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Recent studies have shown that the combination of external dampers and cross-ties can overcome their respective deficiencies while retaining their respective merits. Inspired by the advantages of a viscous damper (VD) and a cross-tie on a single stay cable, the coupled damping effect of a parallel-connected viscous mass damper (PVMD) and a grounded cross-tie on a single stay cable is investigated in this paper. The complex wave number equations of the cable–PVMD–cross-tie system are first formulated through the complex modal analysis. Subsequently, the asymptotic and iterative complex wave numbers are compared to evaluate the applicability of the asymptotic and iterative solutions. Furthermore, parametric studies are carried out to investigate the effects of the stiffness coefficients and the installation positions of the cross-tie on the first supplemental modal damping ratio and frequency of the cable. Finally, the installation positions of the cross-tie are optimized to achieve the optimal vibration control of the cable with the PVMD and the cross-tie.

Free vibration of a taut cable with a parallel-connected viscous mass damper and a grounded cross-tie