In the current work, an accurate modified couple stress-based cylindrical micro-panel model is developed in the framework of sinusoidal shear deformation theory. The classical strain tensors and curvature tensor components in a modified couple stress-based model are given with consideration of the geometric curve of cylindrical panels. In conjunction with a general Lagrange procedure, the proposed model is implemented to derive a system of Mathieu-Hill equations of governing dynamic stability behaviors of the cylindrical micro-panels. The Navier-type solution and Bolotin's method are applied to predict the principle unstable regions of the micro-panels with simply-supported boundary condition. As an application of the proposed model, the size-dependent stability of a functionally graded graphene nanoplatelets reinforced composite (FG-GNPRC) cylindrical micro-panel under axial oscillation compression is investigated for the first time. It is assumed that the weight fraction of graphene nanoplatelets (GNPs) is graded in the panel thickness. The effective Young's modulus of FG-GNPRC is determined based on a modified Halpin–Tsai model, while the mixture rule used to evaluate the effective Poisson's ratio and the mass density. The parameter studies are performed to examine the effect of dimensionless length parameter, GPL distribution patterns, GPL size and shape, length-to-span ratio and radius-to-span ratio on the size-dependent dynamic stabilities of FG-GNPRC cylindrical micro-panels.

在当前的工作中，在正弦剪切变形理论的框架内建立了一个精确的基于耦合应力的改进的圆柱微面板模型。考虑到圆柱面板的几何曲线，给出了基于耦合应力模型的经典应变张量和曲率张量分量。结合一般的拉格朗日程序，实施所提出的模型以导出控制圆柱微面板动态稳定性行为的Mathieu-Hill方程组。应用Navier型解和Bolotin方法，以边界条件为准的情况预测微面板的主要不稳定区域。作为建议模型的应用，首次研究了功能梯度石墨烯纳米片增强复合材料（FG-GNPRC）圆柱形微面板在轴向振荡压缩下的尺寸依赖性稳定性。假设石墨烯纳米片（GNP）的重量分数按面板厚度分级。FG-GNPRC的有效杨氏模量基于改进的Halpin-Tsai模型确定，而混合规则用于评估有效泊松比和质量密度。进行参数研究以检验无量纲长度参数，GPL分布模式，GPL尺寸和形状，长度与跨度比和半径与跨度比对FG-GNPRC圆柱微管尺寸相关动态稳定性的影响面板。