Damping and Frequency of Simplified Cable-Network-Damper System with Cross-Tie Fixed to Ground

The dynamics of cable network with both cross-ties and dampers are important for cable vibration mitigation. A simplified cable-network-damper system was proposed. It is comprised of two parallel cables and a cross-tie fixed on ground. The cross-tie was simplified as linear spring elements. Based on the string theory, the complex frequency equation of the system was deduced according to the boundary conditons at the fixed end of the cables and displacement continuity and force equilibrium equations at the mounting position of the cross-tie. Then the damping and frequency values were derived by numerical iteration. In the cases of the third and fourth vibration modes, effects of spring stiffness and location on the maximum damping ratio, the optimal damping coefficient and the corresponding frequency were analyzed. It is found that there are odd and even modes in the system vibration; and these two modes have different vibration characteristics. With the increasing in the stiffness of the cross-tie fixed on ground, the upper limit of maximum damping value is increased 2.0-2.4 times of the maximum modal damping ratio of a single cable-damper system; however, the optimal cross-tie locations become less and separated.