Dampers are widely used for mitigating cable vibrations, particularly for rain-wind vibrations which often occur in low-frequency modes with large vibration amplitudes. However, it has been observed in existing bridges that a long cable attached with a damper still experiences vortex-induced vibrations in high-frequency modes with a mode shape having a node close to the position of the damper. Therefore, this study proposes to add a device to suppress such high-mode cable vibrations. Three typical dampers are respectively considered as the additional device, i.e., a viscous damper (VD), a high-damping rubber (HDR) damper and a tuned mass damper (TMD). A theoretical model of a shallow cable under two transverse forces at different locations is applied for dynamic analysis. Multimode damping of a cable equipped with two dampers is investigated based on numerical solution of the system frequency equation, and maximal high-mode damping is pursued by optimizing parameters of the dampers on the cable consecutively and simultaneously. Results show that the three types of dampers can all improve damping of the cable modes vulnerable to vortex-induced vibrations. When an additional VD is installed between the original VD and the closer cable end, a decrease in the viscous coefficient of the original damper can improve damping of the higher-order modes. When an HDR damper is installed on the cable between the VD and the nearer anchorage, damping in more low modes is decreased as compared to the case when a VD is installed because of the stiffness of the HDR damper. The HDR damper mainly induces a change in the mode shape of high cable modes and hence the original damper can dissipate more vibration energy. In the case of adding a TMD, no adverse effect on cable damping is found in all the modes. Finally, the procedure for designing two dampers to control both low-mode and high-mode cable vibrations is provided.
