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Three-dimensional random vibrations of a high-speed-train–bridge time-varying system with track irregularities are studied in this paper. The rail irregularity is regarded as a random process. By extending the pseudo-excitation method, three kinds of rail irregularity are transformed into a pseudo load vector of the coupled system. A finite element model is used to describe the bridge and a spatial multi-body mass–spring–damping model is adopted to represent a moving railway car. Monte Carlo simulations are implemented to validate the presented method. A detailed case study on the train–bridge coupled system is conducted; it is focused on the effects of three kinds of rail irregularity on the stochastic characteristics of the dynamic responses of the system. The effect of randomness on the level of safety and the riding comfort created by the coupled system are also discussed. The results demonstrate that track irregularities may have a greater impact on the transverse response of the coupled system than on the vertical responses.

Simply supported pre-stressed concrete box-girder bridges are the most common bridge type found on high-speed railway and urban rail transit lines in China. A field experiment has been conducted on the Pixian Viaduct of the Chengdu–Dujiangyan Intercity Railway, where two kinds of simply supported pre-stressed concrete box-girder bridges with a standard span of 32 m are used, one single track and the other double track. Characteristics of the noise underneath the box-girder, far from the bridge, and near the bridge gap were measured and analyzed in the time and frequency domains during high-speed train passage, as was the vibration of the box-girder’s bottom plate. The variations of noise with distance and train speed at locations 1.5 and 9 m above ground level were measured and fitted using mathematical formulae. A simplified formula to predict near-field bridge-borne noise was proposed and verified. The peak bridge-borne noise frequency and its tonal characteristic at 50 and 63 Hz for the double-track and single-track box-girders, respectively, were interpreted in terms of bridge vibration and sound radiation efficiency, respectively. The vibration/noise transfer function and coherence were evaluated, showing that vibration resonance is more significant than acoustic coincidence and that the former is more important in terms of noise reduction.

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In order to study the random vibration performance of trains running on continuous beam bridge with vertical track irregularity, a time-domain framework of random analysis on train-bridge coupling system is established. The vertical rail irregularity is regarded as a random process. A multibody mass-spring-damper model is employed to represent a moving railway car and the bridge system is simulated by finite elements. By introducing the pseudo excitation algorithm into the train-bridge interaction dynamic system, expressions of the mean value, standard deviation, and power spectral density of the nonstationary random dynamic responses of bridge and vehicles are derived. Monte-Carlo simulations are implemented to validate the presented method. A comprehensive analysis of the train-bridge coupling system with vertical track irregularity is conducted focusing on the effect of the randomness of the vertical rail irregularity on the dynamic behavior of the running train and the three-span continuous concrete bridge. Moreover, stochastic characteristics of the indicator for assessing the safety and the riding quality of the railway cars running on continuous beam bridge are carried out, which may be a useful reference in the dynamic design of the bridge.