压电元件驱动的功能梯度弹性薄板的屈曲

考虑功能梯度薄板,其上下表面嵌有压电执行元件.根据逆压电效应将电压转换成作用于板上的等效电载荷.假设梯度材料的弹性参数为板厚度方向坐标的幂函数,基于经典板理论,导出了功能梯度弹性薄板小挠度屈曲平衡微分方程.利用双三角级数展开法,得到了四边简支具有压电元件的功能梯度矩形板的临界屈曲载荷,在此基础上通过数值例子讨论了弹性板的几何尺寸、材料梯度指数的变化对临界电压(载荷)的影响.研究结果表明,材料的梯度指数对临界电压有重要影响,并且通过调整作用于执行元件上的电压的大小和方向,可实现对结构稳定性的有效控制.

The buckling analysis of functionally gradient thin elastic plate bonded piezoelectric patches

For a hybrid rectangular plate comprised of a functionally graded materials substrate and piezoelectric patches perfectly bonded on its top and bottom surfaces as actuators, the equivalent actions were obtained by considering the inverse piezoelectric effect. Based on the classical theory of plate, the equilibrium differential equation was derived for the buckling analysis of thin elastic plate with functionally graded structure considering small deflection. The functionally graded material properties obeyed a power law across the thickness. The critical buckling loads were presented for a simply supported rectangular plate made of functionally graded material bonded piezoelectric patches by using bi-triangle series expansion method. The numerical examples were given and the influences of the plate aspect ratio and functionally gradient index on the buckling voltage were discussed. These results show that the stability can be controlled effectively by means of regulating the magnitude and direction of voltage applied on actuators.