Nonlinear vibration characteristics of pre- and post-buckled FG-GRMMC laminated plates with in-plane auxeticity

The nonlinear vibration of a laminated plate constituting of graphene reinforced metal matrix composite (GRMMC) materials possessing in-plane negative Poisson's ratio in pre-and post-buckled status is investigated in this work. The volume fraction of graphene remains constant in each layer but changes along the thickness direction of the plate to obtain functionally graded (FG) patterns. The plate rests on a Pasternak-type foundation and the post-buckling state of the plate is only caused by the thermal load or the compressive edge load. The nonlinear motion equations of the plate with the effect of the out-of-plane shear deformation are established and then solved by a two-step perturbation approach. The perturbation solutions provide a platform to study the influences of the FG arrangement, volume fraction of graphene and foundation stiffness on the post-buckled vibration of FG-GRMMC laminated plates. As the GRMMC material properties are dependent on temperature, the thermal effect on the linear and nonlinear frequencies of the plates for compressive post-buckling is also investigated. The numerical results of the linear and nonlinear frequencies of post-buckled FG GRMMC laminated plates under thermal and compressive loads are respectively illustrated and discussed in detail.