纵向脉冲作用下压电层合杆的动力分析

Dynamic Analysis of Piezoelectric-Elastic Layered Bar Under Longitudinal Impulse

利用波动理论对自由端受瞬时纵向冲击力作用下的压电层合杆进行了动力分析,在截面平面假设下,建立了力电耦合下层合杆的波动方程;用Laplace变换方法对波动方程式进行求解,求得了位移和电势的解析表达式;给出了杆内不同时间段的位移场和电势场的传播规律以及它们之间的关系,讨论了弹性模量以及弹性层和压电层厚度比对波场传播速度、位移及电势的影响。计算结果表明:杆中电势沿高度方向为线性分布,纵向脉冲传播的速度随弹性模量的增大而增加,但随压电层的厚度增加而减小。

Using the theory of wave motion,the dynamical property of a piezoelectric-elastic layered bar under longitudinal impulse loads at the free end was analyzed. The equations of wave propagation in the layered bar were established on the plane cross-section assumption. Displacement and electric potential expressions were obtained by solving the equations with Laplace transform. The relationship between the displacement and the electric potential and their propagation in the bar were given. The influences of elastic modular and the thickness ratio of piezoelectric layer and elastic layer on wave speed,displacement and electric potential were discussed. The result shows that the electric potential distributes linearly along the thickness direction,and the velocity of longitudinal impulse increases with the Young modulus and reduces with the increase of piezoelectric layer thickness.