Optimization-based design of tuned mass dampers for pedestrian bridges with multiple significant vibration modes

Pedestrian bridges often experience excessive vibration levels due to their low natural frequency. Equipping the bridge with tuned mass dampers (TMDs) is a commonly used solution to address this problem. Guidelines widely used in engineering practice for the vibration serviceability assessment of pedestrian bridges, such as the Sétra guideline, employ a mode-by-mode assessment. This approach is not well suited for bridges with closely spaced modes where the response consists of contributions from multiple modes. In this study, we propose a gradient-based optimization method for designing TMDs for pedestrian bridges with several significant vibration modes, in order to obtain more cost-effective TMD designs. Two cases studies of existing footbridges are presented and benchmarked against the conventional Sétra design method. The results show a significant reduction in total TMD mass.