tNonlinear free vibration of symmetrically laminated magneto-electro-elastic rectangular plate resting onan elastic foundation is studied analytically. The plate is considered to be simply supported on all edges.It is also assumed that the magneto-electro-elastic body is poled along the z direction and subjectedto electric and magnetic potentials between the upper and lower surfaces. To model the motion of theplate, the first order shear deformation theory along with the Gauss’s equations for electrostatics andmagnetostatics are used. Then equations of motion are reduced to a single nonlinear ordinary differentialequation which is solved analytically by multiple scales method. The results are compared with thepublished results and good agreement is found. Some numerical examples are presented to investigatethe effects of several parameters on the linear and nonlinear behavior of these plates.
