The Theoretical Analysis of Mechanical and Electrical Field of Piezoelectric Materials for Multi-Layered, Wedge shape and circlular boundary problems

• Main Authors: Wang Szu Yuan, 王思元
• Other Authors: 馬劍清
• Format: Others
• Language: zh-TW
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/27663250611977010469

碩士 === 國立臺灣大學 === 機械工程學研究所 === 91 === 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 anti-plane deformation with the in-plane electric field is studied by mathematical analysis. The geometric configuration of the problems include the infinite plane, the multilayered medium, the wedge shape and the circular ring. The Fourier transform technique in conjunction with the image method 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. Furthermore, the image method is extended to solve the problems of wedge shape and circular boundary with the aid of conformal mapping. The problems of screw dislocation in piezoelectric materials are also investigated by analytical method in this paper. 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 screw dislocations are discussed in detail from numerical calculations.