The proposed work fills a gap of study on size-dependent large amplitude free vibration of functionally graded graphene platelets-reinforced composite (FG-GPLRC) annular sector microplates. Based on a four-variable higher-order shear deformation plate theory, the von Kármán large deflection assumption and the modified couple stress theory (MCST), the governing equations for the discrete nonlinear free vibration of the multilayer FG-GPLRC annular sector microplate without considering the external loads are established by the principle of virtual work. The NURBS-based isogeometric analysis (IGA) in conjunction with a displacement control strategy are utilized synthetically to acquire linear natural frequencies and nonlinear-to-linear natural frequency ratios for the microplates numerically. Comparisons and convergence study are carried out to verify accuracy and correctness of IGA and iteration method in present formulation. Detailed parametric studies are performed to present an insight into the influences of distribution pattern and weight fraction of the graphene platelets, sector angle and material length scale parameter on the behaviors of linear natural frequencies and large amplitude responses of the microplates under different boundary conditions.

拟议的工作填补了功能梯度石墨烯片增强复合材料（FG-GPLRC）环形扇形微板尺寸相关的大振幅自由振动的研究空白。基于四变量高阶剪切变形板理论，vonKármán大挠度假设和修正偶应力理论（MCST），多层FG-GPLRC环形扇形微板离散非线性自由振动的控制方程外部负载是根据虚拟工作原理确定的。基于NURBS的等几何分析（IGA）与位移控制策略结合在一起，可用于以数字方式获取微孔板的线性固有频率和非线性与线性固有频率之比。进行了比较和收敛研究，以验证IGA和迭代方法在当前配方中的准确性和正确性。进行了详细的参数研究，以了解石墨烯血小板的分布模式和重量分数，扇形角和材料长度比例参数对线性自然频率和不同边界条件下微板的大幅度响应的影响。