带压电层功能梯度悬臂板非线性动力学分析

Nonlinear dynamics of a functionally graded rectangular cantilever plate with piezoelectric

分析了在热环境条件下受横向载荷作用的、带压电功能梯度材料悬臂板的非线性动力学问题。基于von Karman理论和Reddy一阶剪切变形理论,推导出了带压电功能梯度悬臂板的动力学方程。利用Galerkin法对偏微分方程进行离散,对离散后的方程进行数值模拟,分析中考虑了组分材料热物参数对温度变化的依赖性,讨论了材料组分指数、控制电压对系统非线性动力学行为的影响,结果表明正电压减小了板的振幅,负电压增大了板的振幅,而随着材料体积分数指数的增大,板的振幅也在变大。

The nonlinear dynamics of a functionally graded rectangular cantilever plate with piezoelectric subjected to transverse loads in thermal environments is investigated in this paper. The governing equations of the functionally graded plate are based on yon Karman theory and Reddy＇ s first-order shear deformation plate theory that includes thermal effects. Galerkin method is used to reduce the non-linear partial differential equations to ordinary non-linear differential equations. The influences of gradient con- stants and control voltage on the nonlinear vibration are discussed. The results show that the positive voltage decreases the amplitude while the negative voltage increases the amplitude of the plate. With the increase of N, the oscillation amplitude increases.