本文以改良過的三維軸對稱有限元素分析壓電圓盤(環)的三維振動問題，以期能應用在盤(環)形行波式超音波馬達定子的設計中。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，成為能夠分析壓電材料軸對稱與非軸對稱振動的軸對稱元素。
最後由特徵值問題所得到的自然頻率以及模態，討論壓電圓盤(環)作為馬達定子的動態特性：自然頻率、接觸點位置以及橢圓形軌跡，以及在不同幾何形狀下的改變趨勢。本文的結果將與其他文獻做比較。

In order to understand the dynamic characteristics of an ultrasonic motor stator, we proposed a modified two- dimensional axisymmetric finite element model to analyze the three-dimensional vibrational problem of piezoelectric annular and circular plates. In this work, displacement fields are properly assumed and the electric effect is included. Following the finite element method, analyses of axisymmetric and nonaxisymmetric vibration of circular and annular plate, and also the stator of ultrasonic motors can be conducted in a convenient way.
Natural frequency, location of contact point and elliptic locus of the stator are then calculated. Effects by different geometry design and selected circumferential wave number are discussed. Comparisons of some typical examples are made between the present work and those available in the literature.

摘要 …………………………………………………………i
目錄 …………………………………………………………ii
表目錄 …………………………………………………………v
圖目錄 …………………………………………………………vi
第一章 序論 ……………………………………………………1
1-1 前言 ………………………………………………………1
1-2 文獻回顧 …………………………………………………3
1-3 研究方法 …………………………………………………7
第二章 壓電理論 ………………………………………………8
2-1 壓電現象 …………………………………………………8
2-2 線彈性壓電理論 ………………………………………10
2-3 機電耦合因數 …………………………………………16
第三章 軸對稱壓電圓形板及環形板之三維振動分析 ………18
3-1利用有限元素法推導壓電體之運動方程式 ……………18
3-2 軸對稱壓電圓板之三維自由振動理論推導 ……………20
第四章 三維壓電圓盤之自由振動分析 ……………………25
4-1 電位能邊界條件 ………………………………………25
4-2 特徵值問題 ……………………………………………26
4-3 文獻比較 ………………………………………………27
4-3-1 圓形壓電平板自然振動分析(一) …………………27
4-3-2 圓形壓電平板自然振動分析(二) …………………28
4-3-3 環形複合壓電平板自然振動分析(一) ……………28
4-3-4 環形複合壓電平板自然振動分析(二) ……………29
第五章 幾何比例對馬達定子動態特性的影響 ……………41
5-1 行波式超音波馬達簡介 ………………………………41
5-2 定子自由振動特性 ……………………………………44
5-3 單層壓電圓盤 …………………………………………56
5-4 單層壓電圓環 …………………………………………57
5-5 複合壓電圓盤 …………………………………………61
5-6 複合壓電圓環 …………………………………………63
5-7 結論 ……………………………………………………70
5-8 未來研究方向 …………………………………………71
參考文獻 ………………………………………………………73
附錄 ………………………………………………………………77

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