Nonlinear free vibration analysis of the rectangular conductive elastic plate in magnetic field based on homotopy perturbation method

Abstract This article tries to investigate the nonlinear free vibrations of the rectangular conductive elastic plate in uniform magnetic fields under the classic plate theory considering nonlinear strain‐displacement. The formulation of the governing equations integrates the electromagnetic forces arising from the motion of the plate. The nonlinear motion equations are dimensionless, which takes the effect of in‐plane inertia into account. The equations are solved by the Galerkin method and homotopy perturbation method (HPM). The effectiveness of the solution is verified. According to the solutions by HPM, the effects of the initial conditions, length‐to‐thickness ratio, and magnetic induction intensity on the nonlinear free vibrations behavior of conductive elastic plates are discussed.