压电圆柱体在冲击外力作用下动应力与瞬态电势的动态效应和响应历程

Dynamic focusing effect and response histories of piezoelectric solid cylinders subjected to impact pressures on the external boundary

提出了一种简便的求解压电圆柱体在冲击外力作用下的动应力和瞬态电势的响应历程的解析方法.在求解过程中,将压电圆柱体动力学耦合场方程的解看成是由一个满足非齐次混合边界条件的电弹性准静态解和一个仅满足齐次混合边界条件的电弹性动态解的叠加.通过有限汉克尔变换、Lap lace变换及其反变换,获得压电圆柱体在冲击外力作用下的动应力和瞬态电势的解析表达式.实例计算结果表明,对于不同材料的压电圆柱体圆心处的动应力和瞬态电势的动态集中效应有所不同,并且随着电弹性波在柱体外边界的不断反射和波头在圆心处的不断会聚碰撞,会产生各种不同的周期性振荡.

A simply analytical method was presented to solve the response histories of dynamic stresses and transient electric potential in piezoelectric solid cylinders subjected to impact pressures on the external boundary. During the course of solving, the electroelastic dynamic equilibrium equation is decomposed into a homogeneous quasi-static equation,which satisfies the inhomogeneous boundary conditions, and an inhomogeneous dynamic equation,which satisfies homogeneous boundary conditions. Utilizing the finite Hankel transform, Laplace transform and their inverse transformation, the analytical expressions of dynamic stresses and transient electric potential in the piezoelectric solid cylinder are obtained. From practical examples, it is found that dynamic focusing effect of dynamic stresses and transient electric potential at the center of piezoelectric solid cylinders are dependent on different piezoelectric materiak. Because electroelastic waves accumulate at the center, and reflect at the external boundary, the dynamic stresses and transient electric potential occur in periodic oscillation.