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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

The paper addresses a mathematical model describing the dynamic response of an elongated bridge supported by elastic pillars. The elastic system is considered as a multi-structure involving subdomains of different limit dimensions connected via junction regions. Analytical formulae have been derived to estimate eigenfrequencies in the low frequency range. The analytical findings for Bloch-Floquet waves in an infinite periodic structure are compared with the finite element numerical computations for an actual bridge structure of finite length. The asymptotic estimates obtained here have also been used as a design tool in problems of asymptotic optimization.

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