Based on theoretical analysis and experiments, this article proposes a new model for a magnetorheological (MR) damper. The proposed model with a smooth and concise form can interpret the bi-viscous and hysteretic behaviors of the MR damper very well. The parameters in the model have definite physical meanings. The bi-viscous and hysteretic behaviors can be characterized by two parameters 0 and A3. The proposed model makes it convenient to study the effects of the bi-viscous and hysteretic behaviors on the performance of a system with a MR damper. As one application of the model, a vibration isolation system with a MR damper is investigated, and the effects of bi-viscous and hysteretic behaviors on system performances are studied by numerical methods and theoretical analysis.

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