Free Vibration and Damping of a Taut Cable with an Attached Viscous Mass Damper

Studies on vibration control of stay cables in cable-stayed bridges have been keenly interested by researchers and engineers in designing new bridges and assessing in-service bridges. Mitigation of undesired cable vibration can be achieved by attaching a damping device. A Viscous Mass Damper (VMD) is composed by the arrangement a rotational Viscous Damper (VD) and an inertial mass element in parallel, which has been used to control seismic in many buildings in Japan; however, it has not been studied to apply in field of cable vibration control. This paper proposes the application of VMD to robustness in suppressing cable vibration. Oscillation parameters of the cable-VMD system are investigated in detail using an analytical formulation of the complex eigenvalue problem and compared with Viscous Damper (VD). Asymptotic formulas to calculate the complex eigenvalue solutions and the damping ratios of the cable with VMD installed in the proximity of the cable end are proposed, discussed and compared with the exact solutions. Further, the influence of elastic support on the VMD effectiveness of a cable-VMD system is analyzed and examined. Lastly, a case study is provided to justify the proposed methodology. The results of this study show that VMD can improve the cable damping ratio more efficiently than VD where the maximum damping ratio of VMD is larger than that of VD, and the increased damping ratio is higher when the relative modes are higher. The paper also provides necessary insights into the dynamics of the cable-VMD system and a useful tool for selecting optimal parameters of VMD for stay cables.