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研究生：	賴政宏 Lai, Cheng-Hung
論文名稱：	應用微分值積法於旋轉截頭圓錐薄殼之自由振動分析 Free Vibration Analysis of Rotating Truncated Conical Shells 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：	2007
畢業學年度：	95
語文別：	中文
論文頁數：	51
中文關鍵詞：	旋轉截頭圓錐薄殼、微分值積法
外文關鍵詞：	Rotating Truncated Conical Shells, Differential Quadrature Method
相關次數：	點閱：71 下載：1
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查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

本文是利用微分值積法（Differential Quadrature Method）來分析封閉式旋轉截頭圓錐薄殼的自然振動行為。文中先建立以Love薄殼理論為基礎的旋轉截頭圓錐薄殼運動方程式，再以微分值積法的規則將旋轉截頭圓錐薄殼的偏微分控制方程式轉化為代數方程式，從而求解特徵值問題可得薄殼之自由振動頻率及模態。本研究的數值結果收斂性良好，且與文獻的結果相符，驗證了使用微分值積法來分析旋轉截頭圓錐薄殼的準確性。本研究探討不同邊界條件、半頂點角、圓錐切割比例對封閉式旋轉截頭圓錐薄殼之自然頻率的影響，數值結果顯示應用微分值積法於旋轉截頭圓錐薄殼的自然振動分析除了相當方便與快速外，更具備了良好的準確性。

In this thesis, the free vibration behavior of rotating truncated conical shells based on Love’s thin shell theory is studied by using the differential quadrature method (DQM). The governing equations of motion of free vibration of rotating truncated conical shell in the differential form are reduced to a set of algebraic equations by applying the differential quadrature formulation. Natural frequencies of the rotating truncated conical shells are obtained. The accuracy of the DQM is assured by comparing numerical results obtained by the DQM with results in the literature. Furthermore, effects of boundary conditions, semi-vertex angle and the ratio of truncation on the natural frequencies of rotating truncated conical shells are studied. Numerical results show the efficiency, good accuracy, and convenience of the DQM.

摘要......................................................i
英文摘要..................................................ii
致謝......................................................iii
表目錄....................................................vi
圖目錄...................................................vii

第一章	緒論..............................................1
  1-1  前言...............................................1
  1-2  研究動機...........................................2
  1-3  文獻回顧...........................................3
  1-4  本文研究...........................................5

第二章	截頭圓錐薄殼之運動方程式..........................7
  2-1  運動方程式.........................................7
  2-2  位移場.............................................8
  2-3  應變-位移與應力-應變關係式.........................9
  2-4  位移運動方程式....................................12
  2-5  邊界條件..........................................14

第三章  微分值積法.......................................16
  3-1  微分值積法的原理..................................16
  3-2  取樣點............................................17
  3-3  修正關係式........................................18
  3-4  微分值積法的應用..................................21
  
第四章  數值模擬結果與討論...............................25
  4-1  收斂性與準確性分析................................25
  4-2  截頭圓錐薄殼與圓柱薄殼............................26
  4-3  旋轉截頭圓錐薄殼與旋轉圓柱薄殼....................28

第五章	結論.............................................30
參考文獻...............................................32
附錄一.................................................35
自述...................................................51

表目錄

表4-1  封閉式截頭圓錐薄殼在不同邊界條件下的無因次基本頻率.38
表4-2   封閉式截頭圓錐薄殼的無因次自然頻率...........39
表4-3   封閉式截頭圓錐薄殼的無因次自然頻率...........39
表4-4   封閉式截頭圓錐薄殼的無因次自然頻率...........40
表4-5   封閉式截頭圓錐薄殼的無因次自然頻率...........41
表4-6   圓柱薄殼的無因次自然頻率.....................42
表4-7   圓柱薄殼的無因次自然頻率.....................42
表4-8  無限長圓柱薄殼的反向振波無因次自然頻率.............43
表4-9  無限長圓柱薄殼的正向振波無因次自然頻率.............44








