Magnetoelectric effect in three-layer asymmetric structures in the region of bending vibrational modes

A theory of the magnetoelectric effect in three-layer asymmetric structures composed of a piezoelectric layer and two magnetostriction layers with opposite magnetostriction signs is presented. The thickness ratio of the layers is obtained, at which this effect is maximum. It is shown that the sign of the magnetoelectric coefficient changes to opposite (with respect to the initial two-layer structure) with an increase in the third-layer thickness. It is established that the magnetoelectric coefficients of the structures with different arrangements of the layers with positive and negative magnetostriction have opposite signs.