Robust design of a TMD for the vibration serviceability of a footbridge

Footbridges are often designed as slender structures, sensitive to human-induced excitation. In the case where the prevailing vibration serviceability requirements are not met, vibration reduction measures such as tuned mass dampers (TMDs) are needed. Both the prediction of the structural response and the design of the TMD rely on the modal parameters of the footbridge. Measurements after construction of footbridges have shown that it is difficult to accurately predict these modal parameters even with detailed finite element models based on structural drawings. Moreover, these parameters evolve in time due to changing environmental conditions and degradation. It is important to take into account these uncertainties in the vibration serviceability assessment as well as in the design of vibration reduction measures. The present paper proposes a robust optimisation approach for the design of a TMD which accounts for uncertainties in the modal parameters. The aim is to minimise the mass of the TMD, assumed as a measure for the cost, by tuning the mass, stiffness and damping values, while guaranteeing that vibration serviceability is satisfied for a range of possible values of the natural frequency and modal damping. In order to investigate the trade-off between the mass of the TMD (cost) and the level of uncertainty, a multi-interval approach is adopted. The optimal parameters are found to change significantly with the level of uncertainty. The TMD mass and damping increase for a higher level of uncertainty to satisfy the vibration serviceability requirements in all possible cases.