Estimation and monitoring of cable tension is of great significance in the structural assessment of cable-supported bridges. For short cables, the traditional cable tension identification method via frequency measurement has large errors due to the influence of complex boundaries, which affect the accuracy of estimation. A new cable tension estimation method based on mode shape identification with a multiple sensor arrangement on the cable can take the influence of boundary conditions into account and its accuracy has been verified. However, it requires more sensors compared to the traditional frequency-based method, which will significantly increase the cost of long-term monitoring in practice. Therefore, a novel approach for cable tension monitoring considering both cost and accuracy is further proposed in this study. The approach adopts multiple sensors to measure the influence of boundary conditions. Then, only a single sensor is required for long-term monitoring of the cable. In this paper, an analytical model of the cable is firstly established. The influence of boundary conditions is calculated, which ensures the accuracy of mode shape identification. Furthermore, a field experiment is carried out to verify the effectiveness of the new approach. The results have demonstrated the effectiveness and accurateness of the proposed method in long-term short cable tension monitoring.

High-damping rubber (HDR) dampers have the advantages of convenience for various shapes of pressure blocks, aesthetic installation, easy maintenance, temperature stability, etc.; thus, they present good application prospects in the vibration reduction of stay cables. Hence, a model of a taut cable equipped with two types of HDR damper—i.e., HDR damper and tuned mass–high-damping rubber damper (TM-HDR-D)—is established herein. Then, based on this theoretical model, the effect of each damper acting alone and in combination on the cable’s additional modal damping is studied. Finally, an actual cable of a cable-stayed bridge is used to study the effectiveness of two dampers for practical engineering. The results show that, when the TM-HDR-D has a small mass, the total additional modal damping of the cable approximates the superposition of the respective effects of the two dampers. The damping effect of HDR mainly depends on its stiffness and installation position; meanwhile, the damping contribution of TM-HDR-D is mainly related to its tuning frequency and installation position. In practical engineering, the smaller installation mass of TM-HDR-D can make up for the lack of damping enhancement of the cable-end HDR damper.

In practice, the internal rubber dampers are widely installed inside the cable guide pipe between the external viscous damper and the cable anchorage. In order to study the effect of the internal damper on the performance of the external viscous damper, the theoretical analysis model of a taut cable with an internal rubber damper and an external viscous damper is established in this paper, where the internal damper is assumed to be a high damping rubber damper with a flexible support and the external damper is considered to be a linear viscous damper. Then, the numerical iterative formula and approximate solution expression for the cable modal damping ratio are derived. Based on the approximate solution, the parameters of the internal rubber damper are analyzed comprehensively, and its influence on the cable modal damping in cable multimode is studied as well. Results show that, except for the support flexibility of the internal rubber damper, other parameters will have a negative effect on external viscous damper effectiveness. From the perspective of cable multimode vibration control, the installation of an internal rubber damper significantly weakens the modal damping, and this effect is more pronounced in lower frequency modes.