Motion-based design of TMD for vibrating footbridges under uncertainty conditions

Tuned mass dampers (TMDs) are passive damping devices widely employed to mitigate the pedestrian-induced vibrations on footbridges. The TMD design must ensure an adequate performance during the overall life-cycle of the structure. Although the TMD is initially adjusted to match the natural frequency of the vibration mode which needs to be controlled, its design must further take into account the change of the modal parameters of the footbridge due to the modification of the operational and environmental conditions. For this purpose, a motion-based design optimization method is proposed and implemented herein, aimed at ensuring the adequate behavior of footbridges under uncertainty conditions. The uncertainty associated with the variation of such modal parameters is simulated by a probabilistic approach based on the results of previous research reported in literature. The pedestrian action is modelled according to the recommendations of the Synpex guidelines. A comparison among the TMD parameters obtained considering different design criteria, design requirements and uncertainty levels is performed. To illustrate the proposed approach, a benchmark footbridge is considered. Results show both which is the most adequate design criterion to control the pedestrian-induced vibrations on the footbridge and the influence of the design requirements and the uncertainty level in the final TMD design.