Modal damping and stepping-switch control of stay cables with magnetorheological fluid dampers

Recent theoretical studies indicated that semi-active control using magnetorheological (MR) fluid dampers could provide better damping capability than viscous dampers for cable vibration mitigation. However, some challenging problems still remain in implementation of this smart damping technique to real engineering structures, e.g., how does the nonlinearity of MR dampers affect the system response? what are criteria of selecting MR damper size for an actual cable in design stage? which control strategies are cost effective and efficient for semi-active implementation? This paper tries to address these issues. An accurate analysis model of the cable-damper system is first formulated by accounting for the cable inclination and sag effect. The system equivalent modal damping is evaluated through numerical frequency-response analysis and using curve fitting procedure. Because of strong nonlinearity of MR dampers, the equivalent modal damping ratio significantly depends on the cable response level. A universal estimation approach is configured to depict the relationship among the equivalent modal damping ratio, damper response amplitude, cable frequency and applied voltage strength. Based on maximum energy dissipation (optimal modal damping) criteria, a stepping-switch control strategy is proposed for semi-active vibration control of stay cables incorporated with MR dampers. Numerical results show that the proposed stepping-switch control strategy is not only convenient to implement but also very effective to mitigate cable vibration.