Effectiveness of “Detuned” TMD's for Beam-Like Footbridges

Abstract

The dynamic properties of Tuned Mass Dampers (TMD's) used to reduce the vibrations of footbridges are generally based on the optimization criterion of Den Hartog. However the spring, mass and damper of a TMD may possess slight fabrication tolerances or change its damping element properties due to temperature, which can result in a detuning of a TMD. The study presented deals with the influence of a detuning on the performance of a TMD. A simplified model for beam-like footbridges under pedestrian loading is proposed. It is shown that a 2-DOF-system in harmonic stationary motion represents a good approximation of the beam structure under transient time-dependent load. Graphs are given to assess the increase of acceleration and the decrease of effectiveness due to detuning. A case study on a footbridge with a span of 45 m demonstrates its accuracy.