Magnetorheological elastomer (MRE) is a type of magnetic soft material consisting of ferromagnetic particles embedded in a polymeric matrix. MRE-based devices have characteristics of adjustable stiffness and damping properties, and highly nonlinear and hysteretic force–displacement responses that are dependent on external excitations and applied magnetic fields. To effectively implement the devices in mitigating the hazard vibrations of structures, numerically traceable and computationally efficient models should be firstly developed to accurately present the unique behaviors of MREs, including the typical Payne effect and strain stiffening of rubbers etc. In this study, the up-to-date phenomenological models for describing hysteresis response of MRE devices are experimentally investigated. A prototype of MRE isolator is dynamically tested using a shaking table in the laboratory, and the tests are conducted based on displacement control using harmonic inputs with various loading frequencies, amplitudes and applied current levels. Then, the test results are used to identify the parameters of different phenomenological models for model performance evaluation. The procedure of model identification can be considered as solving a global minimization optimization problem, in which the fitness function is the root mean square error between the experimental data and the model prediction. The genetic algorithm (GA) is employed to solve the optimization problem for optimal model parameters due to its advantages of easy coding and fast convergence. Finally, several evaluation indices are adopted to compare the performances of different models, and the result shows that the improved LuGre friction model outperforms other models and has optimal accuracy in predicting the hysteresis response of the MRE device.

Magneto-rheological (MR) materials and their devices are being rapidly developed and have drawn surge of interest for the potential application in vibration control. Among them, a novel shear-mode rotational MR damper (SM-RMRD) with adaptive variable stiffness and damping was developed for adaptive structural control in real-time against different types of earthquakes. To make use of this innovative device perfectly, a robust and reliable model should be developed to simulate the nonlinear and hysteretic behaviours for the application in adaptive control. Accordingly, this research initially presents a new phenomenological model to describe the force response of the SM-RMRD. Then, model parameters are estimated based on experimental data of force, displacement and velocity, which were directly or indirectly obtained from the device under different loading protocols. The field dependence of each model parameter is also investigated so that a general model with current-related parameters is acquired for designing the control strategy. Using the current-dependent model of SM-RMRD, a semi-active controller is developed and implemented to the SM-RMRD to produce the feedback control for the structures in real-time. Finally, the effectiveness of proposed control method is appraised by a numerical study, in which an SM-RMRDs-incorporated three-storey building model with different control strategies are subjected to various scaled benchmark earthquakes. The comparison result verifies the excellent capacity of the proposed controller based on the developed phenomenological model in terms of reducing the storey acceleration and inter-storey drift.