四边简支压电层合厚板的一阶理论解析解

基于一阶剪切变形板壳理论和压电理论,推导了压电层合板结构的基本方程。对四边简支的压电层合板在四边接地、上下表面受外加电压及无外加电压作用时进行了解析求解,求得了电势和位移的表达式,给出了压电层和基体的挠度及电势分布图。

An Analytical Solution to the Static Analysis of a Simply-Supported Piezoelectric Thick Plate

This paper presents an exact Navier-type analytical solution to bending problems of a transversely isotropic piezoelectric thick square plate constructed with three laminas, piezoelectric-elastic-piezoelectric layer. The first-order shear deformation theory is extended to include the piezoelectric response of laminated plate structures. The analytic solutions of deflection and electric potential of the simply-supported smart plate are all obtained by means of the Fourier's series. The electric boundary conditions are being grounded along four vertical edges. The external voltage or non-external voltage on the surfaces of piezoelectric layers is considered. The convergence of the present approach is studied. The electric potential and displacement distribution diagrams of the piezoelectric layers and matrix are also provided. The numerical results show that the moderately thick piezoelectric plate is sensitive to shear deformation.