一种描述磁流变弹性体滞回特性的分数阶导数改进Bouc-Wen模型

Modified Bouc-Wen model based on a fractional derivative for describing the hysteretic characteristics of magnetorheological elastomers

为了准确表征大范围应变幅值、激励频率和磁场下磁流变弹性体(Magnetorheological elastomer,MRE)的力学行为,本文引入黏弹性分数阶导数,提出一种描述磁流变弹性体滞回特性的分数阶导数改进Bouc-Wen模型.分析了各向同性与异性MRE的微观形貌特征,对MRE进行了性能试验,研究发现,MRE的储能和损耗模量随着应变幅值(0~100%)增大先不变后减小,随着频率(0~100 Hz)增大而增大,随着磁场(0~545 mT)增大而增大.在此基础上,基于分数阶导数提出改进Bouc-Wen模型,在Simulink软件中建立仿真模型,利用Oustaloup滤波器算法对分数阶导数项近似计算,对比分析验证了改进模型的有效性,各工况下仿真数据和试验数据的吻合度均高于98%.结果表明:改进Bouc-Wen模型能准确地模拟MRE应力应变滞回曲线,拟合精度较Bouc-Wen模型明显提升,改进模型在较宽的应变幅值、频率和磁场范围内是准确有效的,为实现MRE的工程应用打下基础.

As a new type of magnetic sensitivity smart material,magnetorheological elastomers showing a good magnetorheological effect have been broadly applied in the field of intelligent structures and devices.A viscoelastic fractional derivative element was introduced into the stress-strain relationship of magnetorheological elastomers based on the Bouc-Wen model to accurately characterize the mechanical behavior of magnetorheological elastomers under a wide range of strain amplitude,excitation frequency,and magnetic field and to make it better applied in engineering practice.Further,a modified Bouc-Wen model based on a fractional derivative was proposed to describe the hysteresis characteristics of magnetorheological elastomers.The Bouc-Wen model has good universality and can accurately describe the hysteretic characteristics of the magnetorheological elastomer’s 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 micromorphology characteristics of isotropic and anisotropic magnetorheological elastomers were analyzed,and the performance tests of the magnetorheological elastomers were conducted.The storage and loss modulus of the magnetorheological elastomers initially remain unchanged and then decrease with an increase in strain amplitude(0–100%).Moreover,the storage and loss modulus of the magnetorheological elastomers increase with an increase in frequency(0–100 Hz)and magnetic flux density(0–545 mT).On this basis,a modified Bouc-Wen model was proposed based on the fractional derivative.The simulation model was established using the Simulink software,and the fractional derivative part of the modified model was approximately calculated using the Oustaloup filter algorithm.The effectiveness of the modified model was verified through a comparative analysis.The fitness values of simulation and experimental data under different loading conditions are higher than 98%.Results show that the modified Bouc-Wen model can accurately simulate the stress-strain hysteresis loops of the magnetorheological elastomers,and the fitting accuracy is significantly improved compared with that of the Bouc-Wen model.The modified model is accurate and effective in a wide range of strain amplitudes,frequencies,and magnetic fields,which can lay a foundation for the engineering application of magnetorheological elastomers.