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

Abstract

SUMMARYVibration 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.

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

“…i. As also shown in Figure 5a, when 1 is close to the value given in Equation (33), modal frequency veering occurs between adjacent symmetric modes. ii.…”

“…[23][24][25][26] The number of cross-ties, as well as other key system parameters, have been studied in the context of a more complex cable network. 27 To increase the dissipation capacity of cable networks, hybrid techniques combining cross-ties and dampers have been proposed, [28][29][30][31] and more recently inerter element was integrated into the system by Sun et al 32 A particular hybrid system of a two-cable system with near-anchorage dampers was considered by Zhou et al 33 and Ahmad et al 34 Complex hybrid cable networks with various configurations have also been studied in the context of an existing bridge. 35 Nonlinearity of the cross-ties and stochastic responses of the cable networks have caught attention recently.…”

Free Vibration of a Taut Cable with Two Discrete Inertial Mass Dampers

“…Hence, some hybrid techniques have been further proposed. The idea of combining external dampers with cross-ties for cable vibration control was considered, which not only addresses the deficiencies of these two commonly used countermeasures but also still retains their respective merits [68][69][70][71][72][73]. A hybrid damper system, combining a viscous damper and a tuned mass damper, can overcome the shortcomings of single type of dampers and improve effectiveness and robustness in suppressing cable vibration [74].…”

Cable Force Identification Based on Bending Waves in Substructures

“…Furthermore, considerable studies have confirmed that the bending stiffness of the cable must be considered for the identification of the cable force through the dynamic method. However, there is still no exact equation to value the bending stiffness of these special structures [8,25,26].…”