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研究生： 謝榮哲
Hsieh, Rong-Che
論文名稱： 應用微分值積法於異向性材料平板之三維振動分析
Three-Dimensional Vibration Analysis of Anisotropic 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： 2006
畢業學年度： 94
語文別： 中文
論文頁數： 66
中文關鍵詞： 配置法 、正交性 、微分值積法
外文關鍵詞： Differental Quadrature Method, orthotropic, Collocation Method
相關次數： 點閱：84  下載：1 
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    • 摘要
    題 目：應用微分值積法於異向性材料平板之三維振動分析
    研 究 生：謝榮哲
    指導教授：崔兆棠

    本論文提出以微分值積法來分析異向性材料平板之三維動態特性。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，從而求出異向性材料平板之自然頻率。本文探討了不同邊界條件、材料性質、厚寬比和長寬比對異向性材料平板之自然頻率的影響。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異向性矩形平板的問題可以提供準確的結果。

    Abstract

    Subject:Three-Dimensional Vibration Analysis of
    Anisotropic Rectangular Plates by the
    Differential Quadrature Method

    Student:Rong-Che Hsieh

    Adviser:Siu-Tong Choi

    This thesis presents an application of the differential quadrature method for three-dimensional vibration analyses of rectangular paltes of anisotropic material. The governing equations of anisotropic plates are based on
    the three-dimensional elasticity theory. The formulation of differential quadrature is applied to transform the governing equations
    of free vibration of anisotropic plates into algebraic ones, from which natural frequencies of anisotropic plates are obtained. The influences of different material, thickness-
    to-width ratio and lenth-to-width ratio on natural frequencies of anisotropic rectangular plates with different boundary conditions are studied. 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 anisotropic plates.

    目 錄 摘要..........................................................................i 英文摘要 ....................................................................ii 誌謝 .......................................................................iii 表目錄.......................................................................vi 圖目錄.......................................................................ix 第一章 緒論...................................................................1 1-1 前言..................................................................1 1-2 研究動機..............................................................3 1-3 文獻回顧..............................................................4 1-4 本文研究..............................................................8 第二章 異向性材料平板之統御方程式............................................10 2-1平板之統御方程式......................................................10 2-2邊界條件..............................................................12 2-3無因次化..............................................................13 第三章 微分值積法............................................................15 3-1微分值積法原理........................................................15 3-2 取樣點分布...........................................................18 3-3 微分值積法之應用.....................................................19 3-4 邊界條件修正矩陣的調整...............................................22 3-5求解過程..............................................................24 第四章 數值結果與討論........................................................25 4-1 收斂性與準確性分析...................................................25 4-2 正交性材料平板之振動分析.............................................28 4-3 單斜晶系材料平板之振動分析...........................................29 4-4 三角晶系材料平板之振動分析...........................................30 4-5 六角晶系材料平板之振動分析...........................................31 第五章 結論..................................................................32 參考文獻.....................................................................34 自述.........................................................................66 表 目 錄 表4-1 材料係數...............................................................38 表4-2 不同邊界條件正交性方型平板在不同取樣點下的無因次自然頻率(c/b=0.1)......39 表4-3 SSSS正交性方型平板在不同厚寬比下的無因次自然頻率.......................40 表4-4 SSSS平板面內扭曲振動模態頻率公式解.....................................41 表4-5 CCCC正交性方型平板在不同厚寬比下的無因次自然頻率.......................42 表4-6 CFCF正交性方型平板在不同厚寬比下的無因次自然頻率.......................43 表4-7 SCSC正交性方型平板在不同厚寬比下的無因次自然頻率.......................43 表4-8 CCFF正交性矩形平板在不同厚寬比和長寬比下的無因次自然頻率...............44表4-9 CFFF正交性矩形平板在不同厚寬比和長寬比下的無因次自然頻率...............44 表4-10 SSFF正交性矩形平板在不同厚寬比和長寬比下的無因次自然頻率..............45 表4-11 SFFF正交性矩形平板在不同厚寬比和長寬比下的無因次自然頻率..............45 表4-12 SSSS單斜晶系方型平板在不同厚寬比下的無因次自然頻率....................46 表4-13 CCCC單斜晶系正方平板在不同厚寬比下的無因次自然頻率....................47 表4-14 CFCF單斜晶系方型平板在不同厚寬比下的無因次自然頻率....................48 表4-15 SCSC單斜晶系方型平板在不同厚寬比下的無因次自然頻率....................48 表4-16 CCFF單斜晶系矩形平板在不同厚寬比和長寬比下的無因次自然 頻率...........49 表 4-17 CFFF單斜晶系矩形平板在不同厚寬比和長寬比下的無因次自然頻率...........49 表4-18 SSFF單斜晶系矩形平板在不同厚寬比和長寬比下的無因次自然頻率............50 表4-19 SFFF單斜晶系矩形平板在不同厚寬比和長寬比下的無因次自然頻率............50 表4-20 SSSS三角晶系方型平板在不同厚寬比下的無因次自然頻率....................51 表4-21 CCCC三角晶系方型平板在不同厚寬比下的無因次自然頻率....................52 表4-22 CFCF三角晶系方型平板在不同厚寬比下的無因次自然頻率....................53 表4-23 SCSC三角晶系方型平板在不同厚寬比下的無因次自然頻率....................53 表4-24 CCFF三角晶系矩形平板在不同厚寬比和長寬比下的無因次自然頻率............54 表4-25 CFFF三角晶系矩形平板在不同厚寬比和長寬比下的無因次自然頻率............54 表4-26 SSFF三角晶系矩形平板在不同厚寬比和長寬比下的無因次自然頻率............55 表4-27 SFFF三角晶系矩形平板在不同厚寬比和長寬比下的無因次自然頻率............55 表4-28 SSSS六角晶系方型平板在不同厚寬比下的無因次自然頻率....................56 表4-29 CCCC六角晶系方型平板在不同厚寬比下的無因次自然頻率....................57 表4-30 CFCF六角晶系方型平板在不同厚寬比下的無因次自然頻率....................58 表4-31 SCSC六角晶系方型平板在不同厚寬比下的無因次自然頻率....................58 表4-32 CCFF六角晶系矩形平板在不同厚寬比和長寬比下的無因次自然頻率............59 表4-33 CFFF六角晶系矩形平板在不同厚寬比和長寬比下的無因次自然頻率............59 表4-34 SSFF六角晶系矩形平板在不同厚寬比和長寬比下的無因次自然頻率............60 表4-35 SFFF六角晶系矩形平板在不同厚寬比和長寬比下的無因次自然頻率............60 圖 目 錄 圖2-1 三維矩形平板座標示意圖.................................................61 圖4-1 CCFF正交性方型平板之振動模態圖(厚寬比0.1)..............................62 圖4-2 CFFF正交性方型平板之振動模態圖(厚寬比0.1)..............................63 圖4-3 SSFF正交性方型平板之振動模態圖(厚寬比0.1)..............................64 圖4-4 SFFF正交性方型平板之振動模態圖(厚寬比0.1)..............................65

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