The frequency dependence of harmonic hysteresis effect in magnetoelectric laminated composites

In this study the frequency dependence of harmonic hysteretic magnetoelectric (ME) effect in magnetostrictive-piezoelectric laminate was investigated. Taking into account the nonlinear magnetostrictive effect and the structural vibration, a ME dynamic model was proposed to quantitatively describe the frequency-dependent hysteretic characteristics. The model was validated by comparing the simulated ME response with experiment at both the quasi-static and high frequency conditions. As the frequency increases, the shape evolution of the ME hysteresis loop from crescent to butterfly and ellipse was observed. Moreover, the influences of the magnetic bias field, damping ratio and magnetostrictive loss factor were also investigated. It was found that the dynamic ME hysteresis was the combined result of competition between the first two orders of harmonic components and the corresponding phase shift. The former was controlled by the frequency doubling and the mechanical resonance effect, and the latter was originated from the magnetostrictive loss and mechanical damping.