功能梯度压电旋转圆环的三维解析解

3D analytical solution for a piezoelectric rotating annular plate with functionally graded property

基于三维压电弹性力学方程,采用直接位移法,给出横观各向同性功能梯度压电旋转圆环的三维解析解.设功能梯度压电材料参数是厚度坐标z的任意函数,广义位移分量是径向坐标r的幂函数的线性组合,其中含有9个待定的位移函数,它们是坐标z的函数.结合相应的边界条件,求解控制方程,通过直接积分确定位移函数和相应的积分常数,从而确定旋转圆环的力场和电场.算例展示一种材料的梯度指标对力场和电场的影响.

Three-dimensional （3D） analytical solution for a rotating annular plate made of functionally graded materials with transverse isotropy was obtained. It is based on the basic equations of piezoelectricity and the direct displacement method. The material parameters were assumed as the arbitrary functions of thickness coordinate （z）. The general displacement components （displacement and the electric potential） were assumed as a linear combination of the power -functions of radial coordinate （r） with nine undetermined displacement functions. By means of the boundary conditions with direct integral approach, the governing equations of the annular were solved and the displacement functions and integral constants were given. Thus the general stress fields of the rotating annular were determined. Effects played by gradient index on the distributing of elastic and electric fields were studied humerieally in an example.