KEYWORDS: Vibration control, Bridges, Control systems, Mathematical modeling, Control systems design, Magnesium, Commercial off the shelf technology, Nickel, Structural engineering, Aerodynamics
A mathematical model based on the complex modal theory is formulated to evaluate the damping ratio of cables incorporating smart magneto-rheological (MR) dampers in open-loop control mode, taking into account the damper coefficient, damper stiffness, damper mass, stiffness of the damper support, nonlinearity of the damper, as well as the cable sag and inclination. Based on asymptotic solution of the developed mathematical model, a 'generalized universal formula' is proposed to facilitate the damper design. Comprehensive parametric studies are carried out to analyze the effects on the maximum attainable damping ratio and the corresponding optimal damper coefficient. Making use of the 'generalized universal formula' and results from the parametric studies, design guidelines/procedures for open-loop cable vibration control using MR dampers are developed, for both single-mode optimal control and multi-mode suboptimal control. The guidelines/procedures facilitate the engineering application of MR dampers in mitigating the rain-wind-induced cable vibration on cable-stayed bridges.
A parameter-adaptive three-element model is first developed for a full-scale MR damper based on laboratory tests. The parameters of the model are represented by a set of empirical formulae in terms of displacement amplitude, voltage input, and excitation frequency. The model is then incorporated into the governing equation of cable-damper system for investigation of open-loop vibration control of stay cables in a cable-stayed bridge, by installing the dampers in single- and twin-damper setups respectively. The concept of optimal voltage/current input achieving the maximum damping for the system is put forward and verified. Multi-mode and multi-switch open-loop control methods in single- and twin-damper setups are then developed and a procedure for determining optimal geometric configuration of the twin-damper setup is proposed. The developed analytical formulations and design methods contribute to consummating the design specifications/guidelines for open-loop cable vibration control using MR dampers.
A new smart semi-active device, called magneto-rheological -- tuned liquid column damper (MR-TLCD) has recently been devised by the authors for wind-induced vibration control of tall building structures. The damping performance of this device can be continuously changed and is controllable by altering magnetic filed applied on the MR fluid at the bottom of a U-tube container. Numerical simulations have been conducted to demonstrate its effectiveness in both open-loop and closed-loop control modes, and MR-TLCD prototypes using different solvents in magneto-rheological fluid (MRF) have been manufactured in laboratory. This paper presents an experimental study of an MR-TLCD using one kind of synthetic hydrocarbon -- poly-alpha-olefin (PAO) as solvent of MRF. The prototype is fabricated using a U-tube container with PAO-based MRF, of which the viscosity can be altered in milliseconds by exerting voltage to the electro-magnetic coils at the bottom of the tube. It was tested on a hanging shaking table by positioning it on the top of a structural model which was subjected to ground excitation. Open-loop control tests were carried out with a spectrum of voltage inputs to the MR-TLCD under sweeping sine excitation. The tests show that the smart MR-TLCD can effectively mitigate structural vibration response and a maximum response reduction can be achieved when an optimal voltage input to the damper is exerted, validating the findings of theoretical and simulation studies.
This paper presents theoretical and in-situ experimental studies on semi-active vibration control of bridge cables using magneto-rheological (MR) dampers. The feedback control is accomplished using only one MR damper and one accelerometer collocated near the lower end of the cable. A new control strategy, state-derivative feedback control, is formulated within the framework of reciprocal state space (RSS). This state-derivative feedback control strategy is novel in the sense that it directly uses acceleration information for feedback and state estimation, which is usually the only measurand available in practical cable vibration control implementation. More importantly, the control force commanded by this strategy with an appropriate energy weighting tends to be dissipative and therefore implementable by semi-active MR dampers without clipping. Numerical simulations of state-derivative feedback control for a 115m long stay cable in the cable-stayed Dongting Lake Bridge are conducted under different excitation conditions, and then experimental validation of the prototype cable is carried out in the bridge site with the help of the real-time control system dSPACE. Good agreement is observed between the simulation and experimental results.
As the world's first time implementation of MR-based smart damping technique in bridge structures, a total of 312 semi-active magneto-rheological (MR) dampers have recently been installed on the cable-stayed Dongting Lake Bridge for wind-rain-induced cable vibration control. Prior to the full implementation, a comprehensive field vibration test, has been conducted on the longest cable of 150 m to identify and compare damping performance of the cable-damper system under different damper installation setups and under a wide spectrum of voltage inputs to the MR dampers. Forced vibration experiments were carried out for the cable without damper, with single-damper setup, and with twin-damper setup, respectively. One purpose of this in-situ experimental investigation is to determine the optimal input voltage which achieves maximum system damping for the aim of designing a multi-switch control strategy. Due to geometric nonlinearity of cables and hysteretic nonlinearity of MR dampers, the equivalent modal properties of the cable-damper system are deemed to be amplitude-dependent. Keeping this in mind, a Hilbert transform based method is deployed in the present study to identify the amplitude-dependent natural frequencies and modal damping from the sinusoidal-decay response data. The experimental and identification results show that the equivalent modal damping ratios of the system are noticeably dependent on vibration amplitude and the relevance of the natural frequencies to vibration amplitude is negligible. The single-damper setup is competitive with the twin-damper setup in suppressing in-plane vibration of the cables. However, when mitigation of cable out-of-plane vibration is also required, the twin-damper setup performs much better. For both setups, the value of optimal voltage is found to be mode-dependent and amplitude-dependent.
The newly built cable-stayed Dongting Lake Bridge in Hunan, China has experienced wind-rain-induced cable vibration several times during the past months. A research/implementation project on using semi-active magneto-rheological (MR) dampers for cable vibration control of the bridge is in progress. As part of this ongoing project, one typical stay cable with 115 m length was installed with two MR dampers near the lower anchorage, and accelerometers were deployed on the damped cable and its two neighboring cables for long-term monitoring. After installing the dampers and sensors, wind-rain-induced cable oscillations were observed two times. This paper aims to investigate the vibration characteristics and to identify the equivalent modal damping of the cables with and without MR dampers in one wind-rain-excited event based on in-situ monitoring. In this wind-rain-excited event, the in-plane and out-of-plane responses of the damped cable and its two neighboring free cables were monitored. Equivalent modal damping ratios of the cables in both in-plane and out-of-plane motions are identified by means of spectral analysis of the measured data in conjunction with a curve-fitting technique. Such observed and identified results are beneficial to understanding the coupled motion of cables in wind-rain-excited conditions and the damping contribution of MR dampers to both in-plane and out-of-plane motions. The frequency-domain analysis of the wind-rain-excited responses of the damped and undamped cables also reveals the response characteristics under wind-rain excitation and the damping mechanism of MR dampers in suppressing such oscillation.
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