A modified moving loads’ model is proposed for the vehicle-bridge coupling vibration simulation. Taking the vehicle-bridge interaction model (VBI) as the reference, the accuracy and applicability of the three calculation models, namely, moving loads’ model, moving mass model, and spring-damper-mass model, are compared using the frequently-used railway simply-supported beam with a span of 32 meters as the research object. Influencing factors such as vehicle speed, mass ratio of vehicle and beam, and primary spring stiffness on the dynamic response of the vehicle-bridge system are discussed in detail. The results show that the moving load model has the best performance on the stability of the deviation rate, but its calculation results are smaller than the other two methods as well as the VBI. The values of the deviation rate for the moving mass model and the spring-damper-mass model are large, and the stability of those are insufficient in the range of 80%∼120% of the first resonance velocity. Except for that, the results of the two models are in good agreement with the VBI model. According to above analysis, a modified moving loads’ model with two amplification coefficients, namely, 1.10 for the range of 90%∼105% of the first resonance velocity and 1.05 for other velocities, are proposed, which has higher calculation efficiency and accuracy.

The focus of this paper is to examine the dynamic factor of the suburban railway by utilizing the random vibration approach. Breaking through the previous methods of relying on huge amounts of measured data, herein, the dynamic factor essentially results from two major parts: the dynamic effect caused by moving train loads and that generated by track irregularity, which has clear physical significance. As the internal excitation of the vehicle–bridge system, track irregularity has strong randomness. Based on the dimension reduction method, the spatial domain power spectral density (PSD) of the track irregularity is transformed into the time-domain PSD. Therefore, the randomness of the random process is reduced by exploiting the constraint form of a random function, and then, the typical samples of the track irregularity considering randomness are constructed. Using the vehicle–bridge coupled vibration model, the standard deviation of the dynamic factor is evaluated accounting for the random track irregularity and 99.7% guarantee rate. Finally, the impact coefficient of the track irregularity on the bridge is methodically obtained. The sensitivity of the standard deviation of the dynamic factor to vehicle speed and bridge frequency is analyzed. The given solution methodology can fully take into account the randomness of the track irregularity. Thereby, it provides the dynamic factor formulas as a reference for the dynamic performance evaluation of suburban railway bridges and possible revision of current design specifications.

An analytical solution for vertical vibrations of a simply supported bridge under the action of moving loads is derived and validated. The effect of bridge frequency, span length and vehicle length on the amplification factor of mid-span displacement is discussed using theoretical formulas and numerical results. The study finds and validates that the maximum bridge amplification factor is function of the length ratio of the bridge-to-vehicle. When the speed of the vehicle is high enough to cause bridge resonance, the maximum amplification factor of the bridge is a certain value, which has no relation to bridge’s frequency. The frequency only affects the speed the maximum amplification factor appears. The changes in the amplification factor are analyzed with the bridge-to-vehicle length ratio, which provides a basis for the selection of bridge span length. A simplified, practical formula for calculating the amplification factor is given. The presented results will be particularly useful for railway bridge preliminary design for high-speed trains and assessment of the expected maximum vibration levels.