Free vibrations of a two-cable network with near-support dampers and a cross-link

Abstract

Vibration mitigation of cables is a crucial problem for cable-supported bridges. A hybrid method for cable vibration mitigation that combines cross-ties and dampers has been applied in engineering practice; however, the damping and frequency of this kind of system needs to be further assessed. In this paper, a system of two parallel cables with a cross-link and dampers located near the cable anchorage is proposed and analyzed. Based on displacement continuity and force equilibrium at the damper and spring locations, the characteristic equation of the system is derived by applying the transfer matrix method. The complex characteristic equation is then numerically solved to obtain the modal damping and frequencies. The damping and frequency characteristics are discussed in detail for the case when the two cables are identical. Special attention is given to the case when only one damper is installed, and the approximate damping evaluation formulations are proposed when spring stiffness approaches infinity. Effects of mass–tension ratio, cable length ratio and frequency ratio on damping are also addressed. Finally, a case study of multimode damping optimization for bridge hangers is given. The results of this paper could be useful for vibration mitigation of two parallel cables and further development of design guidelines for cable networks with attached dampers. Copyright © 2015 John Wiley & Sons, Ltd.