The subharmonic resonances of an axially moving graphene-reinforced laminated composite plate are studied based on the Galerkin and multiscale methods. Graphene nanoplatelets (GPLs) are added into matrix material which acts as the basic layer of the plate, and a graphene-reinforced nanocomposite plate is thus obtained. Different GPL distribution patterns in the laminated plate are considered. The Halpin–Tsai model is selected to predict the physical properties of the nanocomposite. Hamilton’s principle is utilized to conduct the dynamic modeling of the plate and the von Kármán deformation theory is used. The velocity is assumed to be a combination of constant and harmonically varied velocities. The natural frequencies of the linear system with constant velocity can be obtained using the eigenvalues of the coefficient matrix of the ordinary differential equations after the governing partial differential equations of motion are discretized through the Galerkin method. The instability regions of the linear system and the amplitude–frequency relations of the nonlinear system considering the harmonically varied velocity are obtained based on the multiscale analysis. The effect of GPL reinforcement on the subharmonic resonances of the linear and nonlinear systems is analyzed in detail.

基于伽辽金和多尺度方法研究了轴向移动石墨烯增强层合复合材料板的次谐波共振。将石墨烯纳米片（GPL）添加到作为板材基础层的基体材料中，从而获得石墨烯增强纳米复合材料板材。考虑了层压板中不同的 GPL 分布模式。选择 Halpin-Tsai 模型来预测纳米复合材料的物理性能。利用汉密尔顿原理对板进行动力学建模，并采用冯卡门变形理论。假设速度是恒定速度和谐波变化速度的组合。通过伽辽金法对运动控制偏微分方程进行离散化后，利用常微分方程系数矩阵的特征值可以得到恒速线性系统的固有频率。基于多尺度分析，得到了线性系统的不稳定区域和考虑简谐变速的非线性系统的幅频关系。详细分析了GPL增强对线性和非线性系统的次谐波谐振的影响。