Free vibration analysis of magnetoelectroelastic plate resting on a Pasternak foundation

Free vibration of a magnetoelectroelastic plate resting on a Pasternak foundation is investigated based on Mindlin theory. The in-plane electric and magnetic fields can be ignored for plates. According to the Maxwell equation and magnetoelectric boundary condition, the variation of electric and magnetic potentials along the thickness direction of the plate is determined. Using Hamilton’s principle, the governing equations of motion for the magnetoelectroelastic plate are derived. Numerical results reveal the effects of the electric and magnetic potentials, spring and shear coefficients of the Pasternak foundation on the vibration frequency. These results may be useful in the analysis and design of smart structures constructed from magnetoelectroelastic materials.