Research PaperNo Access

Vector Form Intrinsic Finite Element Method for Analysis of Train–Bridge Interaction Problems Considering The Coach-Coupler Effect

Y. F. Duan

College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 31000, P. R. China

Search for more papers by this author

S. M. Wang

College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 31000, P. R. China

Search for more papers by this author

, and

J. D. Yau

College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 31000, P. R. China

Department of Architecure, Tamkang University, New Taipei City 25137, Taiwan

E-mail Address: jdyau@mail.tku.edu.tw

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S0219455419500147Cited by:22 (Source: Crossref)

Abstract

In this paper, the vector form intrinsic finite element (VFIFE) method is presented for analysis the train–bridge systems considering the coach-coupler effect. The bridge is discretized into a group of mass particles linked by massless beam elements and the multi-body coach with suspension systems is simulated as a set of mass particles connected by parallel spring-dashpot units. Then the equation of motion of each mass particle is solved individually and the internal forces induced by pure deformations in the massless beam elements are calculated by a fictitious reverse motion method, in which the structural stiffness matrices need not be updated or factorized. Though the vector-form equations resulting from the VFIFE method cannot be used to compute the structural frequencies by the eigenvalue approach, this study proposes a numerical free vibration test to identify the bridge frequencies for evaluating the bridge damping. Numerical verifications demonstrate that the present VFIFE method performs as accurately as previous numerical ones. The results show that the couplers play an energy-dissipating role in reducing the car bodies’ response due to the bridge-induced resonance, but not in their response due to the train-induced resonance because of the bridge’s intense vibration. Meanwhile, a dual-resonance phenomenon in the train–bridge system occurs when the coach-coupler effect is considered in the vehicle model.

Keywords:

Remember to check out the Most Cited Articles!
Remember to check out the structures

