本文以改良過的二維軸對稱有限元素分析壓電傳感器的自由振動問題,並且計算壓電傳感器的振動模態,以期能夠對於複合壓電傳感器的設計有所幫助。文中改良二維軸對稱元素,透過適當的三個自由度位移場假設,再加入電場的效應作為第四個自由度,成為分析壓電材料振動的軸對稱元素。
考慮徑向傳感器之設計，本文將分析壓電材料及金屬在不同的配置，半徑大小，以及不同的厚度下之第一徑向振動頻率，並比較共振模態。本文的結果將與其他的文獻作比較,以證實本文分析方法的正確性。

Free vibration of composite piezoelectric transducers is analyzed by a modified two-dimensional axisymmetric finite element in this study. The modified finite element is formulated based on assumed displacement fields and electric potential, and is capable for three-dimensional analyses of vibration of axisymmetric composite piezoelectric structures.
Different arrangements and radius of piezoelectric disk and metal ring, with various thicknesses will be considered and first radial vibration frequencies are derived and their mode shapes are demonstrated, which might be helpful for the design of radial composite transducers. Also, the results of the present study will be compared with those by other methods.

中文摘要
英文摘要
目錄
表目錄
圖目錄
第一章 序論
1-1 前言
1-2 文獻回顧
1-3 研究方法
第二章 壓電理論
2-1 壓電現象
2-2 線彈性壓電理論
2-3 機電耦合因數
第三章 推導軸對稱壓電圓板之運動方程式
3-1 有限元素法推導壓電體之運動方程式
3-2 軸對稱壓電圓板之自由振動理論推導
第四章 複合壓電圓盤之自然振動頻率分析
4-1 電位能邊界條件
4-2 特徵值問題
4-3 文獻比較
4-3-1 複合壓電圓盤徑向振動分析（一）
4-3-2 複合壓電圓盤徑向振動分析（二）
第五章 幾何形狀與複合配置對壓電傳感器振動的影響
5-1 複合壓電圓盤：內層為壓電材料
5-2 複合壓電圓盤：內層為鋼材
5-3 複合壓電圓盤：最內層與最外層為金屬、中間層
為壓電材料
5-4 結論
參考文獻

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