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

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 reinforcement which uniform, linear and parabolic I II. The third-order shear deformation theory is used to represent the displacement fields, while geometric nonlinearity based on von Kármán assumption. Gram–Schmidt–Ritz method utilized iteration process obtain results. Several effects such as weight fraction graphene nanoplatelets, types distributions, beam geometry, etc. dynamic deflection investigated. It found that reinforced nanoplatelets mostly near top bottom faces stronger than those other different reinforcement. comparison between responses multi-layers FG-GPLRC presented. Some new results given discussed in details they can be considered a benchmark solution for future investigations.