Skip to main content
SpringerLink
Log in

A frequency and amplitude dependent model of rail pads for the dynamic analysis of train-track interaction

  • Article
  • Special Topic: High-speed Railway Infrastructure (II)
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

A frequency and amplitude dependent model is used to describe the complex behavior of rail pads. It is implemented into the dynamic analysis of three dimensional coupled vehicle-slab track (3D-CVST) systems. The vehicle is treated as a 35-degree-of-freedom multi-body system, and the slab track is represented by two continuous Bernoulli-Euler beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The rail pad model takes into account the influences of the excitation frequency and of the displacement amplitude through a fractional derivative element, and a nonlinear friction element, respectively. The Grünwald representation of the fractional derivatives is employed to numerically solve the fractional and nonlinear equations of motion of the 3D-CVST system by means of an explicit integration algorithm. A dynamic analysis of the 3D-CVST system exposed to excitations of rail harmonic irregularities is primarily carried out, which reveals the dependence of stiffness and damping on excitation frequency and displacement amplitude. Subsequently, sensitive analyses of the model parameters are investigated by conducting the dynamic analysis of the 3D-CVST system subjected to excitations of welded rail joint irregularities. Following this, parameters of the rail pad model are optimized with respect to experimental values. For elucidation, the 3D-CVST dynamic model incorporated with the rail pads model is used to calculate the wheel/rail forces induced by excitations of measured random track irregularities. Further, the numerical results are compared with experimental data, demonstrating the reliability of the proposed model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Grassie S L. Resilient railpads: Their dynamic behaviour in the laboratory and on track. P I Mech Eng F-J Rai, 1989, 203: 25–32

    Google Scholar 

  2. Bezin Y, Farrington D, Penny C, et al. The dynamic response of slab track constructions and their benefit with respect to conventional ballasted track. Veh Syst Dyn, 2010, 48: 175–193

    Article  Google Scholar 

  3. Blanco-Lorenzo J, Santamaria J, Vadillo E G, et al. Dynamic comparison of different types of slab track and ballasted track using a flexible track model. P I Mech Eng F-J Rai, 2011, 225: 574–592

    Google Scholar 

  4. Hussein M F M, Hunt H E M. Modelling of floating-slab tracks with continuous slabs under oscillating moving loads. J Sound Vib, 2006, 297: 37–54

    Article  Google Scholar 

  5. Kuo C, Huang C, Chen Y. Vibration characteristics of floating slab track. J Sound Vib, 2008, 317: 1017–1034

    Article  Google Scholar 

  6. Lombaert G, Degrande G, Vanhauwere B, et al. The control of ground-borne vibrations from railway traffic by means of continuous floating slabs. J Sound Vib, 2006, 297: 946–961

    Article  Google Scholar 

  7. Sun Y Q, Dhanasekar M. A dynamic model for the vertical interaction of the rail track and wagon system. Int J Solids Struct, 2002, 39: 1337–1359

    Article  MATH  Google Scholar 

  8. Vostroukhov A V, Metrikine A V. Periodically supported beam on a visco-elastic layer as a model for dynamic analysis of a high-speed railway track. Int J Solids Struct, 2003, 40: 5723–5752

    Article  MATH  Google Scholar 

  9. Zhu S Y, Fu Q, Cai, C B, et al. Damage evolution and dynamic response of cement asphalt mortar layer of slab track under vehicle dynamic load. Sci China Tech Sci, 2014, 57: 1883–1894

    Article  Google Scholar 

  10. Zhai W, Wang K, Cai C. Fundamentals of vehicle-track coupled dynamics. Veh Syst Dyn, 2009, 47: 1349–1376

    Article  Google Scholar 

  11. Zhu S, Cai C. Interface damage and its effect on vibrations of slab track under temperature and vehicle dynamic loads. Int J Nonlinear Mech, 2014, 58: 222–232

    Article  Google Scholar 

  12. Fenander Å. Frequency dependent stiffness and damping of railpads. P I Mech Eng F-J Rai, 1997, 211: 51–62

    Google Scholar 

  13. Bruni S, Collina A. Modelling the viscoelastic behaviour of elastomeric components: An application to the simulation of train-track interaction. Veh Syst Dyn, 2000, 34: 283–301

    Article  Google Scholar 

  14. Alonso A, Gil-Negrete N, Nieto J, et al. Development of a rubber component model suitable for being implemented in railway dynamic simulation programs. J Sound Vib, 2013, 332: 3032–3048

    Article  Google Scholar 

  15. Gil-Negrete N, Vinolas J, Kari L. A nonlinear rubber material model combining fractional order viscoelasticity and amplitude dependent effects. J Appl Mech, 2009, 76: 1–9

    Article  Google Scholar 

  16. Sjöberg M M, Kari L. Non-linear behavior of a rubber isolator system using fractional derivatives. Veh Syst Dyn, 2002, 37: 217–236

    Article  Google Scholar 

  17. Eldred L B, Baker W P, Palazotto A N. Numerical application of fractional derivative model constitutive relations for viscoelastic materials. Comput Struct, 1996, 60: 875–882

