平面应变轴对称压电圆柱壳的随机响应

Random response of piezoelectric axisymmetric cylinder shells in plane strain

提出求解随机激励轴对称压电圆柱壳响应的一种方法,并导出相应的解析表达式。首先给出压电圆柱壳在边界随机激励下的基本方程;然后通过位移与电势的变换,将随机激励变换到运动方程中;再利用L egendre多项式展开位移,应用G a lerk in法化偏微分的运动方程为常微分方程组;最后根据随机振动理论,得到压电圆柱壳位移与加速度响应的均方值,由此可计算随机响应、分析有关因素的影响与机电耦合关系等。分析说明了存在的机电耦合项,及由此产生广义刚度的非对称性。

Piezoelectric structures as a smart sensor system have potential application in engineering. The stochastic vibration of piezoelectric structures is a significant research subject. In the present paper, an approach to solving the stochastic response of piezoelectric axisymmetric cylinder shells is proposed and the analytical expressions for solution are obtained. Firstly, the basic equations of a piezoelectric cylinder shell subjected to boundary stochastic excitations are given. Then, the excitations are incorporated in the differential equations of motion by using the transformations of displacements and electric potentials. And the displacement of the shell is expanded as a series of the Legendre polynomial in space. The partial differential equation of motion is converted into ordinary differential equations by using the Galerkin method. Finally, the expressions of mean-square displacement and acceleration of the shell are derived according to the theory of random vibration. The effects of stochastic excitations on mean-square response, electric potential, and the electrical and mechanical coupling characteristics can be analyzed. It is pointed out that there exists the asymmetry of generalized stiffness matrix due to the electrical and mechanical coupling relationship.