Enhancing vibration control in stay cables: a modified damping formulation with NS-HDR damper

Cables in cable-stayed bridges have low intrinsic damping, and dampers are often used as a countermeasure for cable vibration control. This paper presents an innovative asymptotic formula for calculating the additional damping in stay cables equipped with Negative Stiffness High Damping Rubber dampers (NS-HDR). The NS-HDR damper incorporates negative stiffness through a pre-compressed spring. The analysis employs models of flexural cables with fixed-fixed or hinged-hinged ends to derive the formulation of attainable damping ratio. The results of the study reveal that the NS-HDR damper, with its negative stiffness feature, exhibits a significantly higher added damping ratio in comparison to the conventional HDR damper configuration. To quantify this increased added damping resulting from negative stiffness, a modification factor is proposed. The accuracy and effectiveness of the proposed damping formula are successfully validated using the Finite Difference Method (FDM). Subsequently, the methodology is applied to design the damping of two existing stay cables (137.82m and 167.18m in length). Field measurements reveal that the damping in these cables falls below the required threshold of 0.5%. The proposed NS-HDR damper offers a viable solution to achieve the required damping ratio. These findings contribute significantly to the understanding and optimization of damping in stay cables employing HDR dampers, presenting potential applications in the field of bridge engineering. The research opens up new possibilities for enhancing vibration control and safety in cable-stayed bridges.