Damping enhancement of the inerter on the viscous damper in mitigating cable vibrations

This paper systematically investigates the effect of the inerter on the damping enhancement of a cable with a viscous damper (VD) installed close to the cable end. Three cases are considered, including the inerter installed parallel with the VD (PVID), the inerter placed in series with the VD (SVID), and the inerter installed at a higher location of the VD (HVID). The asymptotic solutions of the three cases are derived, which can predict the cable modal damping ratio when the inerter and the VD cause minimal perturbation in the undamped frequency of the cable. The effect of the inerter on the modal behavior of the cable with the VD is investigated. Based on the constrained static output LQR method, the effects of the inerter on the damping enhancement of the VD in mitigating cable multi-mode vibrations are further evaluated. The results show that the inerter can improve the control performance of the VD when the inertance is less than the optimum value. Further increasing the inertance beyond the optimum value, the optimum modal damping ratio of the cable decreases, and mode crossover is observed for the cable with PVID and HVID. Compared with the case where the VD and the inerter are located at the same location, the case of the HVID is more effective in mitigating cable multi-mode vibrations.