Equivalent circuit method for resonant analysis of multilayer piezoelectric-magnetostrictive composite cantilever structures

In this paper, we discuss a theoretical model by the equivalent circuit method for magnetoelectric (ME) response at resonant frequencies corresponding to bending mode oscillations. A dynamic theoretical model of arbitrary multilayer cantilever with alternating piezoelectric (PE) and magnetostrictive (MS) layers on a substrate (Sub) was conducted. The equivalent circuit of the bending mode vibration has obtained by solving the piezoelectric, magnetostrictive and substrate constitutive equations under boundary conditions. The dependence of resonant frequencies and resonant ME coefficients on the material properties and structural dimensions is investigated. The ME coefficients were normalized by the total thickness of MS and PE layers and quality factor. As a demonstration, our theory for multilayer composite cantilever was then applied to specifically Metglas-AlN-Si systems. Our results demonstrate that the structural dimensions strongly influenced the neutral plane in the composite cantilever and then in turns strongly influenced the ME response. In addition, characteristics of multilayer ME cantilever in static (low frequency) station will be analyzed. The theory shows good agreement with experimental data. Our discussion may be helpful to the designing and fabrication of the giant ME cantilever with more realistic and optimal geometry.