References

1. Y. B. Yang, J. D. Yau and L. C. Hsu, Vibration of simple beams due to trains moving at high speeds, Eng. Struct. 19 (11) (1997) 936–944. Web of Science, Google Scholar
2. Y. B. Yang, M. Li, B. Zhang, Y. T. Wu and J. P. Yang, Resonance and cancellation in torsional vibration of mono-symmetric I-Sections under moving loads, Int. J. Struct. Stab. Dyn. 18 (9) (2018) 1850111. Link, Web of Science, Google Scholar
3. Y. L. Li, S. Y. Zhu, C. S. Cai, C. Yang and S. Z. Qiang, Dynamic response of railway vehicles running on long-span cable-stayed bridge under uniform seismic excitations, Int. J. Struct. Stab. Dyn. 13 (5) (2016) 1550005. Link, Web of Science, Google Scholar
4. Y. B. Yang, M. C. Cheng and K. C. Chang, Frequency variation in vehicle–bridge interaction system, Int. J. Struct. Stab. Dyn. 13 (2) (2013) 1350019. Link, Web of Science, Google Scholar
5. J. D. Yau and Y. B. Yang, Vibration reduction for cable-stayed bridges traveled by high-speed trains, Finite Elem. Anal. Des. 40 (3) (2004) 341–359. Web of Science, Google Scholar
6. L. Lu and J. Li, Longitudinal vibration and its suppression of a railway cable-stayed bridge under vehicular loads, Int. J. Struct. Stab. Dyn. 18 (4) (2018) 1850052. Link, Web of Science, Google Scholar
7. H. Xia, N. Zhang and W. W. Guo, Analysis of resonance mechanism and conditions of train–bridge system, J. Sound Vib. 297 (3) (2006) 810–822. Web of Science, Google Scholar
8. L. Mao and Y. Lu, Critical speed and resonance criteria of railway bridge response to moving trains, J. Bridge Eng. 18 (2) (2011) 131–141. Web of Science, Google Scholar
9. J. D. Yau and Y. B. Yang, Vertical accelerations of simply supported beams due to successive loads traveling at resonant speeds, J. Sound Vib. 289 (1) (2006) 210–228. Web of Science, Google Scholar
10. Y. B. Yang, C. L. Lin, J. D. Yau and D. W. Chang, Mechanism of resonance and cancellation for train-induced vibrations on bridges with elastic bearings, J. Sound Vib. 269 (1) (2004) 345–360. Web of Science, Google Scholar
11. Y. B. Yang and J. D. Yau, Vertical and pitching resonance of train cars moving over a series of simply supported beams, J. Sound Vib. 337 (2015) 135–149. Web of Science, Google Scholar
12. Y. H. Chen and Z. M. Shiu, Resonant curves of an elevated railway to harmonic moving loads, Int. J. Struct. Stab. Dyn. 4 (2) (2004) 237–257. Link, Google Scholar
13. J. D. Yau, Resonance of continuous bridges due to high speed trains, J. Mar. Sci. Technol. 9 (1) (2001) 14–20. Google Scholar
14. S. H. Ju and H. T. Lin, Resonance characteristics of high-speed trains passing simply supported bridges, J. Sound Vib. 267 (5) (2003) 1127–1141. Web of Science, Google Scholar
15. G. Gu, Resonance in long-span railway bridges carrying TGV trains, Comput. Struct. 152 (2015) 185–199. Web of Science, Google Scholar
16. L. Y. Liu, J. D. Yau, F. Zeng and W. D. Wang, Mitigation of resonance for high speed train–bridge systems considering overhanging beam effects, J. Appl. Sci. Eng. 19 (3) (2016) 259–266. Google Scholar
17. Y. B. Yang, J. D. Yau and Y. S. Wu, Vehicle–Bridge Interaction Dynamics (World Scientific Publishing Company, Singapore, 2004). Link, Google Scholar
18. H. Xia and N. Zhang, Dynamic analysis of railway bridge under high-speed trains, Comput. Struct. 83 (23) (2005) 1891–1901. Web of Science, Google Scholar
19. P. Lou, A Vehicle–track–bridge interaction element considering vehicle’s pitching effect, Finite Elem. Anal. Des. 41 (4) (2005) 397–427. Web of Science, Google Scholar
20. W. W. Guo and Y. L. Xu, Fully computerized approach to study cable-stayed bridge–vehicle interaction, J. Sound Vib. 248 (4) (2001) 745–761. Web of Science, Google Scholar
21. F. Yang and G. A. Fonder, An iterative solution method for dynamic response of bridge–vehicles systems, Earthq. Eng. Struct. Dyn. 25 (2) (1996) 195–215. Web of Science, Google Scholar
22. H. Qiao, H. Xia and X. Du, Dynamic analysis of an integrated train–bridge–foundation–soil system by the substructure method, Int. J. Struct. Stab. Dyn. 18 (2017) 1850069. Link, Web of Science, Google Scholar
