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

Abstract

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.

Hysteretic behaviour of uniaxially thermoformed auxetic foams under 3-point bending low-frequency vibration

“…Therefore, a more sophisticated model needs to be applied to replace the linear spring (5) in the concentrated parameter SDOF vibration model. The Bouc-Wen model (BW) is a widely used method to describe the amplitude-dependent hysteresis of magnetorheological [46,47], piezoelectric [48,49] and elastomeric [50] materials, so it is considered a suitable choice for this work. The equivalent mass parameter M l in Eq.…”

“…The parameter e q represents the inverse of the apparent yield point of the nonlinear component of the BW model, and e r describes the ratio of the slope of the hysteresis loop at the velocity direction changing point versus the slope of the linear region [71]. The stiffness The classical BW model is not frequency-dependent [47,53,72] and is therefore unable to capture the noticeable effect of the frequency over the stiffness and damping of the PU foams. According to Nagy's theory, the modulus of open-cell PU foams under compression has a linear dependence to the strain rate on log-log scale; the latter assumption is valid within the low strain rate range of quasi-static and low-speed dynamic and impact tests [54] as described in Eq.…”

“…The parameters e p of the normalized BW model can be calculated using the parameters p of the classical BW model from (15). The parameters p have a clear physical meaning and can provide a rough estimate based on data in open literature [47,70,72,73]. As for the coefficients of frequency dependency in (17), the initial values for the optimization can be obtained by identifying the 5 parameters of the normalized BW model ( 14) at each frequency, and then fitting the curves of the parameters versus frequency.…”

“…The Bouc-Wen (BW) model is a widely used and powerful phenomenological model to describe the different types of hysteresis, such as in the case of magnetorheological [46,47] and piezoelectric [48,49] and elastomeric [50,51] materials. The BW model can describe well the different types of generalized forcedisplacement hysteretic loops.…”