本文提出一簡單且相對完整的位移場，透過軸對稱有限元素的列式，可以分析圓形板及環形板的自由振動，以及在預加負載（包含常見的徑向負載與尚未出現於文獻上的扭轉負載）下之振動情形。
本文對於圓形板及環形板之自由振動及圓形板及環形板承受壓應力下之振動所求得之數值，將分別與ANSYS及部分參考文獻作比較，以了解本文所採用的方法與其他的理論或模擬之間的差異，並探討幾何形狀及邊界條件對於整體結構之自然振動頻率的影響，依據本文所計算而得之結果可知，此法不須對圓板或圓環作過多的切割，即可求得準確之振動頻率。
至於在扭轉預加負載作用下的圓柱及圓管的振動情形，本文的分析結果發現，含有耦合r-z平面與θ方向的振動，這是以往的分析都不曾出現的振動模態，而其原因則是由於本文的位移場所得到的耦合項所造成的結果。

The present study proposes a simple and relatively complete displacement field, which, with the finite element formulation, can be employed in the analyses of the free vibration of circular and annular plates, the vibration with preloading in the radial direction, which is studied quite often, and the vibration with preloading under twisting, which has not yet appeared in the literature.
The present results of the free vibration and the vibration under compressive stresses for circular and annular plates with different boundary conditions and various aspect ratios will be compared with those by ANSYS and other research. From the comparisons, we know that the present method does not need a fine mesh to get accurate natural frequencies of the plates.
As to the vibration for the bar or tube with pretorsional loading, coupled vibration modes in the r-z plane and θ direction, it can be revealed by the present method, and the appearance of these vibration modes may be due to the coupling terms from the proposed displacement field. Also, these vibration modes have not been shown before.

中文摘要 I
Abstract II
Directory III
List of Figures V
List of Tables VI
Symbol Table VIII
1. Introduction 1
2. Vibration Analyses of Circular Plates With and Without Preloading 3
2.1 Free vibration of circular plates 6
2.2 Vibration analyses of circular plates subjected to preloading 7
3. Analysis 11
4. Results and Discussions 17
4.1 Free vibration of circular and annular plates 17
4.2 Vibration analyses of circular and annular plates subjected to radial compression 17
4.3 Vibration analyses of circular and annular cylinders subjected to end twisting 18
5. Conclusions 36
References 37
Appendix 39

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14.李英德，中華民國八十九年一月，博士論文，中山大學機械工程研究所，軸對稱負載作用下圓形板及環形板之三維振動分析。