Nonlinear resonance of graphene platelets reinforced metal foams plates under axial motion with geometric imperfections

In this paper, nonlinear resonance behavior of graphene platelets reinforced metal foams (GPLRMFs) plates under axial motion with initial geometric imperfections is investigated. Material properties, graphene platelets (GPLs) and foams of the plate are assumed to be symmetric with respect to the thickness direction. The Euler-Lagrange principle is employed to derive the equations of motion. Then, the Galerkin principle is applied to discrete nonlinear equations of motion, thus the nonlinear partial differential equations are transformed into nonlinear ordinary differential equations, the single degree of freedom of Duffing equation is obtained by reducing the dimension of the five nonlinear ordinary differential equations and determined by the perturbation method. Numerical results are presented to investigate the effects of the GPLs pattern, the foams distribution, the foams coefficient, the weight fraction of GPLs, the temperature change, axial moving velocity, and the external load on the resonance problem of the GPLRMFs plates under axial motion with geometric imperfections. It can be found that axial moving velocity and initial geometric imperfection have significant impacts on the resonance phenomena.