Motion-Based Design of Semi-Active Tuned Mass Dampers to Control Pedestrian-Induced Vibrations in Footbridges under Uncertainty Conditions

Abstract

Modern slender footbridges are sensitive to human-induced vibrations together with the uncertainty associated with the variation of the operational and environmental conditions. In order to overcome these limitations, semi-active damping devices have been widely employed due to their adequate balance between their effectiveness and their cost when they are used to control the pedestrian-induced vibrations in footbridges. Different design methods have been proposed to guarantee that the footbridges, controlled by these damping devices, meet the vibration service ability limit state without compromising their budget. Among these proposals, the motion-based design method has shown a high performance when it has been implemented to design passive damping devices for footbridges. Herein, the motion-based design method under uncertainty conditions has been adapted and further implemented for the robust optimum design of semi-active tuned mass dampers when they are employed to control the pedestrian-induced vibrations in slender footbridges. According to this method, the design problem can be transformed into two sub-problems: (i) a multi-objective optimization sub-problem; and (ii) a reliability analysis sub-problem. Thus, its main objective is to find the parameters of the semi-active damping device which guarantee an adequate comfort level without compromising its cost. In order to take into account the effect of the modification of the structural modal properties associated with the variation of the operational and environmental conditions, the compliance of the design requirements has been formulated via a reliability index. Therefore, are liability analysis must be performed to assess the probability of failure associated with the above mentioned serviceability limit state.