This paper deals with the nonlinear forced vibration of imperfect penta – graphene plates integrated with piezoelectric actuator layers. The plate is subjected to combination of mechanical, thermal, and electrical loadings. Based on the first order shear deformation plate theory, the governing equations are established taken into account the effect of the von Kármán type of geometrical nonlinearity, the Pasternak type elastic foundations, the damping and the piezoelectric – thermal effects. Four edges of the hybrid plate are assumed to be simply supported and immovable in the in-plane directions. The solution forms that satisfy the boundary conditions are assumed to be trigonometric. The closed form expressions of natural frequency, the frequency ratio – amplitude and the deflection amplitude – time curves are obtained by using the Galerkin and Runge – Kutta methods. The numerical results show positive effects of elastic foundations, negative effect of temperature increment and initial imperfection, considerable effect of geometrical parameters as well as small effect of applied voltage on the nonlinear forced vibration of piezoelectric penta – graphene plate.

本文研究了与压电致动器层集成在一起的不完善的五角石墨烯板的非线性强迫振动。该板要承受机械，热和电载荷的共同作用。基于一阶剪切变形板理论，考虑了vonKármán型几何非线性，Pasternak型弹性基础，阻尼和压电热效应的影响，建立了控制方程。假设混合板的四个边缘被简单地支撑并且在平面内方向上不可移动。满足边界条件的解形式假定为三角函数。固有频率的封闭形式表示，通过使用Galerkin和Runge-Kutta方法可以获得频率比-振幅和偏转振幅-时间曲线。数值结果表明，弹性基础的正效应，温度增量和初始缺陷的负效应，几何参数的显着效应以及施加电压对压电五层石墨烯板的非线性强迫振动的影响很小。