Large amplitude free vibration of symmetrically laminated magneto-electro-elastic rectangular plates on Pasternak type foundation

• An analytical model is presented to analyze the linear and nonlinear free vibration of laminated magneto-electro-elastic plates.
• Negative electric and positive magnetic potentials increase the natural frequency and decrease the nonlinear frequency ratio.
• The shear coefficient of the elastic foundation has more effect on the natural frequency of magneto-electro-elastic plates.

Nonlinear free vibration of symmetrically laminated magneto-electro-elastic rectangular plate resting on an 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 subjected to electric and magnetic potentials between the upper and lower surfaces. To model the motion of the plate, the first order shear deformation theory along with the Gauss's equations for electrostatics and magnetostatics are used. Then equations of motion are reduced to a single nonlinear ordinary differential equation which is solved analytically by multiple scales method. The results are compared with the published results and good agreement is found. Some numerical examples are presented to investigate the effects of several parameters on the linear and nonlinear behavior of these plates.