Closed Form Expression for the Vibration Problem of a Transversely Isotropic Magneto-Electro-Elastic Plate

A closed form expression for the transverse vibration of a magnetoelectroelastic (MEE) thin plate is derived, and the exact solution for the free vibration of a two-layered BaTiO3–CoFe2O4 composite is obtained. Based on the Kirchhoff thin plate theory, the bending problem of a transversely isotropic MEE rectangular plate is investigated, and the governing equation in terms of the transverse displacement is then presented in a rather compact form. The material coefficients for such MEE plate are expressed uniquely by the volume fraction (vf) of the two-layered BaTiO3–CoFe2O4 composite, which indicates a transversely isotropic MEE medium. The natural frequencies of such MEE plate are evaluated analytically, and the effects of different volume fractions on the natural frequency are further discussed.