Dynamic Behaviors of a Two-Cable Network With Two Negative Stiffness Dampers and a Cross-Tie

Abstract

Due to their structural characteristics, stay cables are inherently susceptible to vibrations. Addressing this issue, the research explores the dynamics of a two-cable network system, emphasizing the impact of composite vibration control methods. A system consisting of two horizontal cables is presented, each fitted with negative stiffness dampers (NSDs) at their anchored ends and interconnected by a cross-tie. A complex eigenvalue equation, formulated based on displacement boundary conditions and the continuity of displacement and force, is validated through numerical simulations. The multimode damping effects of the dual NSDs and cross-tie on the two-cable network are explored through parameter analysis and optimization. The results demonstrate that reducing the stiffness of the cross-tie improves the fundamental modal damping ratio, whereas increasing its stiffness or positioning it close to the cable’s midpoint enhances the vibration frequency. The incorporation of NSDs into the hybrid system significantly increases the maximum damping ratio while lowering the optimal damping coefficient. This study presents a method for calculating the range of negative stiffness values, providing insights into the selection of installation positions and stiffness for the cross-tie, thereby facilitating the design of highly effective multimode vibration control solutions for stay cables.