Large amplitude vibration of functionally graded graphene nanocomposite annular plates in thermal environments

Abstract

This paper investigates the large amplitude vibration of functionally graded nanocomposite multilayer annular plates reinforced with graphene platelets (GPLs) in thermal environments. It is assumed that the GPL concentration varies from layer to layer across the plate thickness but remains constant in each individual GPL-reinforced composite (GPLRC) layer, whose elastic modulus is estimated by the modified Halpin-Tsai micromechanics model. Within the framework of first-order shear deformation theory and von Kármán geometric nonlinearity, the governing equations are derived by using the Hamilton’s principle and then solve by the differential quadrature method together with an iterative scheme. Numerical results are presented to show the influences of GPL geometry, distribution pattern and concentration, plate geometry, boundary conditions, as well as temperature rise on the nonlinear vibration behaviour of functionally graded GPLRC annular plates. It is found that dispersing more GPLs within the outer layers substantially decreases the nonlinear frequency ratio, while the effect of GPL geometry is insignificant.