圖目錄

圖2-1  截頭圓錐薄殼示意圖................................45
圖4-1  邊界條件為 ，不同半頂點角，不同轉速之旋轉截頭圓
錐薄殼的自然頻率參數，(a) ，(b) ，(c) ，
(d) ..........................................46
圖4-2  邊界條件為 ，不同半頂點角，不同轉速之旋轉截頭圓
錐薄殼的自然頻率參數，(a) ，(b) ..........48
圖4-3  邊界條件為 ，不同半頂點角，不同轉速及不同振動波形數之旋轉截頭圓錐薄殼的自然頻率參數，(a) ，(b) ，(c) ..................................49
                                    

參考文獻

[1] R. E. Bellman and J. Casti 1971 Journal of Mathematical Analysis and Application 34, 235-238.“Differential quadrature and long-term integration.”
[2] C. H. Chang 1981 The Shock and Vibration Digest 13, 9-17.
“Vibration of conical shells.”
[3] T. Irie, G. Yamada and Y. Tanaka 1984 Journal of Sound and Vibration 92, 447-453.“Natural frequencies of truncated conical shells.”
[4] C. Shu 1996 International Journal of Mechanical Sciences 38, 935-949.“An efficient approach for free vibration analysis of conical shells.”
[5] Y. L. Wang, R. H. Liu and X. W. Wang 1999 Journal of Sound and Vibration 224, 387-394.“Free vibration analysis of truncated conical shells by the differential quadrature method.”
[6] K. R. Sivadas. 1995 Journal of sound and Vibration 186, 99-109.
“Vibration analysis of pres-stressed rotating thick circular conical
shell.”
[7] K. Y. Lam and L. Hua 1997 International Journal of Solids and Structures 34, 2183-2197.“Vibration analysis of a rotating truncated circular conical shell.”
[8] K. Y. Lam and L. Hua 1999 Journal of Sound and Vibration 223, 171-195.“Influence of boundary conditions on the frequency characteristics of a rotating truncated circular conical shell.”
[9] F. Civan and C. M. Sliepcevich 1984 Journal of Mathematical Analysis and Application 101, 423-443.“Differential quadrature for multi-dimensional problems.”
[10] C. W. Bert, S. K. Jang and A. G. Striz 1988 AIAA Journal 26, 612-618.“Two new approximate methods for analyzing free vibration of structural components.”
[11] C. Shu and B. E. Richards 1992 International Journal of Numerical Methods for Fluids 15, 791-798.“Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations.”
[12] C. W. Bert and M. Malik 1996 ASME Applied Mechanics Review 49 , 1-28.“Differential quadrature method in computational mechanics: a review.”
[13] X. Wang and C. W. Bert 1993 Journal of Sound and Vibration162, 566-572.“A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates.”
[14] S.-T. Choi and Y.-T. Chou 2001 Journal of Sound and Vibration 240,
937-953.“Vibration analysis of elastically supported turbomach- inery blades by the modified differential quadrature method.”
[15] Y.-T. Chou and S.-T. Choi 2000 The Chinese Journal of Mechanics 16, 189-195. “Vibration and buckling analyses of beams by the modified differential quadrature method.”
[16] 周玉端，民國八十九年六月，國立成功大學博士論文，台南市，改良型微分值積法及其元素法於結構力學之應用。
[17] S.-T. Choi, Y.-T. Chou and C.-J. Huang 2002 Journal of the Chinese Society of Mechanical Engineers, 23, 1-9.“Buckling and vibration analyses of rectangular plates by the differential quadrature method.”
[18] K. Y. Lam, L. Hua, T. Y. Ng and C. F. Chua 2002 Journal of Sound and Vibration 251, 329-348.“Generalized differential quadrature method for the free vibration of truncated conical panels.”
[19] W. Soedel 1993 Vibrations of Shells and Plates. New York: Marcel Dekker; Second edition.
[20] A. E. H. Love 1927 A Treatise on the Mathematical Theory of Elasticity. New York: Cambridge University Press; Fourth edition.
[21] K. Y. Lam, L. Hua and T. Y. Ng. Studies in Applied Mechanics 50.“Rotating shell dynamics.”

校內：2014-08-30公開
校外：2016-08-30公開

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