Vibration Damping of a Taut Cable with the Hybrid Application of a Viscous Damper and a Tuned Mass Damper

Abstract

Additional damping provided by a viscous damper (VD) may not be sufficient to mitigate the wind-induced vibration of long cables. In this paper, the damping properties of the hybrid application of a VD and a tuned mass damper (TMD) on a taut cable are studied. The VD-TMD-cable system’s characteristic equation is formulated by using complex modal analysis. The modal properties of the VD-TMD-cable system are subsequently discussed. Then, a damper optimization principle is introduced. When optimizing the cable single mode, based on the damper optimization principle, the effects of the damper parameters of the VD and TMD on the damping ratio of the optimized cable mode are investigated. Furthermore, a damper optimization method for cable multimode vibration mitigation is proposed. Finally, case studies are presented to verify the effectiveness of the damper optimization method. It is shown that the hybrid application of the VD and TMD can significantly improve the damping ratios of the cable multimode. The hybrid application approximates the superposition of separate applications if cable lower modes are optimized and outperforms the superposition of separate applications for cable higher modes if cable higher modes are optimized. The optimum modal damping ratios can be obtained efficiently by the proposed damper optimization method for cable multimode vibration mitigation to satisfy the damping requirement. This paper proposes a damper optimization method of the hybrid application of a viscous damper and a tuned mass damper for a bridge taut cable multimode vibration mitigation. To overcome the difficulty involved in the actual implementation of the hybrid application, the authors provide a practical solution based on the findings of this paper, which is to set the optimum conditions of the viscous damper and tuned mass damper for the longest cables of each group, while setting the suboptimum conditions of the viscous damper and tuned mass damper’s for the other cables of each group as long as the modal damping ratios meet the target damping ratio. To achieve this, the following steps are required to be taken: First, select adjacent cables with the similar properties as one group. Second, optimize viscous damper and tuned mass damper parameters for the lower and higher modes of the longest cable in one group, respectively. Third, set the viscous damper and tuned mass damper’s configuration parameters of the other cables in the group equal to the optimum viscous damper and tuned mass damper’s configuration parameters of the longest cable. Check whether the damping ratios of the considered modes of the other cables in the group meet the target damping ratio; if not, just try adjusting the cable modes optimized by the viscous damper and tuned mass damper, which means actually adjusting the viscous damper and tuned mass damper’s installation locations of these dampers to meet the target damping ratio.