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.

The concept of a new real-time controlled TMD based on a semi-active oil damper for human, vortex and wind excitations is described. The desired control force is formulated based on the feedbacks of actual structural acceleration and actual relative motion of damper mass. The associated feedback gains are tuned by the control engineer with respect to the TMD specifications. The desired semi-active control force is generated by a semi-active oil damper with controlled bypass valve in order to minimize energy consumption of the actuator and to maximize fail-safe behaviour, i.e. the system automatically behaves as a correctly tuned passive TMD in case of power break down. The numerical case study of a footbridge demonstrates that the vibration reduction due to the real-time controlled TMD is the same as expected from a passive TMD with approx. 4 times bigger damper mass. On the other hand, for same damper masses, the efficiency of the real-time controlled TMD is far higher than that of the passive TMD without generating greater relative motion amplitudes of the TMD mass.

<p>Tuned mass dampers (TMDs) are widely used to mitigate wind-induced tall building vibrations. However, two major disadvantages of passive TMDs exist. The installation height of pendulum TMDs consumes expensive space and passive TMDs cannot cope with the time-varying excitation frequency of wind loading which will excite several structural modes. Also, the pendulum mass may impact the structure due to seismic excitation which necessitates huge snubbing systems. The presented adaptive TMD System addresses all these shortcomings. The installation height is reduced by up to 50 % by the inclination of the pendulum cables as this method enlarges the radius of the pendulum mass center being equivalent to the reduction of the natural pendulum frequency. The efficiency of the adaptive TMD is improved by adjusting the oil damper characteristics in real-time which allows reducing the pendulum mass up to 20 %. The overdamping control approach activated at wind return periods greater than 10 years reduces the maximum pendulum relative motion by up to 25 %. The adaptive TMD with inclined cables therefore minimizes the installation space which helps to maximize the economic benefit of the building.</p>