Theoretical investigation of magnetoelectric effect in multilayer magnetoelectric composites

The aim of this paper is the modeling of an arbitrary magneto–elasto-electric multilayer constitute by magnetostrictive, piezoelectric and elastic substrate layers under free–free boundary conditions. A dynamic theory corresponding to the driving frequency of magnetoelectric (ME) response coupled flexural and extensional oscillations was constructed. In the proposed model, the influence of thickness dependence of stress, strain and magnetic, electric fields within a sample stack are taken into account. The results of ME voltage coefficient dependent on driving frequency are obtained based on magnetostrictive, piezoelectric and elastic constitutive equations. As a demonstration, the numerical results are given for the Terfenol-D/PZT/Si material system with magnetic field excitation parallel and electric polarization perpendicular to the multilayer, which constituted by bilayer Terfenol-D/PZT placed on a Si elastic substrate. The theoretical model for static ME response in such structures is also established. Based on the model, some calculations on ME response are conducted and discussed. Our results show that in both the static and resonant ME response, the dimensional parameters of the layer sequence, piezoelectric fraction and substrate thickness essentially determined the ME voltage coefficient. Furthermore, the influences of load impedance on the magnetoelectric coupling coefficients are also investigated.