Effects of modeling nonlinearity in cross-ties on the dynamics of simplified in-plane cable networks

Cross-ties are often employed as passive devices for the mitigation of stay-cable vibrations, which have been observed in the field under the excitation of wind and windrain. In-plane cable networks are structural systems derived by interconnecting several stays through transverse cross-ties. This study was motivated by a recent research activity aimed at the study of the free-vibration dynamics for in-plane cable networks. Even though dynamic models for the analysis of the network vibration had been proposed by one of the writers in previous studies, a linear dynamic modeling of the system had been utilized. In this paper, the use of a nonlinear element was introduced to describe the nonlinear behavior of the cross-tie and to account for an 'imperfect' transfer of the restoring force mechanism at the anchorages (collars) between the cross-tie and the stay. The goal of this model is to simulate, perhaps more realistically, failure onset at the anchorages, sometimes experienced on some bridges. The solution to the free-vibration problem for two simplified cable networks was determined by energy-based 'equivalent linearization' (EL), which simulates the nonlinear response in the restrainer through an equivalent linear restoring force component (amplitude-dependent). The first system consists of one stay with one cross-tie, anchoring the cable to the deck; the second system is a double-cable network with nonlinear cross-tie. Performance of both systems was analyzed. Investigation was restricted to the fundamental mode and some of the higher ones. A time-domain lumped-mass algorithm was utilized for the validation of the EL method.