An equivalent single-layer model for magnetoelectroelastic multilayered plate dynamics

An equivalent single-layer model for the dynamic analysis of magnetoelectroelastic laminated plates is presented. The electric and magnetic fields are assumed to be quasi-static and the first-order shear deformation theory is used. The formulation of the model provides for a preliminary fulfillment of the electro-magnetic governing equations, which allows to determine the electric and magnetic potential as functions of the mechanical variables. Then, by using this result, the equations of motion are written leading to the problem governing equations. They involve the same terms of the elastic dynamic problem weighted by effective stiffness coefficients, which take the magneto-electro-mechanical couplings into account. Additional terms, exclusively arising in force of the piezoelectric and piezomagnetic behavior, appear. The electromagnetic inputs are treated as equivalent external distributed axial forces and bending moments. Free and forced vibrations solutions for simply-supported plates are presented to validate the model by comparing the present results with benchmark solutions found in the literature