Dynamic reliability analysis of continuous girder bridge with fractional order dampers under nonstationary random excitation

Due to the improvement of seismic design standards, viscoelastic dampers have been rapidly developed and widely applied in bridge structures. Currently, there is limited research on dynamic reliability analysis of large bridge structures equipped with fractional-order dampers. In this paper, a hybrid method combining the time-domain explicit method and Markov process is proposed for the dynamic reliability analysis of multi-span continuous girder bridges with fractional-order dampers under non-stationary random excitation. This method introduces a fractional damping system and non-stationary random excitation to simulate both the bridge structure and external forces. The response coefficient matrix of the fractional damping structure is solved using the time-domain explicit method, and the response variance is directly calculated using the moment algorithm. The dynamic reliability analysis is then performed by applying the Markov process based on the structural response variance. Compared to traditional methods for structural dynamic reliability analysis, this approach offers higher computational efficiency and greater accuracy. By analyzing the response variance and dynamic reliability of a four-span continuous girder bridge equipped with viscoelastic dampers, the proposed method is validated using the Monte Carlo method.