摘要

本文將探討具壓電加強環雙跨距圓柱薄殼結構的自由振動特性，並考慮基本圓柱薄殼中心面與壓電加強環中心線之位移與轉角和橫斷面之剪切效應及轉動慣量。首先建立第i個跨距圓柱薄殼之應力場、應變場與位移場之關係，利用漢彌爾頓原理進而推導圓柱薄殼結構的運動方程式，而後在利用轉換矩陣法計算分析殼-壓電環整體結構自由振動之模態頻率與相對應之模態形狀函數，最後再探討幾何參數對結構物的模態頻率之影響。
在有限元素法方面，則使用靜態本構方程式推導出其位移場之通解，再藉由應變能項與動能項計算出結構的勁度矩陣與質量矩陣，進而利用Lagrange’s equation 解出系統的模態頻率，且選取不同數目之元素來堆疊此結構，並將結果與模態法之結果作ㄧ比較，進一步確定有限元素法的可行性。在加入適當的電壓找出其具壓電加強環雙跨距圓柱薄殼結構整體之變形。

Abstract

Free vibration characteristics of cylindrical shells with ring-stiffener of piezoelectric are studied. The effects of rotatory inertia and transverse shearing strain of both the shell and stiffener are considered. Further, the warping effect of stiffener also is included. An analytic method is presented to obtain the modal frequencies and their corresponding mode shape functions of the shell with ring-stiffener of piezoelectric.
The shape functions of one element of shell are obtained by solving the equations static equilibrium. Then, the technique of finite element is employed to compute the modal frequencies of the entire structure. The modal frequencies obtained from finite element computation and analytic method, respectively, will be compared to show the feasibility of finite element computation. The effected of applied voltage on the deformation of shell will be investigated.

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