23. N. Zhang and H. Xia, Dynamic analysis of coupled vehicle–bridge system based on inter-system iteration method, Comput. Struct. 114 (2013) 26–34. Web of Science, Google Scholar
24. Y. B. Yang, C. H. Chang and J. D. Yau, An element for analyzing vehicle–bridge systems considering vehicle’s pitching effect, Int. J. Numer. Meth. Eng. 46 (7) (1999) 1031–1047. Web of Science, Google Scholar
25. E. C. Ting, C. Shih and Y. K. Wang, Fundamentals of a vector form intrinsic finite element: Part I. Basic procedure and a plane frame, J. Mech. 20 (2) (2004) 113–122. Web of Science, Google Scholar
26. E. C. Ting, C. Shih and Y. K. Wang, Fundamentals of a vector form intrinsic finite element: Part II. Plane solid elements, J. Mech. 20 (2) (2004) 123–132. Web of Science, Google Scholar
27. C. Shih, Y. K. Wang and E. C. Ting, Fundamentals of a vector form intrinsic finite element: Part III. Convected material frame and examples, J. Mech. 20 (2) (2004) 133–143. Web of Science, Google Scholar
28. E. C. Ting, Y. F. Duan and T. Y. Wu, Vector Mechanics of Structure (Science Press, Beijing, 2012) (in Chinese). Google Scholar
29. C. Y. Wang, R. Z. Wang, C. C. Chuang and T. Y. Wu, Nonlinear dynamic analysis of reticulated space truss structures, J. Mech. 22 (3) (2006) 199–212. Web of Science, Google Scholar
30. T. Y. Wu and E. C. Ting, Large deflection analysis of 3D membrane structures by a 4-node quadrilateral intrinsic element, Thin-Wall Struct. 46 (3) (2008) 261–275. Web of Science, Google Scholar
31. K. H. Lien, Y. J. Chiou, R. Z. Wang and P. A. Hsiao, Vector form intrinsic finite element analysis of nonlinear behavior of steel structures exposed to fire, Eng. Struct. 32 (1) (2010) 80–92. Web of Science, Google Scholar
32. R. Z. Wang, K. C. Tsai and B. Z. Lin, Extremely large displacement dynamic analysis of elastic–plastic plane frames, Earthq. Eng. Struct. Dyn. 40 (13) (2011) 1515–1533. Web of Science, Google Scholar
33. T. Y. Wu, Nonlinear analysis of axial-symmetric solid using vector mechanics, Comput. Model. Eng. Sci. 82 (2) (2011) 83–112. Web of Science, Google Scholar
34. T. Y. Wu, Dynamic nonlinear analysis of shell structures using a vector form intrinsic finite element, Eng. Struct. 56 (2013) 2028–2040. Web of Science, Google Scholar
35. Y. F. Duan, K. He, H. M. Zhang, E. C. Ting, C. Y. Wang, S. K. Chen and R. Z. Wang, Entire-process simulation of earthquake-induced collapse of a mockup cable-stayed bridge by vector form intrinsic finite element (VFIFE) method, Adv. Struct. Eng. 17 (3) (2014) 347–360. Web of Science, Google Scholar
36. Y. F. Duan, S. M. Wang, R. Z. Wang, C. Y. Wang and E. C. Ting, Vector form intrinsic finite element based approach to simulate crack simulation, J. Mech. 33 (6) (2017) 797–812. Web of Science, Google Scholar
37. Y. F. Duan, S. M. Wang, R. Z. Wang, C. Y. Wang, J. Y. Shih and C. B. Yun, Vector form intrinsic finite element analysis for train and bridge dynamic interaction, J. Bridge Eng. 23 (1) (2018) 04017126. Web of Science, Google Scholar
38. Y. B. Yang and J. D. Yau, Resonance of high-speed trains moving over a series of simple or continuous beams with non-ballasted tracks, Eng. Struct. 143 (2017) 295–305. Web of Science, Google Scholar
39. Y. J. Wang, Q. C. Wei and J. D. Yau, Interaction response of train loads moving over a two-span continuous beam, Int. J. Struct. Stab. Dyn. 13 (1) (2013) 1350002. Link, Web of Science, Google Scholar
40. G. Shen, Optimization and simulation of inter-vehicle connections for high speed and medium speed trains, J. China Rail. Soc. 19 (1997) 19–24 (in Chinese). Google Scholar
41. T. Y. Lee, K. J. Chung and H. Chang, A new implicit dynamic finite element analysis procedure with damping included, Eng. Struct. 147 (2017) 530–544. Web of Science, Google Scholar
42. T. Y. Lee, K. J. Chung and H. Chang, A new procedure for nonlinear dynamic analysis of structures under seismic loading based on equivalent nodal secant stiffness, Int. J. Struct. Stab. Dyn. 18 (3) (2018) 1850043. Link, Web of Science, Google Scholar