中文摘要：

针对含压电层功能梯度材料（FGM）悬臂板的非线性动力学问题,提出了基于von-Karman理论和Reddy三阶剪切变形理论的FGM板动力学方程,建立了以表面覆盖（P/FGM/P）和埋置压电层（FGM/P/FGM）的FGM板模型,利用Galerkin法对偏微分方程组进行离散,通过Runge-kutta算法求解方程组并对系统进行数值分析,得出控制电压和压电层铺设方式对系统非线性动力学行为有很大的影响,板的横向振幅随着正电压的升高而减小,随着负电压的增大则增大,另外控制电压对P/FGM/P混合板振动的影响更为显著。

英文摘要：

To solve problem of the nonlinear dynamics of FGM cantilever plate with piezoe1ectric layers,the governing equations of FGM plate are proposed,based on von-Karman theory and Reddy＇s third-order shear deformation plate theory.FGM cantilever plate with piezoe1ectric layers embedded（FGM/P/FGM） and covering the surface（P/FGM/P） is discussed,including thermal and mechanical effects.Galerkin method is used to reduce the nonlinear partial differential equations to ordinary non-linear ones;Runge-kutta numerical simulation is used to solve and analyze the equations.The influences of control voltage and different piezoe1ectric layers models on the nonlinear vibration are discussed,and control voltages have a more significant influence on amplitude of（P/FGM/P） plate.