Free vibration of functionally graded-GPL reinforced composite plates with different boundary conditions

A first order shear deformation theory based finite element approach is used in this paper to investigate the free vibration behaviour of functionally graded thin, moderately thick and thick multi-layer composite plates reinforced with graphene nanoplatelets (GPLs). The effect of four different layer-wise variations of GPL distribution along the thickness and all possible plate edge boundary condition combinations on the natural frequencies of the plate are investigated. The effective Young's modulus for each layer and distribution type is determined using the modified Halpin-Tsai model, and mass density and Poisson's ratio are calculated based on the rule of mixture. Initially, present results are verified by comparing with available reported results. Thereafter, the method is used to conduct a parametric study, focusing on the effect of length to thickness ratio, different boundary conditions, GPL distribution patterns, percentage weight fraction of GPL, and geometry and size of GPL on the natural frequencies and percentage increase in natural frequencies.