四边简支压电功能梯度矩形薄板的屈曲

Buckling Analysis of Simply-supported Piezoelectric Functionally Gradient Rectangular Thin Plate

基于经典板理论,假设材料的电弹参数为板厚方向坐标的幂函数,采用含压电耦合项的修正层合理论,推导了压电功能梯度薄板在电载荷作用下的屈曲方程,并利用Navier解,得到四边简支矩形薄板在均匀电场下的屈曲临界电压.在此基础上,讨论了板的几何尺寸、材料梯度指数的变化和中面变形等因素对临界电压(电载荷)的影响.结果表明,压电材料的梯度化对其稳定性产生较大的影响.

Based on the classical plate theory and assumption the electroelastic properties varying with a power form of thickness coordinate variables, the buckling equations of piezoelectric functionally gradient thin plate subjected to applied electric field are derived by means of a modified classical laminate theory involving piezoelectric coupling terms. Critical voltage for a simply-supported rectangular thin plate under uniform electric field is presented by using Navier solutions. The influences of the geometrical size of plate, functionally gradient index and displacement at mid-plane of plate on the critical voltage are discussed. It was found that the effects of the gradient index are significant, so we should pay more attention to checking the buckling intensity in designing and applying piezoelectric functionally gradient materials.