A common framework for the robust design of tuned mass damper techniques to mitigate pedestrian-induced vibrations in lively footbridges

The dynamic response of modern slender footbridges is usually sensitive to both the pedestrian actions and the uncertainties associated with their inherent structural behavior. Thus, tuned mass dampers have been widely integrated in the design of these structures to guarantee the fulfillment of the vibration serviceability limit state during their overall life cycle. Three different techniques of tuned mass dampers (active, semi-active and passive) are usually considered for this purpose. Although there are algorithms for the robust design of each particular technique, however, this specificity makes difficult the implementation of all these techniques in practical engineering applications. Herein, the motion-based design method under uncertainty conditions is proposed and further implemented to create a common framework for the robust design of all these techniques when they are employed to mitigate pedestrian-induced vibrations in slender footbridges. According to this method, the design problem may be transformed into the combination of two sequential sub-problems: (i) a reliability multiobjective optimization sub-problem; and (ii) a decision-making sub-problem. Subsequently, the performance of this proposal has been validated through a numerical case study in which the dynamic response of a steel footbridge has been controlled by three different tuned mass damper techniques designed according to the proposed common framework.