Nonlinear structural analysis of the Victor-Neels suspension footbridge under large amplitude vibrations

This paper examines the dynamic behaviour of a suspended pedestrian bridge, with emphasis on the geometric non-linearities arising from the quadratic relationship between cable stiffness and displacement. The Victor-Neels bridge built in Eiffel (Germany) served as a case study. A detailed numerical model was developed using in in-house non-linear finite element model and calibrated through an experimental campaign involving pedestrian-induced vibrations. Modal parameters were identified, and hanger tension measurements enabled refinement of the model to accurately reproduce the actual behaviour of the bridge. Non-linear dynamic numerical analyses conducted with a set of sine-sweep excitations of varying amplitude revealed a stiffness increase beyond a certain vibration threshold, leading to smaller displacement amplitudes and a shift in the resonant frequency compared to linear predictions. Although linear analyses tend to be conservative, they may overestimate displacements and encourage unnecessary structural measures such as oversized designs or Tuned Mass Dampers (TMDs). The study further assessed the performance of linear TMDs under both linear and non-linear conditions. When tuned to the shifted frequency obtained from non-linear analysis, TMD efficiency improved, allowing comparable damping performance with a reduced mass. These findings open perspectives for optimizing TMD design and for developing non-linear TMDs featuring speeddependent damping to further mitigate vibration amplitudes.