A non-linear theoretical model including bending and longitudinal vibration effects was developed for predicting the magneto electric (ME) effects in a laminate bar composite structure consisting of magnetostrictive and piezoelectric multi-layers. If the magnitude of the applied field increases, the deflection rapidly increases and the difference between experimental results and linear predictions becomes large. However, the nonlinear predictions based on the present model well agree with the experimental results within a wide range of applied electric field. The results of the analysis are believed to be useful for materials selection and actuator structure design of actuator in actuator fabrication. It is shown that the problem for bars of symmetrical structure is not divided into a plane problem and a bending problem. A way of simplifying the solution of the problem is found by an asymptotic method. After solving the problem for a laminated bar, formula that enable one to change from one-dimensional required quantities to three dimensional quantities are obtained. The derived analytical expression for ME coefficients depend on vibration frequency and other geometrical and physical parameters of laminated composites. Parametric studies are presented to evaluate the influences of material properties and geometries on strain distribution and the ME coefficient. Analytical expressions indicate that the vibration frequency strongly influences the strain distribution in the laminates, and that these effects strongly influence the ME coefficients. It is shown that for certain values of vibration frequency (resonance frequency), the ME coefficient becomes infinity; as a particular case, low frequency ME coefficient were derived as well.

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