Theoretical formulation for in-plane free vibrations of the cross-tied multi-cable-beam model in cable-stayed bridges

Abstract

In the field of vibration control on cable-stayed bridges, the countermeasure using cross-ties to suppress unfavorable vibrations of cables is receiving widespread attention. By adding cross-ties to connect different cables to form a cable network system, it can not only effectively improve the geometric configurations of cables but also enhance the in-plane stiffness of the overall structure. Currently, existing studies face the following two issues: (1) focus on the network composed of cables and cross-ties, but the effects of bridge deck vibrations are commonly overlooked; (2) even when bridge deck vibrations are considered, the modeling incorporates only a single cable. Therefore, this paper establishes a multi-aligned-cross-tie multi-cable-beam model to enable the description of vibrations for both bridge deck and multiple cables. Based on the governing differential equations of the beam and cables, by introducing the transfer matrix method (TMM), a theoretical modeling and derivation pattern suitable for linear dynamic problems of the cable-beam-cross-tie coupled system is formulated. Four numerical examples are analyzed, namely one-aligned-cross-tie double/three-cable-beam model and double/three-aligned-cross-tie three-cable-beam model. Meanwhile, the corresponding finite element models (FEMs) are also established, and the frequencies and mode shapes are compared with those obtained by the present method. The results show that the solving strategy in this paper is credible and feasible.