Semi-Active Control of Three-Dimensional Vibrations of an Inclined Sag Cable with Magnetorheological Dampers

Three-dimensional semi-active vibration control of an inclined sag cable with discrete magnetorheological (MR) dampers is investigated in this paper using the finite difference method (FDM). A modified Dahl model is used to describe the dynamic property of MR damper. The nonlinear equations of motion of cable-dampers system are first established, which accounts for coupling between in-plane and out-of-plane motions, and also for the displacement of the support points. A MR damper can be considered as a variable friction damper approximately, so a semi-active control strategy based on the modulated homogeneous friction algorithm is proposed. Taking a typical short cable as an example, the vibration reduction ability with optimally controlled MR dampers is verified numerically by comparison with the viscous damper tuned to a single mode response. The analysis show that, if the conditions are fulfilled at which the optimal tuned viscous damper is designed, the MR damper and the viscous damper are performing equally well; however, if the response of the cable is dominated by several modes, the MR damper can achieve better vibration reduction effect compared with viscous damper. Especially, if the amplitude of the support point motion less than a threshold value, MR damper can prevent subharmonic excitation caused by support point motion from taking place, consequently, MR damper achieves significant vibration reduction compared to viscous damper. In addition, the influence of measurement noise on control effect and the robustness of the proposed semi-active control rule are also examined.