Modified Bouc-Wen Model Based on Fractional Derivative and Application in Magnetorheological Elastomer

To accurately characterize the mechanical behavior of magnetorheological elastomer (MRE) under a wide range of strain amplitude, excitation frequency, and magnetic field, the viscoelastic fractional derivative was introduced, and a modified Bouc-Wen model based on fractional derivative for MRE in a nonlinear viscoelastic region was established. The Bouc-Wen model can accurately describe the hysteretic characteristics of the MRE nonlinear viscoelastic region, but it cannot accurately simulate magneto-viscoelasticity and frequency dependence. The fractional derivative can express this characteristic with fewer parameters and higher accuracy. The model's validity was verified by fitting the experimental data of stress and strain measured in shear mode. By analyzing the coupling relationship between the model parameters and strain amplitude, frequency, and magnetic flux densities, a method of parameter identification under multi-loading conditions was proposed, and the modified model parameters were identified. The results reveal that the modified Bouc-Wen model can accurately characterize the mechanical properties of the nonlinear viscoelastic region of MRE, and the fitting accuracy is significantly improved compared with the Bouc-Wen model. The expression of the model parameters obtained from the method of parameter identification under multi-loading conditions is accurate in a wide range of strain amplitude, frequency, and magnetic flux density. The fitness values of simulation data and experimental data under identified and non-identified conditions exceed 90%, showcasing the effectiveness of the modified Bouc-Wen model and the feasibility of the parameter identification method under multi-loading conditions.