简支矩形压电薄板弯曲的解析解

Analytical Solution of Simply supported Rectangular Piezoelectric Thin Plate

基于薄板小挠度弯曲理论,忽略平面内电场强度,推导了压电板弯曲的平衡方程,分别采用Navier和Levy解法,获得了四边简支矩形压电薄板位移、应力和电势的解析表达式,数值算例表明两种解析方法所得结果一致。研究了厚度对压电矩形薄板弯曲特性的影响,对比不同压电材料矩形薄板弯曲特性,分析了压电板位移和电势与其材料参数之间的关系。

Piezoelectric plate bending equilibrium equation is derived based on the thin plate bending theory and ignoring in-plane electric field.Navier and Levy methods are used to obtain the analytical expressions of a simply supported rectangular piezoelectric plate displacement,stress and electric potential.Numerical examples show that the results by two different analytical methods are consistent.The effect of piezoelectric rectangular thin plate thickness on bending behavior is also studied.The relation between material parameters and displacement as well as electric potential of piezoelectric plate are analyzed by comparing the bending properties of different piezoelectric material plate.