Skip to main content
SpringerLink
Log in

Introduction to Non-linear Stability Investigations

  • Chapter
  • First Online:
Rail Vehicle Dynamics

  • 2870 Accesses

Abstract

The stability investigations for the wheelset in Chap. 10, the bogie in Chap. 11, and for a bogie vehicle in Chap. 12 assume that the system can be described by linear equations.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. ORE. Wechselwirkung zwischen Fahrzeug und Gleis. Bericht über das Preisausschreiben zur Lösung des Schlingerproblemes (Interaction between vehicle and track. Report on the competition to solve the hunting problem.). ORE-report to question C 9. Work result Nr. 2 Vol. 1. Utrecht, UIC, ORE (1957)

    Google Scholar 

  2. G.-P. Bracker, Einfluß der Gehänge- und Tragfederkräfte auf das Laufverhalten freier Lenkradsätze im geraden Gleis. Dissertation, TH München (1966)

    Google Scholar 

  3. H. Dillmann, Einfluß der Schlupfabhängigkeit der Reibung auf den Bogenlauf zweiachsiger Schienenfahrzeuge mit freien Lenkachsen - Auszug aus einer Dissertation (Influence of creep dependency of friction on the curving behavior of two-axled railway vehicles with free steering axles). Glas. Ann. 83(12), 420–433 (1959)

    Google Scholar 

  4. K. Inderst, C.T. Müller, Energiefluß beim Schlingern von Schienenfahrzeugen (Flow of energy during hunting of railway vehicles). Research report, laboratory Minden of DB, o. J. (1967). (not published; from the estate of C. Th. Müller, O. Krettek)

    Google Scholar 

  5. K. Kämpfe, Schwingungsverhalten eines zweiachsigen Eisenbahnfahrzeugs mit freien Lenkradsätzen und reibungsbehafteten Kopplungen beim Lauf im geraden Gleis (Dynamic behaviour of a two-axled railway vehicle with free steering wheelsets and friction couplings running on straight track). PhD thesis, TH München (1961). (Text, pictures and equations)

    Google Scholar 

  6. A. Schmidt, D. Moelle. Ermittlung der Grenzzykelbewegungen der nichtlinearen Drehgestelldynamik, Vergleich zwischen Hybridsimulation und digitalen Grenzzykelberechnungen (Determination of limit cycle motions in nonlinear bogie dynamics. Comparison between hybrid simulation and digital limit cycle analysis). Report Nr. B 099006 EDS 019, MAN München, MAN Neue Technologie München and TU Berlin, ILR (1982)

    Google Scholar 

  7. J. Salin, Regards en arrière. Revue Générale des Chemins de Fer 100, 216–221 (1981)

    Google Scholar 

  8. A.D. de Pater, The approximate determination of the hunting movement of a railway vehicle by aid of the method of Krylov and Bogoljubov. Appl. Sci. Res. 10, 205–228 (1961)

    Article  MATH  Google Scholar 

  9. J.P. Meijaard, A.D. DePater, Railway vehicle system dynamics an chaotic vibration. Int. J. Nonlinear Mech. 24, 1–17 (1989)

    Article  MathSciNet  Google Scholar 

  10. R.R. Huilgol, Hopf-Friedrichs bifurcation and the hunting of a railway axle. Q. J. Appl. Mech. 36, 85–94 (1978)

    MathSciNet  MATH  Google Scholar 

  11. X. He, R.R. Huilgol, Application of Hopf bifurcation at infinity to hunting vibrations of rail vehicle trucks, in Dynamics of Vehicles on Roads and Tracks. Proceedings of the 12th IAVSD Symposium held in Lyon, France, August 1991. Supplement to Vehicle System Dynamics, vol. 20, ed. by G. Sauvage (Swets & Zeitlinger, Amsterdam/Lisse, 1992), pp. 240–253

    Google Scholar 

  12. N.K. Cooperrider, J.K. Hedrick, E.H. Law, C.W. Malstrom, The application of quasilinearization techniques to the prediction of nonlinear railway vehicle response, in The Dynamics of Vehicles on Roads and on Tracks. Proceedings of the IUTAM Symposium held at Delft, The Netherlands, August 1975, ed. by H.B. Pacejka (Swets & Zeitlinger, Amsterdam, 1976), pp. 314–325

    Google Scholar 

  13. J.K. Hedrick, Nonlinear system response: quasi-linearization methods, in Nonlinear System Analysis and Synthesis: Volume 1 - Fundamental Principles. Presented at the Winter Annual Meeting of the American Society of Mechanical Engineers; New York, December 5–10, 1976, ed. by J.K. Hedrick, H.M. Paynter (1978), pp. 97–124

