| Summary: | 碩士 === 國立成功大學 === 機械工程學系 === 85 ===
In this paper, free axisymmetric and antisymmetric vibrations of an annular or non-annular plate of variable thickness have been studied on the based on the classical theory of plates. The plate is elastically restrained against rotation, translation and in-plane forces along the edges and its thickness can be expressed in terms of power series. The Frobenius method is employed to solve the forth order ordinary differential equation and obtained four linearly independent fundamental solutions, then we can express an exact, closed-form general solution in terms of the four fundamental solutions. By differentiating the four fundamental solutions with respect to radial coordinate triple, we can see two of them are singular at the origin. For a non-annular plate, the frequency equations are expressed in terms of four fundamental solutions; For an annular plate, the frequency equations can be expressed only in terms of two of the four fundamental solutions which are regular at the origin after been differentiated triple with respect to radial coordinate. Finally, examples about uniform and nonuniform plates are given and the results are compared with those in the existing literature to illustrate the accuracy and validity of the analysis.
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