Abstract
The relative motion of transverse cable dampers is smaller than predicted by the taut string model because of the effects of bending stiffness and fixed support conditions. As a result of the reduced damper motion, the dissipated energy per cycle is reduced as well, which may explain why damping measurements on real stay cables with transverse dampers often show lower cable damping ratios than expected from the taut string theory. To compensate for the reduced damper motion and damper efficiency, respectively, a semi-active cable damper is proposed. The controllable damper is realized by a hydraulic oil damper with real-time controlled bypass valve whereby the resulting damper force is purely dissipative. The proposed control law is clipped viscous damping with negative stiffness. The viscous coefficient is adjusted in real time to the actual frequency of vibration to generate optimum modal damping while the negative stiffness component partially compensates for the reduced damper motion due to the flexural rigidity and fixed support conditions of the cable. The measurements of the prototype semi-active hydraulic damper are used to derive a precise model of the semi-active damper force including the control force constraints due to the fully open and fully closed bypass valve. This model is used to compute the cable damping ratios of the first four cable modes, for typical damper positions, for a taut string model and for a cable model with flexural rigidity and fixed supported ends. The obtained cable damping ratios are compared to those resulting from the passive linear viscous damper being optimized to the first four cable modes. The results demonstrate that the proposed semi-active cable damper with the consideration of the minimum and maximum control force constraints significantly enhances the cable damping of the first four modes compared to the linear viscous damper.
Highlights
Stay cables are susceptible to vibrations because of their low inherent damping [1,2]
The results demonstrate that the proposed semi-active cable damper with the consideration of the minimum and maximum control force constraints significantly enhances the cable damping of the first four modes compared to the linear viscous damper
The adopted control law is clipped viscous damping with negative stiffness whose viscous coefficient is adjusted to the actual frequency of motion in real time generating optimum modal damping and the negative stiffness force helps to increase the damper motion in order to dissipate more energy than the passive damper
Summary
Stay cables are susceptible to vibrations because of their low inherent damping [1,2]. The common procedure is to optimize the viscous damper coefficient to the targeted modes in order to guarantee at the required damping in lowest and highest targeted modes whereby the damper position is automatically minimized [19] This analytical method is based on optimum modal damping, assuming that the cable can be modelled as a taut string, i.e., a cable without bending rigidity and with supported ends [14,15,16]. The experimental investigations on a single strand with fixed support end conditions and bending rigidity described in [23,24] demonstrate that the cable motion at typical damper positions is reduced by 20% to 40% compared to the taut string model prediction This means that the cable damping ratio due to a transverse damper is at least 20% to 40% smaller than expected from the closed-form solution 1/2 a/L (a: damper position, L: cable length, valid for a/L ≈ 1 %) being valid for a taut string behaviour. The expressions (10) and (11) are only valid for a taut string, i.e., a cable with supported ends and without flexural rigidity, and a transverse damper being optimized to one targeted mode and not to several modes as commonly specified for real stay cables
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