Semiactive Control of Nonlinear Parametric Vibration of Super-Long Stay Cable in Cable-Stayed Bridge Installed with Magnetorheological Fluid Damper

As the stay cables of cable-stayed bridges become longer, parametric resonance with a large amplitude is more easily triggered, which becomes a vibration hazard of super-long stay cables. An increasing number of practical applications of vibration mitigation on stay cables demonstrate that vibration control strategies can effectively facilitate hazard mitigation and improve cable-stayed bridge reliability and service life. This study proposes a semiactive control approach to reduce the parametric vibration of super-long stay cables in cable-stayed bridges installed with magnetorheological fluid damper (MRFD). First, using the cable’s gravity sag curve equation, an equation governing the combined stay cable-bridge deck-damper control system was established to consider the effect of the chordwise force of cable gravity. Subsequently, a targeted LQR-based optimal active control law is proposed to provide the target control force in the semiactive control. The parametric influences on the performance of the LQR-based optimal active control were analysed to provide insight into the proposed control strategy. Since the semiactive control could achieve almost the same control efficacy of the targeted optimal active control, a semiactive control strategy employing MRFD is proposed to mitigate the parametric vibration of a super-long stay cable. Based on the proposed semiactive control strategy, the system was attached with the MRFD of the longest cable, S36, in the designed prototype long cable-stayed bridge. The efficacy of the established semiactive control system was also analysed. The analysis results confirm that the proposed semiactive control strategy and designed semiactive control system can perform similar to the LQR-based optimal active control. The semiactive control system attached to the MRFD can mitigate the parametric vibration of super-long stay cables in cable-stayed bridge engineering practice.