Theory of magnetoelectric effect for bending modes in magnetostrictive-piezoelectric bilayers

In a magnetostrictive-piezoelectric bilayer the interaction between the magnetic and electric subsystems occurs through mechanical deformation. A model is discussed here for the resonance enhancement of such magnetoelectric (ME) interactions at frequencies corresponding to bending oscillations. The thickness dependence of stress, strain, and magnetic and electric fields within a sample are taken into account so that the bending deformations could be considered in an applied magnetic or electric field. The frequency dependence for longitudinal and transverse ME voltage coefficients have obtained by solving electrostatic, magnetostatic, and elastodynamic equations. We consider boundary conditions corresponding to bilayers that are free to vibrate at both ends, or simply supported at both ends, or fixed at one end. It is shown that the bending resonance and consequent enhancement in ME coupling occurs at the lowest frequency for a bilayer that is fixed at one end and free at the other end. The model is applied to a specific case of permendur-lead zinconate titanate bilayer. The theory is in very good agreement with representative data.