    Article  MATH  Google Scholar 

  18. Rossikhin Y A, Shitikova M V. Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids. Appl Mech Rev, 1997, 50: 15–67

    Article  Google Scholar 

  19. Enelund M, Olsson P. Damping described by fading memory-analysis and applications to fractional derivative models. Int J Solids Struct, 1999, 36: 939–970

    Article  MATH  MathSciNet  Google Scholar 

  20. Berg M. A model for rubber springs in the dynamic analysis of rail vehicles. P I Mech Eng F-J Rai, 1997, 211: 95–108

    Google Scholar 

  21. Blom P, Kari L. A nonlinear constitutive audio frequency magneto-sensitive rubber model including amplitude, frequency and magnetic field dependence. J Sound Vib, 2011, 330: 947–954

    Article  Google Scholar 

  22. Sjöberg M. Nonlinear isolator dynamics at finite deformations: An effective hyperelastic, fractional derivative, generalized friction model. Nonlinear Dyn, 2003, 33: 323–336

    Article  MATH  Google Scholar 

  23. Podlubny I. Fractional Differential Equations. San Diego: Academic Press,1999: 41–117

    MATH  Google Scholar 

  24. Spanos P D, Evangelatos G I. Response of a non-linear system with restoring forces governed by fractional derivatives-time domain simulation and statistical linearization solution. Soil Dyn Earthq Eng, 2010, 30: 811–821

    Article  Google Scholar 

  25. Zhai W. Vehicle-Track Coupled Dynamics (in Chinese). Beijing: Science Press, 2007. 71–85

    Google Scholar 

  26. Zhai W, Xia H, Cai C, et al. High-speed train-track-bridge dynamic interactions-Part I: Theoretical model and numerical simulation. Int J Rail Transport, 2013, 1: 3–24

    Article  Google Scholar 

  27. Falomi S, Meli E, Malvezzi M, et al. Determination of wheel-rail contact points: Comparison between classical and neural network based procedures. Meccanica, 2009, 44: 661–686

    Article  MATH  MathSciNet  Google Scholar 

  28. Ignesti M, Innocenti A, Marini L, et al. Wheel profile optimization on railway vehicles from the wear viewpoint. Int J Nonlinear Mech, 2013, 53: 41–54

    Article  Google Scholar 

  29. Meli E, Falomi S, Malvezzi M, et al. Determination of wheel-rail contact points with semianalytic methods. Multibody Syst Dyn, 2008, 20: 327–358

    Article  MATH  Google Scholar 

  30. Pombo J, Ambrosio J. Application of a wheel-rail contact model to railway dynamics in small radius curved tracks. Multibody Syst Dyn, 2008, 19: 91–114

    Article  MATH  Google Scholar 

  31. Shabana A A, Zaazaa K E, Escalona J L, et al. Development of elastic force model for wheel/rail contact problems. J Sound Vib, 2004, 269: 295–325

    Article  Google Scholar 

  32. Chen G, Zhai W M. A new wheel/rail spatially dynamic coupling model and its verification. Veh Syst Dyn, 2004, 41: 301–322

    Article  Google Scholar 

  33. Shen Z, Hedrick J, Elkins J. A comparison of alternative creep-force models for rail vehicle dynamic analysis. In: Proceedings of the 8th IAVSD symposium, 1984. 591–605

    Google Scholar 

  34. Zhai W M. Two simple fast integration methods for large-scale dynamic problems in engineering. Int J Numer Methods Eng, 1996, 39: 4199–4214

    Article  MATH  Google Scholar 

  35. Jin X S, Wen Z F. Effect of discrete track support by sleepers on rail corrugation at a curved track. J Sound Vib, 2008, 315: 279–300

    Article  Google Scholar 

  36. Zhu S, Cai C. Stress intensity factors evaluation for through-transverse crack in slab track system under vehicle dynamic load. Eng Fail Anal, 2014, 46: 219–237

    Article  Google Scholar 

  37. Zhai W, Wang K. Lateral hunting stability of railway vehicles running on elastic track structures. J Comput Nonlinear Dynam, 2010, 5: 520–530

    Article  Google Scholar 

  38. Zhai W, Wang S, Zhang N, et al. High-speed train-track-bridge dynamic interactions-Part II: Experimental validation and engineering application. Int J Rail Transport, 2013, 1: 25–41

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, 610031, China

    ShengYang Zhu & ChengBiao Cai

  2. China Railway Construction Heavy Industry Co. Ltd., Zhuzhou, 412005, China

    Zhen Luo

  3. China Railway Longchang Materials Co. Ltd., Longchang, 642150, China

    ZhongQi Liao

Authors
  1. ShengYang Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. ChengBiao Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhen Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. ZhongQi Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to ChengBiao Cai.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhu, S., Cai, C., Luo, Z. et al. A frequency and amplitude dependent model of rail pads for the dynamic analysis of train-track interaction. Sci. China Technol. Sci. 58, 191–201 (2015). https://doi.org/10.1007/s11431-014-5686-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-014-5686-y

Keywords

Search

Navigation