In-plane free vibrations of shallow cables with cross-ties

Connecting stay cables with cross-ties is the most promising solution for vibration control of long cables in cable-stayed bridges. Existing studies have been focusing on the influences of the cross-tie configurations and properties on the dynamics of the formed cable networks, mostly based on the taut-string model of cables. However, the cross-ties are particularly aimed at long cables whose in-plane vibrations can be significantly affected by the sag effect. This paper therefore presents an analytical method to investigate free in-plane vibrations of shallow cable networks with cross-ties, using the linear theory of shallow cables. A two-shallow-cable network with one viscoelastic cross-tie is studied in detail to appreciate the sag effect on the dynamics of the cable network. It is shown that the sag effect couples vibrations of the cable segments divided by the cross-ties and changes the modal interactions substantially. When the cross-tie is rigid, curve veering occurs between frequency curves of the system with respect to varying cross-tie location, as compared with curve intersection in the absence of the sag effect. When the cross-tie is flexible, generally, mode shapes of the cable segments and the whole cable are not antisymmetric nor symmetric, and the sag then affects nearly all the vibration modes. Furthermore, taking into account the damping effect of the cross-tie, the frequency loci in the complex plane regarding the increment of cross-tie damping coefficient can still be categorized by the corresponding undamped and clamped frequencies while the modal interaction becomes more complicated. Quantitatively speaking, when the sag parameter is in the practical range of existing cable-stayed bridges, the first and second vibration modes of the cable networks are considerably affected and need to be considered for practice.