In order to further study the nonlinear characteristics of the resonance magnetoelectric coefficient and vibration mode at the resonance frequency, three-layer magnetoelectric composite with length direction magnetization and thickness direction polarization is investigated in the article. Firstly, based on the Z-L model and the numerical solution characteristics of magnetization intensity, the magnetization intensity function is fitted, and the dynamic parameters of the giant magnetostrictive material, including dynamic piezomagnetic coefficient, dynamic elastic compliance coefficient, and dynamic magnetic permeability, are further derived. The effects of bias magnetic field and prestress on the corresponding composite are analyzed. Secondly, based on the nonlinear magnetostrictive constitutive equation, a symmetric magneto-elastic-electric equivalent circuit model of magnetoelectric laminate composite is established, and the expression of magnetoelectric coefficient is derived. The variation curve with bias magnetic field and prestress is analyzed, which is consistent with the conclusions of existing literature [Zhou H M, Ou X W, Xiao Y, Qu S X, Wu H P 2013 Smart Mater. Struct. 22 035018; Zhou H M, Li C, Xuan L M, Wei J 2011 Smart Mater. Struct. 20 035001]. Finally, in order to compare with the theoretical results, the same parameters are set by using COMSOL software, and the corresponding magnetoelectric coefficient frequency curve is plotted. The two results are in good agreement with each other, and the maximum peak modal vibration shape is extracted, making it easy to observe the vibration of the magneto electric laminated composite in the length direction. The results indicate that the theoretical model of this symmetric magneto-elastic-electric equivalent circuit and the numerical simulation method using COMSOL software are feasible, thereby laying the foundation for further nonlinear analysis of magnetoelectric laminate composite and making it possible to design high-precision magnetoelectric micro devices.
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