Free vibration of a taut cable with internal high damping rubber dampers and an external negative stiffness damper

Frequent vibration events on the long stay cables highlight the need to control their multi-mode vibrations. Compared to commonly used viscous dampers for cable vibration control, the negative stiffness damper (NSD) demonstrates its superior performance. However, a single NSD is incapable of providing sufficient supplemental damping for a super-long cable, especially for the multi-mode vibration mitigation. The combined internal high damping rubber (HDR) dampers and the external NSD for cable vibration control is proposed to achieve better multi-mode control performance in this study. First, the complex modal analysis of a taut cable coupled with an external NSD and two internal HDR dampers is conducted to reveal the coupling performance of the damping system. The asymptotic and iterative solutions of transcendental equation obtained in complex modal analysis are derived, respectively. Subsequently, the comparison of asymptotic and iterative solutions verifies the applicability of asymptotic solutions. Finally, parametric studies are performed to investigate the effect of the parameters of NSD and the coupling configuration on their combined control performance. Results show that the coupling schemes with different configurations can possess a wider effective modal range or a better damping effect in the narrower modal ranges according to different damping targets. It provides a diversified solution for multi-mode damping enhancement of stay cables.