Nonlinear flutter mechanism of a single-layer truss bridge deck based on hysteresis loop and energy budget analysis

The dynamic mechanism of limit cycle oscillation (LCO) and subcritical Hopf bifurcation for a single-layer truss bridge deck, which are of great significance for the flutter design of bridges and have received little research attention before, was studied in this study. Firstly, a two-degree-of-freedom bending-torsion coupled nonlinear self-excited force model was proposed, and the equations to solve the work and energy of aerodynamic forces were derived. Further, the time-varying characteristics of nonlinear self-excited forces were investigated, as well as their contribution to accurately predicting nonlinear flutter response. It was found that self-excited forces contain higher-order octave components, as identified through the hysteresis loop analysis method. Subsequently, the characteristics of the self-excited forces under varying wind speeds were summarized via the analysis of the work done by the self-excited forces. The energy feedback mechanism of LCO was revealed, which highlighted the important role of non-wind-induced and linear terms of self-excited torsional moment in the generation of LCO. Finally, the driving mechanism of the subcritical Hopf bifurcation was explained by combining hysteresis loop analysis, energy budget analysis, and damping ratio as a function of vibration amplitude analysis. It is found to result from the competition between self-excited torsional moment and torsional nonlinear mechanical damping.