To accurately predict the optimum supplemental modal damping ratio of the cable and the corresponding size of the inertial mass damper (IMD), combined effects of the cable sag, the cable flexural rigidity, and the boundary conditions on the control performance of the cable with the IMD are well investigated in this refined study. An analytical model of the cable-IMD system considering these effects is developed. The equation of motion of the cable-IMD system is transformed into a complex eigenvalue problem through the finite difference method. Experimental results from a scaled cable model with an IMD are then used to verify theoretical solutions. Three typical cables in actual cable-stayed bridges are selected for case studies. The results show that the theoretically predicted modal damping ratios of the cable with an IMD, taking into account the sag and the flexural rigidity, agree well with those identified from experimental results, while would be often overestimated with a taut-cable model. Moreover, experimental damping ratios of the cable always fall between those theoretically calculated with fixed ends or pinned ends for each case. Finally, to be conservative in actual design, it is recommended to use the cable-IMD system model with fixed ends to calculate the required damper size and predict the resulting modal damping ratio of the cable, since the corresponding theoretical solution often gives the lower bound of supplemental damping ratio of the cable.

Recently, inertial mass dampers (IMDs) have shown superior control performance over traditional viscous dampers (VDs) in vibration control of stay cables. However, a single IMD may be incapable of providing sufficient supplemental modal damping to a super-long cable, especially for the multimode cable vibration mitigation. Inspired by the potential advantages of attaching two discrete VDs at different locations of the cable, arranging two external discrete IMDs, either at the opposite ends or the same end of the cable is proposed to further improve vibration mitigation performance of the cable in this study. Complex modal analysis based on the taut-string model was employed and extended to allow for the existence of two external discrete IMDs, resulting in a transcendental equation for complex wavenumbers. Both asymptotic and numerical solutions for the case of two opposite IMDs or the case of two IMDs at the same end of the cable were obtained. Subsequently, the applicability of asymptotic solutions was then evaluated. Finally, parametric studies were performed to investigate the effects of damper positions and damper properties on the control performance of a cable with two discrete IMDs. Results showed that two opposite IMDs can generally provide superior control performance to the cable over a single IMD or two IMDs at the same end. It was also observed that attaching two IMDs at the same end of the cable had the potential to achieve significant damping improvement when the inertial mass of the IMDs is appropriate, which seems to be more promising than two opposite IMDs for practical application.

Recent studies have demonstrated that inerter-based dampers exhibit superior performance in mitigating cable vibration over conventional passive viscous dampers (VDs). This paper develops a new inerter-based damper called the eddy-current inertial mass damper (ECIMD), which consists of a rotary eddycurrent damping element and a paralleled ball screw inertial mass element.Inspired by the advantages of two VDs on a single stay cable, the damping of a stay cable with two ECIMDs, either at opposite cable ends or the same cable end, was investigated through theoretical analysis, experimental study, and parameter optimization. First, the mechanical model of the ECIMD was derived from the geometrical configuration, and its effectiveness was verified through mechanical performance tests on two ECIMD prototypes. Subsequently, theoretical analysis models of the cable-ECIMD system were established by considering the cable sag, flexural stiffness, and boundary conditions. Furthermore, control performances of a model cable attached with two ECIMDs were experimentally evaluated. Finally, the multimode damping effect of two ECIMDs at the same cable end was highlighted through parameter optimization. Results show that when two ECIMDs are installed at opposite cable ends, the coupled single-mode damping effect of two ECIMDs is approximately the sum of individual contributions from each ECIMD. When mechanical properties of two ECIMDs at the same cable end can match well with each other, the coupled single-mode and multimode damping effect of two ECIMDs can be significantly enhanced compared with that of a single ECIMD installed at a further distance away from the cable anchorage.