压电材料静力耦合机理的三维解析及简化分析

Three Dimensional and Simplified Analysis on Static Electromechanical Mechanism of Piezoelectric Materials

在三维压电材料本构方程的基础上，推导出了用位移和电势表示的三维横观各向同性材料的平衡微分方程．考虑到平面问题的广泛性，推导得到了三维压电材料的弹性常数在二维情况下的表达式，为二维理论分析作出了准备．同时，还考察了受垂直于极性轴的轴向力的压电材料的三维解析解，得到了这种情况下的位移和电势分布情况．进而。

Some basic problems of three dimensional piezoelectric materials were discussed. On the basis of the constitutive equations of three dimensional piezoelectric materials, the equilibrium differential equations of three dimensional transverse isotropic materials in terms of displacements and voltage were derived. Considering the popularity of plane problems, the expression of the elastic constant of three dimensional piezoelectric materials under two dimensional condition were also derived, which made preparations for the two dimensional theoretic analysis. Meanwhile, the three dimensional analytical solutions of piezoelectric materials under actions of the axial force vertical to polaxis were investigated to obtain the displacement and voltage distribution under this situation. The relationship between elastic constants and engineering constants of piezoelectric materials was analyzed.