Investigated herein are the nonlinear vibration characteristics of a rectangular microsheet comprising micro fiber composite with graphene (GP) skin under coupled excitations. Owing to the good thermal conductivity of GP, the heat sink performance of the GP skin is also considered. In this study, the constitutive relation for the microsheet is established by applying the Eringen theory and the governing equations for nonlinear dynamics of the microsheet are obtained from the principle of conservation of energy. The Green and Naghdi’s generalized thermo-elasticity theory and the Galerkin weighted residual method are employed to describe the thermo-elasticity coupling effect of the MFC-GP microsheet. The positive piezoelectric effects of graphene and MFC are also taken into consideration. Next, the coupled ordinary differential equations of thermo-elasticity-electricity are obtained by the Galerkin discrete method. Finally, the nonlinear frequency response equations of the microsheet are derived through the multi-scale method. By using the global residual harmonic balance method, nonlinear vibration characteristic of the MFC-GP microsheet are discussed with respect to nonlocal parameters, volume fraction of graphene, and aspect ratio, which have a significant impact on the dynamic behaviors of the microsheet. The findings will provide a theoretical guidance for engineering design of such microsheets.

本文研究了矩形微片的非线性振动特性，该矩形微片包括在耦合激励下具有石墨烯（GP）表层的微纤维复合材料。由于GP具有良好的导热性，因此还考虑了GP蒙皮的散热性能。在这项研究中，通过应用Eringen理论建立了微片的本构关系，并从能量守恒原理获得了微片非线性动力学的控制方程。采用格林和纳格迪的广义热弹性理论和Galerkin加权残差法来描述MFC-GP微片的热弹性耦合效应。还应考虑石墨烯和MFC的正压电效应。下一个，通过Galerkin离散法得到热弹性-电耦合的常微分方程。最后，通过多尺度方法推导了微片的非线性频率响应方程。通过使用全局残余谐波平衡方法，针对非局部参数，石墨烯的体积分数和纵横比，讨论了MFC-GP微片的非线性振动特性，这对微片的动态行为有重要影响。这些发现将为此类微片的工程设计提供理论指导。针对非局部参数，石墨烯的体积分数和纵横比，对MFC-GP微片的非线性振动特性进行了讨论，这对微片的动态行为有重要影响。这些发现将为此类微片的工程设计提供理论指导。针对非局部参数，石墨烯的体积分数和纵横比，对MFC-GP微片的非线性振动特性进行了讨论，这对微片的动态行为有重要影响。这些发现将为此类微片的工程设计提供理论指导。