As smart materials, magnetorheological elastomers (MREs) have been broadly applied in the field of intelligent structures and devices. In order to mathematically represent the dynamic behavior in a wide range of strain amplitude, excitation frequency and magnetic field; a nonlinear model with a fractional element was developed for MREs in a linear viscoelastic regime. The identification of model parameters was realized through fitting experimental data of dynamic moduli measured in shear mode, and the identified parameters exhibited good repeatability and consistency to reflect the rationality of this nonlinear dynamic model. Considering material elasticity and viscosity, the dependence of model parameters on strain amplitudes and magnetic fields was analyzed to interpret the dynamics of MREs. The fitted results displayed an excellent agreement with the experimental results on the dependence of dynamic moduli on strain amplitudes and magnetic fields. Using the predictor-corrector approach, predicted results on the stress-strain hysteresis loop were calculated based on identified parameters to further validate the proposed model by comparing with experimental results and predicted results of the revised Bouc-Wen model. This proposed model is expected to facilitate the dynamic analysis and simulation of MRE based vibration systems with a high precision accuracy.

中文翻译：

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基于分数粘弹性的磁场中磁流变弹性体非线性动力学模型

作为智能材料，磁流变弹性体（MRE）已广泛应用于智能结构和设备领域。为了数学地表示在很宽的应变幅度、激励频率和磁场范围内的动态行为；为线性粘弹性体系中的 MRE 开发了具有分数元素的非线性模型。模型参数的识别是通过对剪切模式下测得的动态模量的实验数据进行拟合来实现的，识别的参数具有良好的重复性和一致性，反映了该非线性动力学模型的合理性。考虑到材料弹性和粘度，分析了模型参数对应变幅度和磁场的依赖性，以解释 MRE 的动力学。拟合结果与实验结果非常吻合，即动态模量对应变幅度和磁场的依赖性。使用预测器-校正器方法，基于确定的参数计算应力-应变滞后环的预测结果，通过与实验结果和修正 Bouc-Wen 模型的预测结果进行比较，进一步验证所提出的模型。该模型有望以高精度促进基于 MRE 的振动系统的动态分析和仿真。基于确定的参数计算应力-应变滞后回线的预测结果，通过与实验结果和修正 Bouc-Wen 模型的预测结果进行比较，进一步验证所提出的模型。该模型有望以高精度促进基于 MRE 的振动系统的动态分析和仿真。基于确定的参数计算应力-应变滞后回线的预测结果，通过与实验结果和修正 Bouc-Wen 模型的预测结果进行比较，进一步验证所提出的模型。该模型有望以高精度促进基于 MRE 的振动系统的动态分析和仿真。