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

Abstract

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. \ud \ud 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. \ud \ud 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

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

“…To increase the dissipation capacity of cable networks, hybrid techniques combining cross‐ties and dampers have been proposed, and more recently inerter element was integrated into the system by Sun et al A particular hybrid system of a two‐cable system with near‐anchorage dampers was considered by Zhou et al and Ahmad et al Complex hybrid cable networks with various configurations have also been studied in the context of an existing bridge . Nonlinearity of the cross‐ties and stochastic responses of the cable networks have caught attention recently …”

Stochastic unilateral free vibration of an in-plane cable network

“…A three-cable system, installed on the Fred Hartman Bridge [24,27] and labeled as BSL network, is considered in this study as a benchmark case (Fig. 1).…”

“…More recently, nonlinear dynamic response of a network at incipient failure, due to snapping or slackening of the transverse restrainers, has gained the attention of the researchers. A new model was developed by the authors [27] for the prediction of oscillations on a cable network in the presence of a nonlinear restoring-force effect in the connectors. The "Equivalent Linearization Method" (ELM) was used [27,28].…”

“…A new model was developed by the authors [27] for the prediction of oscillations on a cable network in the presence of a nonlinear restoring-force effect in the connectors. The "Equivalent Linearization Method" (ELM) was used [27,28]. It was found that, by comparing the ELM solution to direct time-domain integration, the ELM is still accurate for predicting the free vibration.…”

Analytical and experimental investigation on a multiple-mass-element pendulum impact damper for vibration mitigation

“…Equations are first reduced to state-space form, before deriving the dynamic response of the system from initial time τ ¼ 0. Derivation of the state-space system is discussed in Appendix A; it is obtained from the model used in previous studies [28]. In order to ensure adequate and accurate solution, the integration time step must be selected as a function of λ and the number of particles N. Discussion is omitted for brevity.…”