Non-stationary random vibration analysis of railway bridges under moving heavy-haul trains

Zhihui Zhu, Lidong Wang, Zhiwu Yu, Wei Gong, Yu Bai

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33 Citations (Scopus)


This paper presents a non-stationary random vibration analysis of railway bridges under moving heavy-haul trains by the pseudo-excitation method (PEM) considering the train-track-bridge coupling dynamics. The train and the ballasted track-bridge are modeled by the multibody dynamics and finite element (FE) method, respectively. Based on the linearized wheel-rail interaction model, the equations of motion of the train-ballasted track-bridge coupling system are then derived. Meanwhile, the excitations between the rails and wheels caused by the random track irregularity are transformed into a series of deterministic pseudo-harmonic excitation vectors by the PEM. Then, the random vibration responses of the coupling system are obtained using a step-by-step integration method and the maximum responses are estimated using the 3σ rule for the Gaussian stochastic process. The proposed method is validated by the field measurement data collected from a simply-supported girder bridge (SSB) for heavy-haul trains in China. Finally, the effects of train speed, grade of track irregularity, and train type on the random dynamic behavior of six girder bridges for heavy-haul railways are investigated. The results show that the vertical acceleration and dynamic amplification factor (DAF) of the midspan of the SSB girders are influenced significantly by the train speed and track irregularity. With the increase in the vehicle axle-load, the vertical deflection-to-span ratio (γ) of the girders increases approximately linearly, but the DAF and vertical acceleration fail to show clear trend.

Original languageEnglish
Article number1850035
Number of pages21
JournalInternational Journal of Structural Stability and Dynamics
Issue number3
Publication statusPublished - 1 Mar 2018


  • Heavy-haul railway
  • pseudo-excitation method (PEM)
  • random vibration
  • time-dependent system
  • track irregularity
  • train-track-bridge coupling system

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