Free vibration analysis of a magneto-electro-elastic doubly-curved shell resting on a Pasternak-type elastic foundation

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.