Frequency-domain method for non-stationary stochastic vibrations of train-bridge coupled system with time-varying characteristics

When a train passes over a bridge, the vibrations of the vehicles and the bridge are the result of non-stationary stochastic processes due to the time-dependent characteristics of the coupled vehicle-bridge system. The aim of this study is to generalize the frequency domain method to investigate the non-stationary random vibration of the coupled system subjected to the excitation of track irregularities with consideration of time-dependent characteristics. To illustrate the method, a three-span simply supported bridge traversed by a single railway vehicle is adopted as an example. The time-dependent frequency response function (FRF) of the coupled system is theoretically derived through solving ordinary differential equations with variable complex coefficients, and the perturbation method is adopted to improve the calculation efficiency. By combining this with Priestley's Evolutionary Spectra theory, the evolutionary power spectral density (PSD) of the non-stationary random response of the system is then derived. The transitions will occur when the wheels cross the joints between each bridge span and between the bridge and the adjacent roadway. By adopting mode shapes of the full structure, the change of states of the vehicle crossing multiple bridge spans and moving onto the roadway can be solved as a continuous process without separation. The proposed method is validated by comparisons with the Monte Carlo method, showing higher accuracy and efficiency when calculating the time-varying standard deviation of the response. It is found that the vibration of the vehicle is approximately stationary but with large variance due to the random track irregularities, while the bridge vibration follows a strongly non-stationary process with small randomness and is more related to the moving mass effect.