An efficient hybrid method for dynamic interaction of train–track–bridge coupled system

Zhihui Zhu, Lei Zhang, Wei Gong, Lidong Wang, Yu Bai, Issam E. Harik

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


An efficient hybrid method (HM) is proposed by combining the direct stiffness method (DSM) and the mode superposition method (MSM) for analyzing the train–track–bridge coupled system (TTBS). The train and the track are modeled by applying the multi-body dynamics and the DSM, respectively. The bridge is modeled by applying the MSM that is efficient in capturing the dynamic behavior with a small number of modes. The train–track subsystem and the bridge subsystem are coupled by the interaction forces between them. The computational efficiency is significantly improved because of the considerably reduced number of equations of motion of the TTBS. Numerical simulations of a train traversing an arch railway bridge are performed and the results are compared with the field test data and the data from other methods, demonstrating the efficiency and accuracy of the proposed method.

Original languageEnglish
Pages (from-to)1084-1093
Number of pages10
JournalCanadian Journal of Civil Engineering
Issue number9
StatePublished - 2020

Bibliographical note

Funding Information:
This work was supported by the National Natural Science Foundation of China [grant numbers 51678576, 51378511], the National Key R&D Program of China [grant number 2017YFB1201204], and the Special Projects of Science and Technology in Hunan Province (grant number 2015GK1001).

Publisher Copyright:
© 2020, Canadian Science Publishing. All rights reserved.


  • Computational efficiency
  • Direct stiffness method
  • Dynamic analysis
  • Mode superposition method
  • Train–track–bridge coupled system

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Environmental Science (all)


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