Nonlinear Dynamics Analysis of Active Control System for Parametric Vibration of Super-Long Stay Cable Coupled with Bridge Vibration

Abstract

Abstract The large amplitude parametric resonance of stay cables coupled with bridges is a prominent hazard for super-long-stay cables in cable-stayed bridges. To provide insight into the nonlinear behavior of the parametric vibration of stay cables and the influence of the active control system on the nonlinear behavior, the nonlinear dynamic characteristics, bifurcations, and chaotic motions were investigated in the case of 1:2:1 internal resonance, 1:1:1 primary resonance, and 2:1:2 main parametric resonance. The stay cable’s gravity sag curve equation, including the chordwise force of gravity, is used to establish the equation governing the combined stay cable-bridge deck active control system to consider the effect of the chordwise force of cable gravity. Multiple scales were used to obtain averaged equations. Based on the average equations and taking the longest cable S36 in the prototype super-long-span cable-stayed bridge as the study object, the frequency-response and frequency-phase characteristics were analyzed, and the influence of the stay cable parametric vibration adopting an active control system was studied. The classical fourth-order Runge-Kutta method analyzes nonlinear dynamic behaviors, such as bifurcations and chaotic motions. The numerical results obtained here indicate that, in the case of a 1:2:1 internal vibration, increasing the excitation amplitude may result in chaos in the system, and the active control system can effectively avoid the existence of chaos. The analytical results also demonstrate that the active control system effectively mitigates the nonlinear parametric vibration of a super-long-stay cable coupled with vibration in cable-stayed bridges.