Multi-Mode Vibration Control of Super-Long Stay Cables with Negative Stiffness and Stockbridge Dampers

Installing mechanical dampers near the cable anchorage is a commonly used measure for suppressing rain-wind-induced vibrations (RWIVs) of stay cables. However, the high-mode vortex-induced vibrations (VIVs) are still observed on super-long stay cables installed with dampers. To this end, the study presents the combination of a negative stiffness damper (NSD) and Stockbridge dampers (SDs) to simultaneously suppress cable RWIVs and VIVs. In the proposed cable–NSD–SDs system, the NSD is installed near the cable anchorage to suppress cable RWIVs, and the SDs are installed at a higher location to suppress cable VIVs. First, the generalized characteristic equation of the cable–NSD–SDs system is derived for computing the coupled damping effect. Subsequently, a novel design method of an NSD and two SDs for mitigating cable multi-mode vibrations is proposed, and its effectiveness is numerically verified on an ultra-long stay cable of the Sutong Bridge. Finally, the control performance of an NSD and two SDs for the cable under white noise and harmonic excitations is emphatically evaluated and compared. Results indicate that the NSD–SDs system is quite effective for mitigating high-mode vibrations of super-long stay cables. Compared with the cable–NSD system, the cable acceleration response of the cable–NSD–SDs system is reduced by over 35%.