Due to their high lateral flexibility and low inherent damping, stay cables are prone to dynamic excitations. Application of dampers to improve the energy dissipation capacity of stay cables and mitigate their excessive vibrations has been extensively studied, and design tools have been proposed to select the optimum damper size and predict the maximum achievable damping ratio of a cable-damper system. In this study, the effectiveness of external viscous dampers in controlling stay cable vibrations is investigated by considering the negative stiffness behavior of passive dampers. An analytical model is developed to include the damper stiffness effect for further refinement of existing damper design tools, of which the influence of cable sag, cable flexural stiffness, and damper support stiffness has already been considered. The performance of passive negative stiffness dampers (NSDs) and conventional zero or positive stiffness dampers (PSDs) is investigated in detail via parametric studies using the refined design formula. In particular, a criterion is defined for selecting the negative stiffness in NSD based on the stability limits. Two design examples are presented to illustrate the application of the proposed refined damper design tool to the selection of optimum damper size and evaluation of damper performance for a passive viscous PSD and NSD. Results show that compared with the conventional viscous dampers, a passive NSD demonstrates superior performance in stay cable vibration control. Results are also compared and verified with the numerical solution of the proposed analytical model.

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