Optimum design of viscous inerter damper targeting multi-mode vibration mitigation of stay cables

Abstract Installation of transverse dampers near the cable-deck anchorage is a commonly used method for the vibration mitigation of stay cables. Recent studies have demonstrated that the viscous inerter damper (VID) is an efficient scheme for controlling specific cable mode vibrations. However, it is desirable to suppress cable vibrations in multiple-modes in real-world applications. To design the VID parameters for mitigating multi-mode cable vibrations, an optimum design procedure is developed in this paper based on the output feedback control theory. In the proposed design approach, the VID is regarded as a special output feedback control system in which only the cable velocity at the damper location is used as the feedback. The optimum damping coefficient of the VID for a given inertance is obtained by minimizing the performance index of the cable-VID system. Varying the inertance of the VID yields optimum design parameters when the minimum peak of the performance index is met. The effectiveness of the proposed design method is demonstrated by comparing with other design methods on a design example of a prototype cable. Results show that the cable modal damping ratios obtained by the proposed strategy could satisfy Irwin’s criterion. Compared with the viscous damper, the VID can achieve better control performance in mitigating cable multi-mode vibrations. However, the advantage of the VID for the first cable mode and the highest designed mode tends to degrade as the order of the design cable mode increases.