Analytical investigation on free nonlinear vibration of thin rectangular magneto-electro elastic plate on an onlinear fundation

In this paper, nonlinear free vibration of magneto-electro-elastic rectangular thin platebased on classical plate theory is investigated. The plate is supported by a nonlinear foundation and simply-supported boundary condition is assumed along all edges. The plate is considered in two forms; uniformly distributed one-layered plate and the functionally graded one. The plate is subjected to electric and magnetic potentials between top and bottom surfaces. Equations of motion of this smart plate are obtained by using classical plate theory along with the Gauss laws for electrostatics and magnetostatics. Then the partial differential equations has been converted to an ordinary differential equation using Galerkin method. The obtained nonlinear equation of motion is solved analytically by using multiple time scales method and an analytical relation for nonlinear natural frequency has been obtained. The accuracy of this relation has been validated by comparing the results of literature.Using this relation, the effects of several parameters like plate's dimension, foundation parameter and electric and magnetic potentials on the nonlinear response of the plate are studied.