The effects of different parameters on the nonlinear dynamic characteristics of macrofiber composite (MFC) microsheet with graphene (GP) skin under non-uniform thermal field are investigated. Firstly, the physical parameters of the MFC–GP structure are calculated by the mixing rule, and the constitutive equations of the structure are set up by employing the Eringen theory. The nonlinear dynamic equations of the microsheet are obtained by using Hamilton’s principle. Then, the heat conduction equations of the microsheet are considered, adopting Green and Naghdi’s generalized thermoelasticity theory. According to the Galerkin weighted residual method, the thermoelasticity coupling equations of the structure are obtained. Meanwhile, the influence of the positive piezoelectric effect of GP and MFC on the vibration response of the structure is also investigated. The nonlinear dynamic governing equations including displacement, coupled thermoelasticity, and electricity field are discretized by the Galerkin method. The effects of non-local parameter, volume fraction of GP, and thermal and electricity coupling coefficients on structural dynamic behavior are discussed in the numerical simulation.

中文翻译：

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非均匀热场中石墨烯蒙皮复合微片的非线性动力学

研究了不同参数对非均匀热场下具有石墨烯（GP）表层的大纤维复合材料（MFC）微片的非线性动力学特性的影响。首先，利用混合法则计算出MFC-GP结构的物理参数，并采用Eringen理论建立结构本构方程。微薄板的非线性动力学方程是根据汉密尔顿原理获得的。然后，采用格林和纳格迪的广义热弹性理论，考虑了微片的导热方程。根据Galerkin加权残差法，得到了结构的热弹性耦合方程。与此同时，还研究了GP和MFC的正压电效应对结构振动响应的影响。非线性动态控制方程包括位移，耦合热弹性和电场，通过Galerkin方法离散化。在数值模拟中讨论了非局部参数，GP的体积分数以及热电耦合系数对结构动力特性的影响。