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| 研究生： |
李政儒 Li, Jheng-Ru |
|---|---|
| 論文名稱： |
非均勻 Timoshenko 曲樑的平面外振動分析 Out-of-Plane Vibrations of a Curved Non-uniform Timoshenko Beam |
| 指導教授： |
李森墉
Lee, Sen-Yung |
| 學位類別： |
碩士 Master |
| 系所名稱： |
工學院 - 機械工程學系 Department of Mechanical Engineering |
| 論文出版年： | 2010 |
| 畢業學年度： | 98 |
| 語文別： | 英文 |
| 論文頁數： | 53 |
| 中文關鍵詞： | 平面外振動 、Timoshenko曲樑 、非均勻樑 、自由振動 |
| 外文關鍵詞： | out-of-plane vibration, curved Timoshenko beam, non-uniform beam, free vibration |
| 相關次數： | 點閱：99 下載：2 |
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於非均勻 Timoshenko 曲樑的平面外振動分析中，首先利用漢米爾頓原理求得三個耦合的微分方程式，進而藉由兩個具有物理意義的參數簡化原來三個耦合的微分方程式以便於分析。經由消去縱向位移及彎曲旋轉角後，三個耦合的微分方程式非耦合化，而成為一個以扭轉旋轉角為因變數的六階微分方程式。縱向位移及彎曲旋轉角亦可表示成以扭轉旋轉角為因變數的關係式。如果非均勻曲樑的材料及幾何變化可利用多項式的形式表示，那麼非均勻 Timoshenko 曲樑的平面外振動真確解即可獲得。最後再以一些極端的例子來說明推導的正確性，並討論邊界條件、曲樑錐度、曲樑細長比、及曲樑中心角對第一、二和三自然頻率的影響。
The three coupled governing differential equations for the out-of-plane vibrations of a curved non-uniform Timoshenko beam are derived via the Hamilton’s principle. Two physical parameters are introduced to simplify the analysis. By eliminating all the terms with the flexural displacement parameter, then reducing the order of differential operator acting on the angle parameter of the rotation due to bending, one uncouples the three governing characteristic differential equations with variable coefficients and reduces them into a sixth-order ordinary differential equation with variable coefficients in terms of the torsional angle for the first time. The explicit relations between the flexural displacement and the angle of the rotation due to bending and the torsional angle are also revealed. It is shown that if the material and geometric properties of the beam are in arbitrary polynomial forms, then the exact solutions for the out-of-plane vibrations of a curved non-uniform Timoshenko beam can be obtained. Several limiting cases are studied. Finally, the influence of the boundary conditions, the taper ratio, the slender ratio, and the arc angle parameter on the first three natural frequencies of the curved beams is explored.
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校內：2012-07-29公開校外：2012-07-29公開