Nonlinear free vibration of a transversely isotropic rectangular magneto-electro-elastic thin plate with simply supported boundary conditions is studied for the first time 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- by using Galerkin method. A perturbation method is used to solve the obtained equation analytically and a closed-form solution is obtained for the nonlinear frequency of a rectangular magneto-electro-elastic plate. Numerical examples are carried out to show the effects of several parameters on the nonlinear behavior of these plates.
