本文使用有限元素列式，透過以線性壓電理論為基礎的變分方程式，假設適當的三個位移場並加入電場作為第四個自由度，分析壓電圓盤受外加電壓負荷下所產生的形變及應力。為了得到比較準確的節點應力，透過應力重建的步驟，由理論上較準確的高斯點應力，經由最小平方法，求取節點應力，以了解壓電體或複合壓電體的應力分布情況。
同時也分析了文獻上幾個型的例子，並與其他分析方法或實驗的結果比較，確立本文方法之可用性以及準確度。

A finite element is formulated to analyze the deflection and stresses of circular and annular piezoelectric plates underloading of applied electrical potential. The element is based on linear piezoelasticity with displacement field and electrical potential properly assumed. To obtain more accurate nodal stresses , stress recovery is applied which derive nodal stresses from the theoretically accurate stresses at Gaussin points by the least square method.
Typical example in the literature are solved by the present method , comparisons are made with those by other methods and experiments to test the validity and accuracy of the present method.

摘要 ……………………………………………………………………i
目錄 ……………………………………………………………………iii
表目錄 …………………………………………………………………v
圖目錄 …………………………………………………………………vi
第一章 緒論 ………………………………………………………1
1–1 前言 ………………………………………………………1
1–2 文獻回顧 …………………………………………………2
1–3 研究方法 …………………………………………………5
第二章 壓電理論 …………………………………………………6
2–1 壓電現象 …………………………………………………6
2–2 線彈性壓電理論 …………………………………………7
第三章 軸對稱壓電圓形板及環形板之運動方程式 ……………15
3–1 採用有限元素法推導壓電體之運動方程式 ……………15
3–2 軸對稱壓電環形板之三維自由振動方程式 ……………17
3–3 電位能邊界條件 …………………………………………20
3–4 應力位移轉換 ………………………………………22
第四章 結果與比較分析 ……………………………………28
4–1 文獻比較 ………………………………………………28
4–1–1 單層圓形壓電平板之分析 ………………………………28
4–1–2 複合圓形致動器分析(一) ………………………………29
4–1–3複合環形致動器分析(二) ………………………………30
第五章 幾何尺寸對於致動器影響 ………………………………42
5–1 單層壓電圓盤 ……………………………………………42
5–2 複合壓電圓盤 ……………………………………………42
5-3 結論 ………………………………………………………47
參考文獻 ………………………………………………………………48
附錄 ……………………………………………………………………51

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