Uncertainty propagation of flutter analysis for long-span bridges using probability density evolution method

Dynamic and aerodynamic uncertainties are inevitably involved in the wind-bridge system due to some unknown information or complicated environment conditions. The deterministic aeroelastic flutter study is unable to account for these uncertainties and fail to describe the fragility or risk of flutter instability of the bridge. To achieve the uncertainty propagation of flutter analysis for long-span bridges, the advanced probability density evolution method is introduced. The increase of wind speed is treated as a time-varying parameter incorporated into the generalized density evolution equation. The two-dimensional bimodal and three-dimensional multi-mode methods for bridge flutter analysis are utilized to track the probability density evolution of damping ratio and frequency of each mode. The probability of flutter critical wind speeds can then be readily determined. The probability density evolution process is applied to a simply supported beam bridge with quasi-flat box girder and a suspension bridge with closed-box girder by considering the uncertainties of the structural properties and flutter derivatives. The probability density evolution method is proved to produce a reasonable result which shows a good agreement with Monte Carlo method, but requires fewer sample points, which improves the computational efficiency.