Dynamic behaviour of double-cable systems connected by a rigid cross-tie in long-span cable-supported bridges: a unified approach

Installing cross-ties between adjacent cables in cable-supported bridges are an effective vibration suppression measure. For a double-cable system connected by a rigid cross-tie (DCS_RCT), this article establishes a generalised dynamic model that comprehensively considers the cross-tie location, cable bending stiffness, sag, tension, inclination angle and mass per unit length. Then, a frequency equation for solving the dynamic characteristics of the system is developed, and its accuracy is verified by comparing to the results reported in the literature for symmetric systems and a numerical simulation model for asymmetric systems. As a parametric model, the proposed frequency equation can be used conveniently in the design of DCS_RCT. Finally, the effects of the cross-tie location, cable length, bending stiffness, tension, mass per unit length, and inclination angle on the dynamic characteristics of DCS_RCT are analysed. The novelty lies in the refined generalised dynamic model for DCS_RCT in cable-stayed and suspension bridges. The frequency equation reveals two distinct frequency modes and quantifies the opposite sensitivity of crossover cable positions in symmetric and asymmetric systems, providing a novel framework for cable vibration suppression. These findings advance the understanding of the DCS_RCT mechanism and offer direct guidance for optimising vibration control in multi-cable bridge systems.