In this paper, a molecular dynamics (MD)-based multiscale analysis is employed to investigate the free vibration of graphene reinforced laminated composite plates from the atomic scale to the macroscopic behavior. The atomic models of graphene with different sizes, poly (methyl methacrylate) (PMMA) and graphene/PMMA composites with different graphene volume fractions are constructed, and Poisson's ratio as well as elastic moduli are in good agreements with the MD results. Then the efficiency parameters of the Young's and shear moduli of graphene/PMMA composites are derived at the micro scale via the extended Halpin-Tsai micromechanics model, and are employed subsequently to the vibration analysis at the macro scale. Based on the first order shear deformation theory and meshless method, the governing equation of functionally graded graphene reinforced composite (FG-GRC) quadrilateral plates is derived and discretized to analyze the vibration behavior. The effects of geometrical parameter, graphene volume fraction and distribution pattern are investigated on the dimensionless frequency of FG-GRC quadrilateral plates. The multiscale analysis in this paper combines the simulation of material properties at the atomic scale and the response of structure at the macro scale, which provides a feasible way to study the vibration behavior of composite structures.

在本文中，基于分子动力学 (MD) 的多尺度分析用于从原子尺度到宏观行为研究石墨烯增强层压复合板的自由振动。构建了不同尺寸石墨烯、聚甲基丙烯酸甲酯(PMMA)和不同石墨烯体积分数的石墨烯/PMMA复合材料的原子模型，泊松比和弹性模量与MD结果吻合良好。然后通过扩展的 Halpin-Tsai 微观力学模型在微观尺度上推导出石墨烯/PMMA 复合材料的杨氏模量和剪切模量的效率参数，并随后用于宏观尺度的振动分析。基于一阶剪切变形理论和无网格方法，推导出功能梯度石墨烯增强复合材料 (FG-GRC) 四边形板的控制方程并对其进行离散化以分析振动行为。研究了几何参数，石墨烯体积分数和分布模式对FG-GRC四边形板无量纲频率的影响。本文的多尺度分析结合了原子尺度的材料特性模拟和宏观尺度的结构响应，为研究复合结构的振动行为提供了一种可行的方法。