Due to the inherent nonlinear nature of magnetorheological (MR) dampers, one of the challenging aspects for developing and utilizing these devices to achieve high performance is the development of models that can accurately describe their unique characteristics. In this review, the characteristics of MR dampers are summarized according to the measured responses under different conditions. On these bases, the considerations and methods of the parametric dynamic modelling for MR dampers are given and the state-of-the-art parametric dynamic modelling, identification and validation techniques for MR dampers are reviewed. In the past two decades, the models for MR dampers have been focused on how to improve the modelling accuracy. Although the force-displacement behaviour is well represented by most of the proposed dynamic models for MR dampers, no simple parametric models with high accuracy for MR dampers can be found. In addition, the parametric dynamic models for MR dampers with on-line updating ability and the inverse parametric models for MR dampers are scarcely explored. Moreover, whether one dynamic model for MR dampers can portray the force-displacement and force-velocity behaviour is not only determined by the dynamic model itself but also determined by the identification method.
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