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Significance Statement
Stay cables are prone to large amplitude vibrations due to their low inherent damping. The common countermeasure is to connect transverse passive oil dampers to the cables at approx. 3% of cable length in order to guarantee sufficient damping in the first four cable modes against rain wind induced vibrations. Since stay cables may be up to 580 m in case of the world largest cable-stayed bridges the damper position of 3% of cable length implies that the required stroke of the dampers becomes large and the damper support structure tall whereby the dampers and their supports are costly. Innovative damping systems are therefore required that generate the same cable damping but at reduced damper position. The presented paper describes a semi-active cable damping system that is based on a controllable oil damper with one collocated sensor. The collocated displacement sensor is needed to measure the actual cable displacement at damper position from which the collocated velocity and the actual frequency of vibration are determined in real-time. Based on these states and only two parameters, i.e. cable tension force and damper position, the command force is computed which is the superposition of a viscous force and a negative stiffness force. A controllable oil damper is adopted to track in real-time the command force. Each cable damper is controlled by its decentralized real-time controller within a single control loop. Hence, every cable damper is controlled according to the actual vibration state of the corresponding cable. The efficiency of the described semi-active stay cable damping systems allows reducing the damper position to approx. 50% of the required position of passive dampers that are optimally tuned to mitigate the first four cable modes. The semi-active damping system is also tested for the typical situations when modes 1 and 3 and modes 2 and 4 are vibrating at the same time which confirms its superior efficiency compared to passive oil dampers. Hence, the proposed semi-active damping system represents an efficient and robust tool for stay cable damping.
Journal Reference
Smart Materials and Structures, Volume 24, Number 11 (2015).
F Weber1,2 , H Distl3
[expand title=”Show Affiliations”]- Maurer Switzerland GmbH, Neptunstrasse 25, CH-8032 Zürich, Switzerland
- Formerly senior scientist at Empa, Swiss Federal Laboratories for Materials Science and Technology, Structural Engineering Research Laboratory, Überlandstrasse 129, CH-8600 Dübendorf, Switzerland (part of this research was developed by F. Weber at Empa
- Maurer Söhne Engineering GmbH & Co. KG, Frankfurter Ring 193, D-80807 Munich, Germany
Abstract
This paper derives an approximate collocated control solution for the mitigation of multi-mode cable vibration by semi-active damping with negative stiffness based on the control force characteristics of clipped linear quadratic regulator (LQR). The control parameters are derived from optimal modal viscous damping and corrected in order to guarantee that both the equivalent viscous damping coefficient and the equivalent stiffness coefficient of the semi-active cable damper force are equal to their desired counterparts. The collocated control solution with corrected control parameters is numerically validated by free decay tests of the first four cable modes and combinations of these modes. The results of the single-harmonic tests demonstrate that the novel approach yields 1.86 times more cable damping than optimal modal viscous damping and 1.87 to 2.33 times more damping compared to a passive oil damper whose viscous damper coefficient is optimally tuned to the targeted mode range of the first four modes. The improvement in case of the multi-harmonic vibration tests, i.e. when modes 1 and 3 and modes 2 and 4 are vibrating at the same time, is between 1.55 and 3.81. The results also show that these improvements are obtained almost independent of the cable anti-node amplitude. Thus, the proposed approximate real-time applicable collocated semi-active control solution which can be realized by magnetorheological dampers represents a promising tool for the efficient mitigation of stay cable vibrations.
© 2015 IOP Publishing Ltd
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