臺灣博碩士論文加值系統

在探討非等向性中空圓盤在旋轉的情況下，以一階剪切變形板理論與古典板理論的理論基礎，假設五個獨立的變數得到三個方向的位移，使用漢米敦原理，由能量法找出運動方程式。再利用迦了金方法假設符合邊界條件與運動方程式的解的形式，代入統御方程式可以求解垂直方向的自然振動頻率。在內徑固定，外徑自由的邊界條件下，以自然振動與受穩態載重的情形，討論幾何條件、轉速與材料性質對自然頻率與振幅的影響，藉此探討兩種平板理論的適用範圍。再配合有限元素法數值模擬軟體ABAQUS來求解圓盤轉動的問題，與理論解做比較。

In discussing problems about rotating anisotropic annular disk, by Mindlin plate theory and classical plate theory, we assume five unknowns to acquire displacement of three directions with Hamilton principle and find out equation of motion by energy method. Then we assume the forms of solution that satisfy the boundary conditions and equation of motion with Galerkin method and substitute them in to governing equation to solve the natural frequency of transverse vibration. In the boundary condition that inside clamped and outside traction free, discussing the influence of geometric conditions, angular velocity and material on natural frequency and amplitude, we study the application of these two plate theory in free vibration and under static loading. Finally we solve the problem of rotating disk with the finite element analysis software ABAQUS to compare with theoretical solution.

第一章 導論………………………………………………………………………1
1.1 研究動機與目的………………………………………………………1
1.2 研究方法………………………………………………………………1
1.3 文獻回顧………………………………………………………………2
1.4 本文大綱……………………………………………………………3
第二章 非等向性材料的性質與平板理論
2.1 非等向性材料………………………………………………………….5
2.2 剪切板理論 ( Mindlin Plate Theory )…………………………………7
2.3 古典板理論 ( Classical Plate Theory )……………………………….11
第三章 剪切板理論
3.1 漢米敦原理 ( Hamilton''s Principle )對於質點和物體的分析………13
3.2 位能與動能……………………………………………………………16
3.2-1 應變能…………………………………………………………16
3.2-2 轉動效應………………………………………………………18
3.2-3 系統的非保守能………………………………………………18
3.2-4 系統的動能……………………………………………………19
3.3 統御方程式之推導……………………………………………………20
3.4 邊界條件………………………………………………………………22
3.5 解題方法………………………………………………………………25
3.5-1 Galerkin Method ……………….……………………………...25
3.5-2 無因次化解題…………………………………………………33
3.6 Static load對圓盤的穩態響應………………………………………..36
第四章 利用古典板理論解圓盤轉動問題
4.1 位能與動能………………………………………………………………….38
4.1-1 系統的位能……………………………………………………38
4.1-2 系統的動能……………………………………………………40
4.2 漢米敦原理推導統御方程式………………………………………….41
4.3 解題方法……………………………………………………………….43
4.4 Static Load對圓盤的穩態響應………………………………………..51
4.5 軸對稱時之古典板理論推導…………………………………….……52
第五章 結果與討論
5.1 自由振動……………………………………………………………….56
5.2 靜態負載……………………………………………………………….61
5.3 ABAQUS數值解……………………..………………………………..63
第六章 結論與未來展望…………………………………………………………64
文獻參考……………………………………………………………………………..66
附表…………………………………………………………………………………..68
附圖…………………………………………………………………………………..81
附錄A……………………………………………………………………………….100

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