Vibration of a multiphase magneto-electro-elastic simply supported rectangular plate subjected to harmonic forces

Nonlinear forced vibration of a magneto-electro-elastic rectangular plate is studied based on the first-order shear deformation theory. The excitation force is harmonic, the boundary condition is considered to be immovable simply supported, and the plate rests on a viscoelastic foundation. The electric and magnetic fields are assumed to be applied along the thickness direction, and different magneto-electric boundary conditions are considered. Magneto-electric behavior of the plate is modeled using Gauss’ laws for electrostatics and magnetostatics. The system is discretized using Galerkin method and then multiple time scale method is used to solve the obtained equation analytically. As a result, closed-form solutions are obtained for the frequency responses of the plate in the primary and subharmonic resonances. Time history and phase portraits of the plate are also obtained numerically. Some examples are carried out to validate the proposed model and to investigate the effects of electric and magnetic potentials, material properties, and plate size on the frequency responses of these smart multiphase plates.