Comparison of TMD designs for a footbridge subjected to human-induced vibrations accounting for structural and load uncertainties

A vibration serviceability assessment of footbridges is required in design stage to evaluate the response to human-induced excitation. If the calculated response does not meet the desired criteria for vibration comfort, a Tuned Mass Damper (TMD) can be installed as a vibration mitigation device. The TMD mass, stiffness and damping constant must be tuned to the modal parameters of the structure to obtain the desired response reduction. The response prediction and TMD design rely on a good knowledge of the modal parameters of the footbridge and usually assume that the response is governed by a perfect harmonic loading causing resonance. Differences between the predicted and actual modal parameters may lead to both an unreliable response prediction and a suboptimal TMD performance. Therefore, a robust design of the TMD is proposed accounting for uncertainties in the modal parameters. Realistic walking scenarios of continuous pedestrian traffic are simulated to obtain an effective response reduction by the TMD. In this contribution, the robust design of a TMD is demonstrated for a slender footbridge accounting for reasonable levels of uncertainties in the modal parameters. Numerical optimisation is therefore applied and vibration serviceability requirements are imposed as design constraints. The obtained TMD parameters are compared to those obtained from the formulae proposed by Asami, determining the stiffness and damping constant as a function of its mass. It is found that the TMD mass can be further reduced when the TMD parameters are tuned independently from each other compared to the classical design according to Asami but a higher computation cost is needed. Furthermore, an increasing degree of robustness against variations in the modal parameters is obtained by increasing the TMD mass and damping.