Stay cables in cable-stayed bridges are subjected to various types of dynamic excitation mechanisms under environmental loads. The excited vibrations can have a large amplitude because of low vibration frequencies and small inherent damping of cables. As cables become longer (the longest cables are around 600 m in cable-stayed bridges with a main span of 1000 m), more modes are vulnerable to wind and rain-wind induced vibrations, posing challenges to vibration mitigation. This paper presents a comprehensive review of recent advances in stay cable vibration mitigation, including theoretical modeling of cable damping system and techniques for enhancing multimode damping. Recent results on cable damping measurements, understanding of cable vibrations, and relevant aerodynamic countermeasures are also recalled. The reflections can provide guidance for cable vibration control design of cable-supported bridges and for the maintenance/upgrade of cable vibration mitigation system of existing bridges.

Stay cable vibration mitigation: A review

The parametrically excited lateral vibration of a mass-loaded string is investigated in this paper. Supposing that the mass at the lower end of the string is subjected to a vertical harmonic excitation and neglecting the higher-order vibration modes, the equation of motion for the mass-loaded string can be represented by a Mathieu's equation with cubic nonlinearity. Based on the stability criterion for Mathieu's equation, the critical conditions inducing parametric resonance are clarified. Theoretical analysis shows that when the natural frequency fs of the string lateral vibration and the vertical excitation frequency f satisfy fs= (n/2)f, n= 1, 2, 3, ..., parametric resonance occurs in the case of no damping. For a damped system, parametric resonance most likely occurs when f is close to 2fs, and depends on the damping of the system and the vertical excitation. The critical excitation has been derived at different frequencies. If the natural frequency of the mass vertical vibration happens to be twice that of the string lateral vibration, the parametric resonance may occur due to a small disturbance. Numerical simulations show that the lateral vibration of the string does not increase infinitely at parametric resonance because the parametric excitation is self-tuned due to the coupling between the vertical and lateral vibrations. Finally, the theoretical results are supported by some experimental work.

Theoretical and Experimental Study on the Parametrically Excited Vibration of Mass-Loaded String

Even though cable-stayed bridges have been built for a long time, simplified procedures have been used for characterization of their dynamic response and design purposes. These procedures were essentially directed towards representation of the overall bridge response, with no consideration to cable vibrations. Researchers have recently stressed the importance of cable vibrations on the overall behavior, with the possibility of alteration of the overall bridge response due to cable dynamics. Identification of these complex cable-deck vibration modes, wherein cables and deck vibrate together, then becomes an issue of paramount importance. Analytical studies have been conducted in the past to come up with a methodology to accurately simulate the cable-deck vibration characteristics. But these studies have only looked at the dynamic response of the bridge in completed configuration, and the issues related to variation in vibration characteristics as the bridge is built have not been addressed. For cable-stayed bridges with serious vibration problems, use of tuned mass dampers is being explored and wind-tunnel studies on scaled model of cable-stayed bridges have demonstrated their effectiveness in mitigating vibration problems. This study is directed towards devising a modeling strategy to accurately represent the static and dynamic behavior of the US Grant Bridge and the proposed LAW93C Bridge. Static behavior is judged based on bridge response to moving loads, and dynamic behavior looks at structural vibration characteristics. It is observed that the model accurately simulates the moving load design envelopes and girder strain profiles. Also, the adopted modeling strategy simulates the superstructure, cable, and complex cable-deck vibration modes within error limits. The effect of

Effect of nonlinearities due to geometry, cables and tuned mass dampers on the analysis of cable-stayed bridges

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.

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

Taking the bending stiffness, cable static sag and cable inclinded angle into consideration, the equations of space vibration of the cable-damper system are formulted in this paper. Applying the variable separation strategy and center difference method, the partial differential equations are discrete in space and a set of complex eigenvalue equations are sovled by state space method. Then both the maximum modal damping ratio and the optimal damper parameters are obtained. Some typical stay cables are investigated for both the in-plane and out-plane vibration modes with different cable parameters and damper parameters. The results show the damping ratio for the first in-plane vibration modes with different cable parameters and damper parameters. The resutls show the dampingn ratio for the first in-plane mode is significantly affected by the cable static sag only, but those for the other modes are affected slightly, and cable static sag do not affect the optimal damper parameter for all modes. However the bending stiffness will changes both the maximum modal damping ratios and the optimal damper parameters. Some valuable suggestions are proposed for the optimal damper design.

Maximum modal damping of cable space vibration control with visco damper in cable-stayed bridge

The stay cables in cable-stayed bridges are prone to exhibiting oscillation of large amplitude due to their large flexibility, small mass, and small damping Continued oscillation of the cables may seriously influence the safety and durability of cable-stayed bridges Apart from the rain-wind-induced cable vibration, large-amplitude oscillation of cables caused by parametric excitation due to support motion was recently observed in cable-stayed bridges This kind of cable oscillation is produced by the deck and/or tower motion induced either by moving traffic or by buffeting response of gust wind The oscillation mechanism and control methods of stay cables excited by the deck and/or tower motion are less studied than the rain-wind-induced vibration In this paper, a nonlinear dynamic model for the simulation and analysis of a kind of parametrically excited vibration of stay cables caused by support motion in cable-stayed bridges has been proposed The proposed model takes into account the cable inclination and sag effect Based on this model, the oscillation mechanism and dynamic response characteristics of this kind of vibration are analyzed through numerical calculation It is found that under certain conditions, the parametrically excited oscillation of stay cables in cable-stayed bridges may occur due to deck vibration when the natural frequency of a cable approaches to about half of the first modal frequency of the bridge deck system A new vibration control system installed on the cable anchorage is proposed as a possible means to suppress the cable parametric oscillation The numerical simulation results show that the cable oscillation due to motion of the deck and/or tower can be considerably reduced by use of this control device

Cable parametric oscillation and its control for cable-stayed bridges

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Cable parametric oscillation and its control for cable-stayed bridges