層域系統壓電材料之力學與電學耦合的平面問題解析

The Theoretical Analysis of Multi-Layered In-plane Problems for Mechanical and Electrical coupled Piezoelectric Materials

吳文加(wu wen-cha)

指導教授 ： 馬劍清

國立臺灣大學/工學院/機械工程學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.00680

摘要

由於現今工業中壓電材料廣泛應用於各類電子元件如壓電致動器與壓電感測器，因此對於壓電材料系統之相關問題須提出完整的理論架構與分析方法，則壓電材料在工程應用上才可更清楚掌握方向。本文以完整的數學方法解析橫向等向性壓電材料之平面力學與平面電學耦合的二維問題，從簡單的壓電無窮域問題探討至較為困難的壓電多層域問題。
在文中對於不同邊界條件的問題各以不同形式之全場解析解形式表示，主要以傅力葉轉換與逆轉換方法求解出具有映射法物理意義的級數解析解，以及必須做數值積分求得全場數值解的壓電多層域問題。
由於材料內部的缺陷將對壓電材料在應用上造成壽命的影響，因此本文對於差排在壓電材料內受到映射力的形式有完整的描述與探討。映射力形成的方式可由邊界，材料界面，以及差排間互相作用產生，藉由映射力大小即可推測差排移動的方向與裂縫產生的位置，在瞭解這些特性後，我們就可以分析與設計所需求的壓電材料。

關鍵字

理論 ； 平面問題 ； 壓電

並列摘要

The piezoelectric effect is applied to many engineering applications because it couples the electrical and mechanical fields. Currently, piezoelectric materials are widely used in electromechanical sensors, actuators and electro-optic modulators. Hence a detailed investigation on piezoelectric materials is needed. In this paper, piezoelectric materials with transversely isotropic symmetry that couples the in-plane deformation with the in-plane electric field is studied by mathematical analysis. The geometric configuration of the problems include the infinite plane and the multilayered medium.
The Fourier transform technique are used to analyze the boundary value problem. The analytical solutions presented with function or series forms are dependent on the complexity of the problem. For the general multilayered medium, a numerical inversion of the Fourier transform is used.
The problems of line dislocation in piezoelectric materials are also investigated by analytical method. The image forces exerted on dislocations are given in explicit forms with the aid of Peach-Koehler equation. The stress and electrical fields, and image forces exerted on line dislocations are discussed in detail from numerical calculations.

並列關鍵字

piezoelectric ； in-plane problem

參考文獻

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