Vibration control of stay cables using semi-active magneto-rheological (MR) dampers

Abstract

The study presented in this thesis concerns the open-loop and closed-loop vibration control of bridge stay cables using semi-active magneto-rheological (MR) dampers. Theoretical investigations and in-situ experiments are carried out in this study. The open-loop vibration control of flat taut cables is first investigated. A mathematical model based on complex modal theory is formulated to evaluate the damping ratio of the cable-damper system in the open-loop control mode, which takes into account the damper coefficient, damper stiffness, damper mass, stiffness of the damper support, and nonlinearity of the damper. Both asymptotic and numerical solutions are obtained. With the formulated model, a parametric study is conducted to investigate the effect of various damper parameters on the effectiveness of the vibration control. Next, the proposed model for flat taut cables is extended for inclined sagged cables. The effects of cable sag and inclination are included in the formulation in terms of the sag-extensibility parameter. Making use of an asymptotic solution, a 'generalized universal formula' is proposed for the damper design, taking into account the sag and inclination of the cable as well as the abovementioned damper parameters. A parametric study is conducted to investigate the effects of cable sag and inclination on the control effectiveness. It turns out that the effect of the sag and inclination is independent of the damper parameters and, therefore, the parametric study carried out for taut cables is also valid for sagged cables. A case study is conducted for a 536 m long stay cable on Stonecutters Bridge to quantify the influence of the sag and inclination in extremely long bridge cables. The theoretical study concludes with the formation of guidelines for the design and implementation of MR dampers for open-loop cable vibration control, either in a multi-mode suboptimal control pattern or in a single-mode optimal control pattern. For the purpose of in-situ experimental verification, the modelling of a full-scale MR damper and its application to the open-loop vibration control of a 114 m long stay cable in Dongting Lake Bridge are accomplished. The concept of an optimal voltage/current input that achieves maximum system damping is proven, and a multi-switch open-loop control strategy is developed. In-situ experiments in the Dongting Lake Bridge site are then conducted to verify the effectiveness of MR dampers for the open-loop vibration control of stay cables under rain-wind excitation and artificial sinusoidal-step relaxation excitation, respectively. In the rain-wind excitation, by measuring the dynamic responses of an MR-damped cable and its two undamped neighbouring cables, the characteristics of rain-wind-induced cable vibration and the effectiveness of MR dampers in suppressing this kind of oscillation are recognized. In the artificial sinusoidal-step relaxation excitation, comprehensive field tests are carried out to investigate the effects of different damper setups, coupling between the in-plane and out-of-plane vibration, various vibration levels, and different current inputs. The experimental findings compare well with the computational predictions. Some key issues concerning the practical implementation of MR dampers to mitigate vibrations in cables are discussed. After exploring the open-loop control, the issue of closed-loop cable vibration control using MR dampers is addressed. A theoretical investigation is first conducted to develop a state-derivative feedback semi-active control strategy using acceleration measurement, which is accomplished with only one MR damper and one accelerometer collocated near the lower end of the cable. The proposed control strategy directly uses information on acceleration for feedback and state estimation, which is usually the only measurand available in the practical implementation of cable vibration control. More importantly, the control force commanded by the state-derivative control strategy based on energy weighting is dissipative force, except for low velocity and small force. It is therefore implementable by semi-active MR dampers without clipping. Numerical simulations of state-derivative feedback control for a stay cable in Dongting Lake Bridge are conducted under sweeping sine excitation and sinusoidal-step relaxation excitation to investigate the effectiveness of the proposed control strategy. A method for determining the equivalent modal damping ratio for semi-active closed-loop control systems is also proposed, which will help to promote the acceptance of semi-active cable vibration control by civil engineers. Finally, the experimental validation of real-time semi-active vibration control using the proposed control strategy is carried out on the same cable in the bridge site. The damping capacity obtained during the semi-active control test is shown to agree well with the results of the simulation. The in-situ experiments prove that the proposed control strategy is practical and effective.