考虑几何与压电非线性行为压电层合轴对称圆板的精确解

研究可移简支及夹支边界条件下,轴对称压电层合圆板在强电场和机械荷载联合作用下的非线性变形.考虑电致伸缩的非线性压电效应及几何非线性的影响,导出轴对称压电层合圆板的控制方程.通过调整坐标轴的位置对控制方程进行简化,得到关于挠度和径向力的4阶非线性控制方程.再通过简单的积分并引入无量刚变量将控制方程等价地化为2阶非线性耦合微分方程组.利用幂级数法得到可移简支及夹支边界条件下强电场和均布荷载共同作用时的挠度、径向力及径向位移的幂级数精确解.通过对双、单压电晶片执行器的数值计算及分析,得到电场、外载对于位移、径向力的影响关系.

Exact Solution of Piezoelectric Laminated Axisymmetric Circular Plates Considering Geometric and Piezoelectric Nonlinearity

The nonlinear deformations of simply supported and fixed supported piezoelectric laminated axisymmetric circular plates are investigated under strong combined electric field and mechanical load.The governing equations of axisymmetric piezoelectric laminated circular plates are obtained as viewed from the nonlinear electrostrictive piezoelectric effects and geometric nonlinearity.The simplified 4 order nonlinear equations with regard to deflection and axial force are obtained by adjusting the location of coordinate,then transformed into 2 order coupled dimensionless nonlinear equations.The exact solution of deflection,axial force and radial displacement of the plates under two boundary conditions are evaluated.The numerical simulation for bimorph and unimorph piezoelectric circular plates verifies the nonlinear deformations and axis-force affected by electric field and load.