Dynamic behavior and damping enhancement of cable with negative stiffness inerter damper

• A novel negative stiffness inerter damper (NSID) for cable vibration control. • Explore cable modal behavior to illustrate damping enhancement principle of NSID. • The equation of cable modal damping ratio to clarify the advantages of the NSID. • The derived design equation of the NSID can mitigate multi-mode cable vibrations. To improve the control performance of stay cables, a novel negative stiffness inerter damper (NSID) that consists of a negative stiffness device in parallel with an eddy current inerter damper is proposed in this study. The novelty of the NSID is that the damper can utilize the damping enhancement of the negative stiffness and inerter for cable vibration control, simultaneously. A further novelty is to carefully explore the modal behavior of the cable based on optimum parameters of the NSID. On this basis, the damping enhancement principle and conditions of the NSID for cable vibration control are demonstrated. In addition, the closed-form equation of the cable modal damping ratio and the design equation of the NSID for multi-mode cable vibration control are derived. And the control efficacy of the NSID is evaluated through the damping enhancement of the design cable modes. The results show that the modal behavior in the n th cable mode can be divided into three distinct regimes according to the negative stiffness and the corresponding optimum inertance, which are underdamped mode, subcritical damped mode, and the ( n − 1) th underdamped mode. In the first regime, the inerter and negative stiffness have similar effects on enhancing damping ratio of the cable and reducing the optimum damping coefficient of the NSID. In the second and third regimes, the mode crossover phenomenon is observed, and the actual damping ratio of the n th cable mode decreases as the negative stiffness or inertance increases. The NSID performs better than the VD, VID, and NSD in mitigating multi-mode cable vibrations. Increasing negative stiffness can further improve the control performance and reduce the optimum inertance and damping coefficient of the NSID.