Structural systems often show nonlinear behavior under severe excitations generated by natural hazards. In that condition, the restoring force becomes highly nonlinear showing significant hysteresis. The hereditary nature of this nonlinear restoring force indicates that the force cannot be described as a function of the instantaneous displacement and velocity. Accordingly, many hysteretic restoring force models were developed to include the time dependent nature using a set of differential equations. This survey contains a review of the past, recent developments and implementations of the Bouc-Wen model which is used extensively in modeling the hysteresis phenomenon in the dynamically excited nonlinear structures.

The Hysteresis Bouc-Wen Model, a Survey

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.

https://iopscience.iop.org/article/10.1088/0964-1726/20/2/023001/pdf

Magnetorheological fluid dampers: a review of parametric modelling

This paper presents an optimal design of a passenger vehicle magnetorheological (MR) damper based on finite element analysis. The MR damper is constrained in a specific volume and the optimization problem identifies the geometric dimensions of the damper that minimize an objective function. The objective function consists of the damping force, the dynamic range, and the inductive time constant of the damper. After describing the configuration of the MR damper, the damping force and dynamic range are obtained on the basis of the Bingham model of an MR fluid. Then, the control energy (power consumption of the damper coil) and the inductive time constant are derived. The objective function for the optimization problem is determined based on the solution of the magnetic circuit of the initial damper. Subsequently, the optimization procedure, using a golden-section algorithm and a local quadratic fitting technique, is constructed via commercial finite element method parametric design language. Using the developed optimization tool, optimal solutions of the MR damper, which are constrained in a specific cylindrical volume defined by its radius and height, are determined and a comparative work on damping force and inductive time constant between the initial and optimal design is undertaken.

http://iopscience.iop.org/article/10.1088/0964-1726/18/1/015013/pdf

Optimal design of a vehicle magnetorheological damper considering the damping force and dynamic range

This paper presents an optimal design of a magnetorheological (MR) shock absorber based on finite element analysis. The MR shock absorber is constrained in a specific volume and the optimization problem identifies geometric dimensions of the shock absorber that minimize a multi-objective function. The objective function is proposed by considering the damping force, dynamic range and the inductive time constant of the shock absorber. After describing the configuration of the MR shock absorber, a quasi-static modeling of the shock absorber is performed based on the Bingham model of an MR fluid. The initial geometric dimensions of the shock absorber are then determined based on the assumption of constant magnetic flux density throughout the magnetic circuit. The objective function of the optimization problem is derived based on the solution of the initial shock absorber. An optimization procedure using a golden-section algorithm and a local quadratic fitting technique is constructed via a commercial finite element method parametric design language. Using the developed optimization tool, optimal solutions of the MR shock absorber, which is constrained in a specific cylindrical volume defined by its radius and height, are determined. Subsequently, a quarter-car suspension model with the optimized MR shock absorber is formulated and the vibration control performance of the suspension is evaluated under bump and sinusoidal road conditions.

https://iopscience.iop.org/article/10.1088/0964-1726/18/3/035012/pdf

Optimal design of MR shock absorber and application to vehicle suspension

The experimental identification of magnetorheological dampers and evaluation of their controllers

Semi-actively controlled magnetorheological (MR) fluid dampers offer rapid variation in damping properties in a reliable fail-safe manner using very low power requirements. Their characteristics make them ideal for semi-active control in structures and vehicle applications in order to efficiently suppress vibration. To take advantage of their exceptional characteristics, a high fidelity model is required for control design and analysis. Perfect understanding of the dynamic characteristics of such dampers is necessary when implementing MR struts in applications. Different models have been proposed to simulate the hysteresis phenomenon of MR dampers. The Bouc–Wen model has been extensively used to simulate the hysteresis behavior of MR dampers. However, considerable differences still exist between the simulation and experimental results. Moreover, the characteristic parameters in the traditional Bouc–Wen model are not functions of the frequency, amplitude and current excitations; therefore, the estimated parameters can characterize the behavior of the tested MR damper under specific excitation conditions and must be re-evaluated if a different combination of excitation parameters is desired. This can be extremely cumbersome and computationally expensive. In this work, a new hysteresis model based on the Bouc–Wen model has been developed to better characterize the hysteresis phenomenon of the MR damper. The proposed model incorporates the frequency, amplitude and current excitation as variables and thus enables us to predict efficiently and accurately the hysteresis force for changing excitation conditions. The proposed modified Bouc–Wen model has been validated against the experimental results through graphical and quantitative analysis in time, displacement and velocity domains and an excellent correlation has been found.

https://iopscience.iop.org/article/10.1088/0964-1726/15/5/004/pdf

A Dominguez

Papers

A new dynamic hysteresis model for magnetorheological dampers