Nonlinear resonant magnetoelectric coupling model for dual-peak phenomenon in magnetoelectric laminates

We investigated the dual-peak phenomenon in the response curve of the magnetoelectric (ME) coupling coefficient versus magnetic field for Terfenol-D/PZT/Terfenol-D tri-layer magnetoelectric laminated composites. Using nonlinear constitutive relations for the magnetostrictive material, an expression for the resonance ME coefficient that considers nonlinear resonance mechanical loss is established with the aid of the equivalent circuit method. The established model effectively predicts the complex behavior related to dual-peak phenomenon in regard to pre-stress, bias magnetic field, frequency of the alternating magnetic field, and nonlinear mechanical loss, and explains the origin of the dual peaks. The response curves obtained are consistent with experimental results. It can be found from the further predictions that in a given resonance frequency band, selecting an appropriate pre-stress can regulate two peaks in dual-peak curve, so that a giant ME coupling effect is obtained on the first peak, or a stronger resonance peak is achieved by adjusting stress to merge two peaks. With our resonance ME dual-peak model, we also demonstrate a giant ME coupling by regulating the dual-peak resonances by pre-stress engineering.