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Rail Vehicle Dynamics pp 81–105Cite as

Vertical Dynamics, Equations of Motion, and Free Vibrations

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Abstract

In the present chapter, the differential equations for the motion of a rail vehicle with two axles will be examined in detail, first for longitudinal and lateral motion with the principle of linear and angular momentum. The reader who is familiar with these concepts can skip Sect. 4.2. Then the possibility to formulate the equations of motion by means of virtual displacements is discussed (Sects. 4.3 and 4.4). In this manner, it is also possible to derive the equations of motion for a vehicle with elastic carbody (Sect. 4.5). Finally, in Sect. 4.6, the solution of a two-axle vehicle (free vibration case) is discussed.

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Notes

  1. 1.

    In special cases, real eigenvalues appear.

References

  1. R. Gasch K. Knothe, R. Liebich, Strukturdynamik, Diskrete Systeme und Kontinua (2. neubearbeitete Auflage) (Structural Dynamics, Discrete Systems and Continua) (Springer, Berlin 2012)

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  2. K. Knothe, H. Wessels, Finite Elemente–Eine Einführung für Ingenieure, 3., überarb. und erw. Aufl. (Finite elements–An introduction for engineers. 3rd ed.) Springer, Berlin, Heidelberg, New York, Barcelona, Hong Kong, London, Mailand, Paris, Singapur, Tokio, 1999

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  3. St. Dietz, Vibration and Fatigue Analysis of Vehicle Systems Using Component Modes. Fortschritt-Berichte VDI (also PhD thesis TU Berlin), Reihe 12, Nr. 401. VDI–Verlag, Düsseldorf (1999)

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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
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  2. Sebastian Stichel
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Correspondence to Klaus Knothe .

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Knothe, K., Stichel, S. (2017). Vertical Dynamics, Equations of Motion, and Free Vibrations. In: Rail Vehicle Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-319-45376-7_4

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  • DOI: https://doi.org/10.1007/978-3-319-45376-7_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45374-3

  • Online ISBN: 978-3-319-45376-7

  • eBook Packages: EngineeringEngineering (R0)

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