Bifurcation and Chaotic Analysis for Cable Vibration of a Cable-Stayed Bridge

Abstract

Cable-stayed bridges are of the most unique and cost-effective designs in modern bridge engineering. A key feature of these structures is that the cables or stays run directly from the tower to the deck. The nonlinear dynamic behavior of these cables can significantly affect the resilience and safety of the bridge. In this context, a deeper understanding of the bifurcation and chaotic mechanisms of cable vibration is highly desirable. Accordingly, in this study the nonlinear dynamic equation of a planar cable is derived for quantitative and qualitative analysis. The nonlinear system is solved asymptotically, using the conventional perturbation and two-timing scale methods, to study the periodic motion of the cables. The obtained solutions are primarily affected by the control parameters and the initial conditions. The asymptotic solutions are also simulated numerically. It is found that the chaotic behavior of cables is greatly affected by the governing parameters, including the cable dimensions, vibration amplitude, damping effect, and excitation frequency. Finally, seven state variables of the nonlinear system are analyzed to investigate the occurrence of bifurcation.