Isogeometric analysis for size-dependent nonlinear free vibration of graphene platelet reinforced laminated annular sector microplates

Abstract

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.