Nonlinear Dynamics Analysis of an Active Vibration Control System for Super‐Long Stay Cable Under Parametric Resonance Coupled With Bridge Motion - Du, Junping; Liu, Min; Zhou, Peng; Xiao, Huigang (Structural control and health monitoring, 2025)
With increasing performance demand in modern cable‐stayed bridges towards long‐span, light‐weight, heavy‐load, and extreme‐condition, the associated vibrations have become such problematic that may significantly confine the performance of the cable‐stayed bridge systems and even may lead to the failure of the systems. Specifically, the growing span of the cable‐stayed bridges may increase the risk of larger and potentially more destructive nonlinear parametric vibrations of super‐long cables coupled with bridge decks. For mitigating parametric vibrations, research studies have shown that active control can not only achieve superior effective vibration mitigation but also provide guidance and methods for semiactive control device design such as magnetorheological (MR) dampers and other intelligent equipment. This paper proposes a novel vibration active controller for the coupled super‐long stay cable–bridge deck and investigates the nonlinear dynamic behaviors of the active controlled parametric vibrations of super‐long stay cable coupled with bridge vibration. Here, a stay cable’s gravity sag curve equation is employed to establish the parametric vibrations model. This sag curve equation includes the chordwise force of gravity. Based on this vibration model, we have provided more comprehensive insight into the nonlinear behaviors of super‐long stay cables and the influence of the active controller on the nonlinear behaviors. The nonlinear dynamic characteristics, bifurcations, and chaotic motions were investigated in the case of 1:2:1, 1:1:1, and 2:1:2 resonance. This study firstly provides richer theoretical insight on the complex nonlinear parametric vibrations of super‐long stay cable coupled with bridge vibration employed with active controller, secondly gives guidance for semiactive control devices design based on the provided active control strategy, and thirdly highlights potential benefits of using active control strategy to mitigate strongly nonlinear parametric vibrations systems.