Acta Scientiarum Naturalium Universitatis Pekinensis

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Solution and Potential Function for Boussinesq Problem of Transversely Isotropic Piezoelectric Media

LI Xiangyong, WANG Minzhong   

  1. Department of Mechanics and Engineering Science, Peking University, Beijing, 100871
  • Received:2005-11-04 Online:2006-09-20 Published:2006-09-20



  1. 北京大学力学与工程科学系,北京,100871

Abstract: Based on the symmetry properties of the material constants, the Boussinesq solution in analytic form was obtained by Fourier transforms for a transversely isotropic piezoelectric half-space submitted with a normal point force and a point charge. The associated potential function was also discussed. By Fourier transforms method, the boundary value problem of partial differential equations was transformed to algebraic equations. Then by the principle of superposition and solving two sets of algebraic equations, the interaction between the point force and the point charge was uncoupled. Compared with the tentative semi-inverse method, the method in this paper is direct and effective.

Key words: transversely isotropic piezoelectric media, Boussinesq solution, potential function

摘要: 基于横观各向同性压电材料的材料系数具有一定的对称性,通过Fourier变换求出了半空间受法向点力与点电荷时的Boussinesq解的解析表达式,并讨论了相应的势函数。文中直接从偏微分方程组的边值问题出发,运用Fourier变换把偏微分方程组转换为代数方程组。利用线性叠加原理,通过求解两组代数方程组,从而分离出点力与点电荷的耦合作用。文中的方法具有直接性,取代了具有试探性的半逆解法。

关键词: 横观各向同性压电材料, Boussinesq解, 势函数

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