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M. Reiterer:
"DAMPING OF PEDESTRIAN-INDUCED BRIDGE VIBRATIONS BY TUNED LIQUID COLUMN DAMPERS";
Talk: GAMM Annual Meeting 2004, Dresden, Deutschland; 2004-03-21 - 2004-03-27.

Recent problems in footbridge construction were the unexpected pedestrian-induced vibrations of London’s Millennium Bridge during its opening day on June 10, 2000, see Dallard et al. [1]. Due to a sufficiently dense population of crossing pedestrians, undesired lateral vibrations occur and give reason to close the bridge on June 12, 2000. The extensive retrofit involves the use of fluid viscous dampers and tuned mass dampers (TMDs) in order to increase the structural damping. Another recent example is the Toda Park pedestrian cable-stayed bridge in Toda city, Japan, see Nakamura and Fujino [2]. Tuned liquid dampers (TLDs) were installed inside the box girder, which were found to be useful in decreasing the vibration level.
In the present investigation it is proposed to apply the more efficient and more economic tuned liquid column damper (TLCD), for suppressing the pedestrian-induced vibration of footbridges. TLCDs have definite advantages over other damping devices, such as low cost of design and maintenance, easy tuning, simple construction and the comparable performance to TMD, see Hochrainer [3]. The TLCD relies on the motion of a liquid mass in a sealed tube-like container to counteract the external motion while a built-in orifice plate induces damping forces to dissipate kinetic energy.
For this study a mathematical model of a coupled bridge/TLCD system is derived and analyzed numerically. The substructure synthesis method is used for deriving the equations of motion for the coupled system. Hence, in a first step the TLCD is separated from the main structure and considered under a general plane motion. Applying the modified Bernoulli equation along the relative non-stationary streamline in the moving frame, see Ziegler [4], yields the nonlinear equation of motion for the TLCD. Subsequently, coupling the separated TLCD with the bridge structure over the resulting forces and the resulting moment, finally, yields the equations of motion for the main structure (footbridge). In order to compare theoretical with experimental results a small-scale testing facility has been constructed in the laboratory of the Institute of Rational Mechanics. In the present model, a general motion of the main structure (footbridge) in vertical, lateral and torsional directions is admitted. A series of free and forced vibration tests of the main structure equipped with a TLCD are performed. Thereby, the pedestrian excitation of the structural model is characterized by different harmonic signals in vertical and lateral direction given through electro-dynamical forces applied contact-less. The TLCD is optimal tuned to the first lateral mode of the main structure and decreases the resonant peak considerably. The experimental results are in good agreement with the theoretical predictions and it can be concluded that the innovative TLCDs are effective damping devices for the control of pedestrian-induced vibrations of footbridges.

[1] Dallard, P., Fitzpatrick, A.J., Flint, A., Le Bourva, S., Low, A., Ridstill Smith, R.M., Willford, M., 2001, `The London Millennium Footbridge’, The Structural Engineer, Vol. 79, 22, p. 17-33.
[2] Nakamura, S., Fujino, Y., 2002, `Lateral Vibration on a Pedestrian Cable-Stayed Bridge’, Structural Engineering International, 4, p. 295-300.
[3] Hochrainer, M.J., 2001, `Control of vibrations of civil engineering structures with special emphasis on tall buildings’, Dissertation, Vienna University of Technology, Vienna.
[4] Ziegler, F., 1998, `Mechanics of Solids and Fluids’, 2nd edition, Vienna-New York, Springer Verlag.