Nonlinear vibration of third-order shear deformable FG-GPLRC beams under time-dependent forces: Gram–Schmidt–Ritz method

Abstract

This study presents nonlinear vibration of functionally graded-graphene platelet-reinforced composite (FG-GPLRC) beams under various time-dependent forces. Their material distributions are characterized by continuous functions with four patterns of reinforcement which are uniform, linear and parabolic I and II. The third-order shear deformation theory is used to represent the displacement fields, while the geometric nonlinearity is based on the von Kármán assumption. The Gram–Schmidt–Ritz method is utilized with iteration process to obtain the linear and nonlinear results. Several effects such as weight fraction of graphene nanoplatelets, types of material distributions, beam geometry, etc. on nonlinear dynamic deflection of the beams are investigated. It is found that the beams reinforced by graphene nanoplatelets mostly near the top and bottom faces are stronger than those with other different patterns of reinforcement. The comparison between the responses of continuous and multi-layers FG-GPLRC beams is presented. Some new results of FG-GPLRC beams are given and discussed in details and they can be considered as a benchmark solution for future investigations.