At present the vibration control of stay cable suffers from low damping effectiveness in single mode vibration caused by the limitation of damper installation position as well as the poor modal compatibility, that is, a rapid degradation performance when the actual mode deviates from the designed optimal mode. In this paper, one practical semi-active magnetorheological (MR) damper based control solution is proposed to address the problems faced in multi-modal vibration control of stay cables. The semi-active pseudo negative stiffness (PNS) control strategy takes full account of the MR damper’s mechanical characteristics and the demands of the stay cable vibration control. Compared with the linear equivalent model, the proposed time-varying model exhibits more details of the damping force and the nonlinear response of the damped stay cable, which shows its essential role in the optimal design of MR-PNS scheme. Then the optimal design method of MR-PNS multi-modal vibration control for stay cable is summarized by taking the first three modes vibration control of the J20 cable in Nanjing Baguazhou Yangtze River Bridge as simulation examples. The simulations of cross-modal, multi-modal and wind-induced vibration cases are conducted respectively, while the results show that the optimal designed multi-modal MR-PNS scheme can simultaneously exceed the passive maximum modal damping ratio within first three modes. The advantages of the proposed MR-PNS method in high damping efficiency and modal compatibility could be verified by comparing with the passive multi-modal damping solution.
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