Dynamic modeling of MR dampers based on quasi–static model and Magic Formula hysteresis multiplier

Abstract

In this research, a novel parametric dynamic model based on quasi-static (QS) model and a Magic Formula hysteresis multiplier, called QSMF model, is investigated to predict accurately and more meaningfully explain the hysteresis behavior of magnetorheological (MR) dampers. The proposed hysteresis model consists of a quasi–static (QS) component inherited from the QS model and a hysteresis multiplier improved from the Magic Formula (MF) operator [1]. The QS mechanical parameters reflect the physical nature while the MF ones characterize the practical nonlinear dynamic responses of MR dampers. This combination enables the model to be flexibly applicable for both design based on quasi-static model and dynamic modeling of MR dampers. In the MF hysteresis component, the original MF model is modified in order to describe MR dampers with high asymmetric hysteresis behavior since each hysteresis branch can be simulated separately. Besides the physical meanings of the parameters, the favorable approach is another advantage of the QSMF model as it contains no differential equation. In addition, the QS parameters can be identified independently via QS experiments. To broaden applicability, the proposed model is formulated for two general operating modes of MR dampers, i.e., shear mode and flow mode. Performances of the model under different excitation conditions are then analyzed and compared with those of the Spencer’s phenomenological model [2] and Pan’s model [3].