压电板壳自由振动的三维精确分析

本文简要评述了压电材料板壳结构的研究现状，着重介绍了近年来我们在压电板壳三维分析方面所做的工作：（1）四边简支横观各向同性压电矩形板的状态空间分析方法：（2）横观各向同性压电圆板和环板的状态空间分析方法；（3）横观各向同性压电圆柱壳和球面各向同性压电球壳耦合振动的精确分析。这些工作都直接从压电弹性力学三维基本方程出发，不引进任何变形假设，因此可作为二维简化理论和数值计算方法的校核标准。文末对今后压电材料板壳的研究方向也作了展望。

Three-Dimensional Exact Analyses of Free Vibrationsfor Piezoelectric Plates and Shells

The present situation of studies on piezoelectric plate and shell structures is briefly reviewed in the paper. Special emphasis is given to the works done recently by us on the three-dimensional analyses of piezoelectric plates and shells. These include: (1) state space method for the analysis of simply supported transversely isotropic piezoelectric rectangular plates, (2) state space method for the analysis of transversely isotropic piezoelectric circular and annular plates, and (3) coupled vibration analyses of transversely isotropic piezoelectric cylindrical shells and spherically isotropic piezoelectric spherical shells. These works are all based on the three-dimensional equations of piezoelasticity without the introduction of assumptions on deformation, and can be the check standard of two-dimensional approximate theories and numerical methods. The research trend of this area in the future is also forecasted in the end of the paper.