A nonlinear dynamic model of magnetorheological elastomers in magnetic fields based on fractional viscoelasticity

摘要

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.