    Google Scholar 

  14. H. True, On the theory of nonlinear dynamics and its application in vehicle system dynamics. Veh. Syst. Dyn. 31(5–6), 393–421 (1999)

    Article  Google Scholar 

  15. A. Schmidt, L. Moelle, Durchführung Rollprüfstandsversuche, MAN-Anteil. Rad/Schiene Forschung, BMFT VorhabenTV79604 (Implementation of roller rig tests). Final report Nr. K 096 991 - EDS, MAN Neue Technologie Munich (1982)

    Google Scholar 

  16. T. Matsudaira, Hunting problem of high speed railway vehicles with special reference to bogie design for the new Tokaido line. Proc. Inst. Mech. Eng. 180, 58–66 (1965)

    Google Scholar 

  17. M. Urabe, Galerkin’s procedure for nonlinear periodic systems. Arch. Ration. Mech. Anal. 20, 120–152 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  18. M. Urabe, A. Reiter, Numerical computation of nonlinear forced oscillations by Galerkin’s procedure. Arch. Math. Anal. Appl. 14, 107–140 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  19. R. Gasch, D. Moelle, Nonlinear bogie hunting, in The Dynamics of Vehicles on Roads and on Tracks. Proceedings of the 7th IAVSD-Symposium held at Cambridge, UK, August 1981, ed. by A.A. Wickens (Swets & Zeitlinger, Lisse/Amsterdam, 1982), pp. 455–467

    Google Scholar 

  20. R. Gasch, D. Moelle, K. Knothe, The effects of nonlinearities on the limit-cycles of railway vehicles, in The Dynamics of Vehicles on Roads and on Tracks. Proceedings of the 8th IAVSD-Symposium held at Cambridge, Mass./USA, August 1983, ed. by J.K. Hedrick (Swets & Zeitlinger, Lisse/Amsterdam, 1984), pp. 207–224

    Google Scholar 

  21. D. Moelle, Digitale Grenzzykelrechnung zur Untersuchung der Stabilität von Eisenbahndrehgestellen unter dem Einfluß von Nichtlinearitäten (Digital limit-cycle analysis for the investigation of the stability of railway vehicle bogies under the influence of nonlinearities.). PhD thesis, Technical University Berlin (1990)

    Google Scholar 

  22. N.K. Cooperrider, The hunting behaviour of conventional railway trucks. J. Eng. Ind. 94, 752–762 (1976)

    Article  Google Scholar 

  23. C. Knudsen, R. Feldberg, H. True, Bifurcations and chaos in a model of a rolling railway wheelset. Philos. Trans. R. Soc. Lond. A 338, 455–469 (1992)

    Article  MATH  Google Scholar 

  24. H. True, Railway vehicle chaos and asymmetric hunting, in The Dynamics of Vehicles on Roads and on Tracks. Proceedings of the 12th IAVSD Symposium held at Lyon/France, August 1991. Supplement to Vehicle System Dynamics, vol. 20, ed. by G. Sauvage (Swets & Zeitlinger, Amsterdam/Lisse, 1992), pp. 625–637

    Google Scholar 

  25. H. True, Does a critical speed for railroad vehicles exist?, in Proceedings of the 1994 ASME/IEE Joint Railroad Conference held in Chicago, Illinois, March 1994, ed. by K.L. Hawthorne, R.J. Hill (1994), pp. 125–131

    Google Scholar 

  26. O. Polach, On nonlinear methods of bogie stability assessment using computer simulations. Proc. Inst. Mech. Eng. Part F: J. Rail Rapid Trans. 220, 13–27 (2006)

    Article  Google Scholar 

  27. S. Stichel, Limit cycle behaviour and chaotic motions of two-axle freight wagons with friction damping. Multibody Syst. Dyn. 8(3), 243–255 (2002)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Aeronautics and Astronautics, Technical University of Berlin, Berlin, Germany

    Klaus Knothe

  2. KTH Royal Institute of Technology, Stockholm, Sweden

    Sebastian Stichel

Authors
  1. Klaus Knothe
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sebastian Stichel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Klaus Knothe .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Knothe, K., Stichel, S. (2017). Introduction to Non-linear Stability Investigations. In: Rail Vehicle Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-319-45376-7_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-45376-7_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45374-3

  • Online ISBN: 978-3-319-45376-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation