Based on theoretical analysis and experiments, this article proposes a new model for a magnetorheological (MR) damper. The proposed model with a smooth and concise form can interpret the bi-viscous and hysteretic behaviors of the MR damper very well. The parameters in the model have definite physical meanings. The bi-viscous and hysteretic behaviors can be characterized by two parameters 0 and A3. The proposed model makes it convenient to study the effects of the bi-viscous and hysteretic behaviors on the performance of a system with a MR damper. As one application of the model, a vibration isolation system with a MR damper is investigated, and the effects of bi-viscous and hysteretic behaviors on system performances are studied by numerical methods and theoretical analysis.

In this paper a single degree-of-freedom semi-active oscillator with time delay is researched. By averaging method, the first-order approximately analytical solution is obtained, and the stability condition is also established based on the Lyapunov theory. The analytical results show that the amplitude and the stability condition of the steady-state solution are all periodic functions of time delay, with the same period as the excitation one. Moreover, another simple case, namely the semi-active oscillator without time delay, is also investigated based on the first-order approximately analytical solution, and the result shows that the steady-state solution in this case is unconditionally stable. The comparisons of the analytical solution and the numerical one are fulfilled, and the results verify the correctness and satisfactory precision of the first-order approximately analytical solution. At last, the selection or design of an appropriate time delay to improve control performance through the first-order approximately analytical solution is studied.

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