Leissa, A.W., Free vibration of the rectangular parallelepiped, Journal of the Acoustical Society of America 48, 290-298, 1970.

    8. Cheung, Y. K. and Chakrabarti, S., Free vibration of thick, layered rectangular plates by a finite layer method, Journal of Sound and Vibration 21, 277-284 1972.

    9. Leissa, A. W. and Zhang, Z. D., On the three-dimensional vibrations of the cantilevered rectangular parallelepiped, Journal of the Acoustical Society of America 73, 2013-2021, 1983.

    10. Srinivas, S. and Rao, A. K., Buckling of thick rectangular plates, American Institute of Aeronautics and Astronautics Journal 7, 1645-1646, 1969.

    11. Srinivas, S. and Rao, A. K., Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates, International Journal of Solids and Structures 6, 1463-1481, 1970.

    12. Brunelle, E. J., Buckling of transversely isotropic Mindlin plates, American Institute of Aeronautics and Astronautics Journal 9, 1018-1022, 1971.

    13. Roufaeil, O. L. and Dawe, D. J., Rayleigh-Ritz vibration analysis of rectangular Mindlin plates subjected to membrane stresses, Journal of Sound and Vibration 85, 263-275, 1982.

    14. Cheung, Y. K., Chan, A. H. and Tham, L. G., A study of the linear elastic stability of Mindlin plates, International Journal of Numerical Methods in Engineering 22, 117-132, 1986.

    15.Wittrick, W. H., Analytic, three-dimensional elasticity solution to some plate problems, and some observations on Mindlin’s plate theory, International Journal of Solids and Structures 23(4), 441-464, 1987.

    16. Doong, J. L., Vibration and stability of an initially stressed thick plate according to a high-order deformation theory, Journal of Sound and Vibration 113, 425-440, 1987.

    17. Brunelle, E. J. and Robertson, S. R., Vibrations of an initially stressed thick plates, Journal of Sound and Vibration 45, 405-416, 1976.

    18. Wang, C. M., Liew, K. M., Xiang, Y. and Kitipornchi, S., Buckling of rectangular Mindlin plates with internal line supports, International Journal of Solids and Structures 30, 1-17, 1993.

    19. Bellman, R. E. and Casti, J., Differential quadrature and long-term integration, Journal of Mathematical Analysis and Application 34, 235-238, 1971.

    20. Civan, F. and Sliepcevich, C. M., Differential quadrature for multi-dimensional problems, Journal of Mathematical Analysis and Application 101, 423-443, 1984.

    21. Bert, C. W., Jang, S. K. and Striz, A. G., Two new approximate methods for analyzing free vibration of structural components, American Institute of Aeronautics and Astronautics Journal 26, 612-618, 1988.

    22. Shu, C. and Richards, B. E., Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations, International Journal for Numerical Methods in Fluids 15, 791-798, 1992.

    23. Bert, C. W., Wang, X. and Striz, A. G., Differential quadrature for static and free vibration analysis of anisotropic plates, International Journal of Solids and Structures 30, 1737-1744, 1993.

    24. Wang, X., Striz, A. G. and Bert, C. W., Free vibrational analysis of annular plates by the DQ method, Journal of Sound and Vibration 164, 173-175, 1993.

    25. Leissa, A. W., Vibration of Plates, NASA SP-160, 1969.

    26. Du, H., Liew, K. M. and Lim, M. K., Generalized differential quadrature method for buckling analysis, ASCE Journal of Engineering Mechanics 122, 95-100, 1996.

    27. Wang, X. and Bert, C. W., A new approach in applying differential quadrature to static and free vibration analyses of beams and plates, Journal of Sound and Vibration 162, 566-572, 1993.

    28. Malik, M. and Bert, C. W., Implementing multiple boundary conditions in the DQ solution of higher order PDE’s: application to free vibration of plates, International Journal for Numerical Methods in Engineering 39, 1237-1258, 1996.

    29. Choi, S. T. and Chou, Y. T., Vibration analysis of elastically supported turbomachinery blades by the Modified Differential Quadrature Method, Journal of Sound and Vibration 240, 937-953, 2001.

    30. Malik, M. and Bert, C. W., Three-dimensional elasticity solutions for free vibration of rectangular plates by the differential quadrature method, International Journal of Solids and Structures 35, 299-318, 1998.

    31. Teo, T. M. and Liew. K. M., Three-dimensional elasticity solutions to some orthotropic plate problems, International Journal of Solids and Structures 36, 5301-5326, 1999.

    32. Liew, K. M. and Teo, T. M., Three-dimensional vibration analysis of rectangular plates based on differential quadrature method, Journal of Sound and Vibration 220, 577-599, 1999.

    33. Hung, K. C., A Treatise on Three-Dimensional Vibration of a Class of Elastic Solids, Ph. D. Thesis, Nanyang Technological University, Singapore, 1996.

    34. Teo, T. M. and Liew, K. M., A differential quadrature procedure for three-dimensional buckling analysis of rectangular plates, International Journal of Solids and Structures 36, 1149-1168, 1999.

    35. Xiang, Y., Numerical Developments in Solving the Buckling and Vibration of Mindlin Plates, Ph.D. Thesis, The University of Queensland, Australia, 1993.

    36. Hinton, E., Numerical Methods and Software for Dynamic Analysis of Plates and Shell, Pineridge Press, Swansea, U.K., 1978.

    37. Gorman, D. J., Free Vibration of Rectangular Plates, Elsevier North Holland: New York, 1982.

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