臺灣博碩士論文加值系統

在壓電平板的應用分析上，由於少有適當且實用的靜、動態分析方法，故在壓電應用上多採用有限元素數值法來評估壓電應用的可行性。本篇論文以Timoshenko beam理論與一階剪力變形平板理論(first order shear deformation plate theory)理論配合基本壓電理論來推導一維及二維壓電薄板模型，用以分析壓電薄板在簡支邊界條件下的靜態行為及若干重要模態下的共振頻率。
文中首先分別應用Timoshenko beam理論及一階剪力變形平板理論推導壓電薄板之分析模型，並以六方晶系的壓電陶瓷PZT-4及PIC151為例，分析壓電薄板的若干面內、面外共振頻率和靜態行為。將其分析結果分別和有限元素軟體(ANSYS)、部份實驗數據及傳統方法做比較驗証，同時亦對壓電薄板之行為特性做若干探討。最後以本文所推導之分析方法，對壓電複合疊層應用之靜、動態分析做初步的研究探討。

Except finite element method, there are no analytical approaches to analyze piezoelectric materials and their applications till now. To this end, This thesis presents two general and simple models to examine the electromechanical responses of piezoelectric materials that are modeled as a one dimensional Timoshenko beam and a two dimensional plate, respectively. These two models, with simply supported boundary conditions and appropriate loading conditions, enable analyze static and dynamic responses
Initially, the beam and plate models are respectively deduced from the Timoshenko beam theory and the first-order shear deformation theory. Then, the models are applied to investigate the static and dynamic characteristics. In terms of analyzing PZT-4 and PIC 151 as a beam and plate, respectively, numerical results of the proposed models are compared with those of ANSYS, the equivalent circuit method, and some experimental data from the literature. Finally, composite piezoelectric laminates are further studied by using the proposed models for plates.

第一章 緒論
1.1背景 1
1.2研究動機 4
1.3文獻回顧 7
1.4內容簡介 9
第二章 壓電理論
2.1壓電效應及壓電材料 11
2.2壓電本構方程式 14
第三章 一維壓電薄板模型
3.1一維壓電平板模型之統御方程式推導 20
3.2邊界條件與系統方程之解 28
3.3數值計算與分析 32
3.4結論 34
第四章 二維壓電薄板模型
4.1二維壓電薄板模型之推導 49
4.2簡支邊界條件下之薄板解析 56
4.3數值計算與分析 60
4.4 結論 63
第五章 壓電複合疊層板
5.1壓電薄板疊層分析 77
5.2數值計算與分析………………………………………..80
5.3結論 82
第六章 結論與展望
6.1本文主要成果……………………………………………91
6.2未來研究方向 92
參考文獻
附錄 A
附錄 B

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