Design formulas for damping of a stay cable with a damper

The performance of a damper in controlling large-amplitude vibrations of a stay cable in a bridge is influenced by essential parameters such as the amount of sag and flexural rigidity of the cable, and the stiffness of the damper support. In this paper, accurate asymptotic formulas are analytically derived for the modal damping ratio of a general cable. The formulation includes the parameters mentioned above and is appropriate for a damper having a finite support stiffness. For a viscous damper, the influential parameters are explicitly incorporated as reduction and modification factors in the modal damping formula, which significantly simplifies the design procedure for stay cables. The analytical results are also extended to high-damping rubber dampers which have recently been encountered in practice. Finally, important formulas relevant to the design of both types of dampers are tabulated.