A nonlinear numerical scheme to investigate the influence of geometric nonlinearity on post-flutter responses of bridges

The present study aims to investigate the influence of geometric nonlinearity on post-flutter responses by developing a full-mode coupled nonlinear flutter analysis method (frequency-domain method) and a time-dependent nonlinear analysis scheme (time-domain method). This approach integrates the three-dimensional (3D) nonlinear finite element model and nonlinear self-excited force described by amplitude-dependent rational functions (RFs). By comparing post-flutter responses obtained from frequency-domain and time-domain methods, not only the influence of geometric nonlinearity on post-flutter responses is quantified, but also the underlying physical mechanism is revealed. The results show that the geometric nonlinear effect will become more significant with the increase of the amplitude and thus will induce a super-harmonic resonance behavior. The behavior is mainly characterized by the higher harmonic frequencies vibrations with higher-order mode shapes involved in the vertical and torsional displacement responses. Meanwhile, the larger the vibration amplitude, the more significant the super-harmonic resonance behavior. Besides, the geometric nonlinear effect will also cause a significant uplifting of the bridge deck in the vertical direction during 3D nonlinear flutter process. The main physical mechanism for the reduction in the amplitude of post-flutter response (dominated by the vibration with fundamental harmonic frequency) after considering the geometric nonlinear behavior is that the vibrations with higher harmonic frequencies play a role of absorbing energy and reducing vibration (similar to tuned mass damper effect) for the vibration with fundamental harmonic frequency. For the long-span suspension bridge with a main span of 1650 m studied in this study, the geometric nonlinear effect may need to be considered when the torsional amplitude at mid-span is only greater than 1.5°.