Damping and tuning of inerter-based dampers for cable vibration mitigation considering girder vibrations

Abstract

As the spans of cable-stayed bridges increase, and with the use of steel towers and girders, bridge stiffness decreases, the bridge frequencies approach the frequencies of the cables. The effect of girder–cable coupling vibrations cannot be ignored in cable vibration control. This study focuses on the performance of inerter-based dampers (IBDs) in cable vibration control when considering girder vibrations. Two types of IBD, a viscous inerter damper (VID) and a tuned inerter damper (TID), are studied. The system dynamics are formulated through complex modal analysis. Damping effects of the VID and TID are evaluated and optimized based on the complex frequency loci of the damped system. The results indicate that the control performance of the VID and TID for the target cable mode is drastically reduced when the ratio between the girder and target cable frequencies is approximately 1. The effects of the girder–cable coupling vibration on the optimal parameters and control performance of the VID and TID for the target cable mode are found to be significant even when the girder-cable frequency ratio is not close to 1, and the effect can be increased for a smaller girder–cable mass ratio. The different evolution characteristics of the girder–cable coupling effect are revealed by comparing the designs and performances of the VID and TID. The effectiveness of the VID and TID to control the system model considering dynamic cable force and cable sag is verified using a numerical model.