Nonlinear Vibration Analysis of Rectangular Magneto-electro-elastic Thin Plates

Nonlinear free and forced vibration of a transversely isotropic rectangular magneto-electro-elastic thin plate with simply supported boundary conditions is studied based on the thin plate theory along with the von Karman's nonlinear strains. The partial differential equation of motion is transformed to an ordinary differential equation using Galerkin method. A perturbation method is used to solve the equation analytically and a closed-form solution is obtained for the frequency response and nonlinear frequency of the magneto-electro-elastic plate. The results are compared with the available results. Numerical examples are carried out to show the effects of several parameters on the nonlinear behavior of these plates.