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Free vibration of a magnetoelectroelastic rectangular plate is investigated based on the Reddy's third-order shear deformation theory. The plate rests on an elastic foundation and it is considered to have different boundary conditions. Gauss's laws for electrostatics and magnetostatics are used to model the electric and magnetic behavior. The partial differential equations of motion are reduced to a single partial differential equation and then by using the Galerkin method, the ordinary differential equation of motion as well as an analytical relation for the natural frequency of the plate is obtained. Some numerical examples are presented to validate the proposed model and to investigate the effects of several parameters on the vibration frequency of the considered smart plate.

Free vibration of a simply-supported magneto-electro-elastic doubly-curved thin shell resting on a Pasternak foundation is investigated based on Donnell theory. The rotary inertia effect is considered in the formulation. Maxwell equations for electrostatics and magnetostatics are used to model the electric and magnetic behavior. The partial differential equations of motion are reduced to a single ordinary differential equation and an analytical relation is obtained for the natural frequency. After validation of the present study, several numerical studies is done to investigate the effects of the electric and magnetic potentials, spring and shear coefficients of the Pasternak foundation, and the geometry of the shell on the vibration frequency.