This article presents the mode shape and frequency analysis of graphene nanoplatelets reinforced composite (GPLRC) microdisk surrounded by viscoelastic foundation using a non-classical continuum theory called modified couple stress theory (MCST). The boundary conditions and non-classical governing equations of size-dependent GPLRC microstructure are derived by adding the higher-order stress and symmetric rotation gradient tensors to the strain energy. The current non-classical model is capable of capturing the size-dependency in the composite microsystem using only one material length scale parameter. Moreover, the mathematical formulation of the GPLRC microdisk based on the classical model can be recovered from the present model by neglecting the material length scale parameter. Finally, the generalized differential quadrature element method (GDQEM) is applied for solving the governing equations are solved using various sets of boundary conditions. Afterward, a parametric study is carried out to study the impacts of the radius ratio, length scale parameter, radial and circumferential mode number, geometry of GPLRC material, and boundary conditions on the frequency responses of the current microsystem by considering MCST. The results demonstrate that when the material length scale factor improves, the impact of the damping factor on the natural frequency of the microsystem decreases.

本文介绍了使用称为修正偶应力理论 (MCST) 的非经典连续介质理论对粘弹性基础包围的石墨烯纳米片增强复合材料 (GPLRC) 微盘的振型和频率分析。通过将高阶应力和对称旋转梯度张量添加到应变能中，导出了尺寸相关 GPLRC 微结构的边界条件和非经典控制方程。当前的非经典模型能够仅使用一种材料长度尺度参数来捕获复合微系统中的尺寸依赖性。此外，通过忽略材料长度尺度参数，可以从现有模型中恢复基于经典模型的 GPLRC 微盘的数学公式。最后，广义微分正交元法 (GDQEM) 用于求解控制方程 使用各种边界条件求解。然后，通过参数研究，通过考虑 MCST 来研究半径比、长度尺度参数、径向和圆周模式数、GPLRC 材料的几何形状和边界条件对当前微系统频率响应的影响。结果表明，当材料长度比例因子提高时，阻尼因子对微系统固有频率的影响减小。通过考虑 MCST，径向和圆周模式数、GPLRC 材料的几何形状以及当前微系统频率响应的边界条件。结果表明，当材料长度比例因子提高时，阻尼因子对微系统固有频率的影响减小。通过考虑 MCST，径向和圆周模式数、GPLRC 材料的几何形状以及当前微系统频率响应的边界条件。结果表明，当材料长度比例因子提高时，阻尼因子对微系统固有频率的影响减小。