Vibration Analysis of a Magnetoelectroelastic Rectangular Plate Based on a Higher-Order Shear Deformation Theory

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.