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

• Published in: Engineering structures 2021-10, Vol.245, p.112855, Article 112855
• Main Authors: Bui, Quoc–Duy, Bai, Xian–Xu, Hung Nguyen, Quoc
• Format: Article
• Language: English
• Subjects: Dampers; Differential equations; Dynamic modeling; Dynamic models; Hysteresis; Hysteresis model; Hysteresis models; Magic Formula; Mechanical properties; Modelling; MR damper; Nonlinear dynamics; Operators (mathematics); Parameter identification; Quasi–static model; Static models
• ISSN: 0141-0296; 1873-7323
• DOI: 10.1016/j.engstruct.2021.112855

•A new parametric dynamic model, named QSMF, based on quasi-static model and hysteresis operator is proposed for MR dampers.•The proposed model is formulated for both shear–mode and flow–mode MR dampers.•It was shown from the research results that the physical nature of MR dampers remains representative in the quasi-static component.•Compared with the Spencer’s and Pan’s models, the QSMF model adapted the damper asymmetric hysteresis responses in a greatly higher accurate fashion. In addition, the QSMF model parameters were easier to approach since there was no differential equation and the QS mechanical parameters could be determined separately through QS experiments or chosen as initial searching values of approximation methods. 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].