Nonlinear Dynamics

, Volume 57, Issue 3, pp 455–467 | Cite as

Interaction of torsion and lateral bending in aircraft nose landing gear shimmy

  • Phanikrishna Thota
  • Bernd Krauskopf
  • Mark Lowenberg
Original Paper

Abstract

In this paper we consider the onset of shimmy oscillations of an aircraft nose landing gear. To this end we develop and study a mathematical model with torsional and lateral bending modes that are coupled through a wheel-mounted elastic tyre. The geometric effects of a positive rake angle are fully incorporated into the resulting five-dimensional ordinary differential equation model. A bifurcation analysis in terms of the forward velocity and the vertical force on the gear reveals routes to different types of shimmy oscillations. In particular, we find regions of stable torsional and stable lateral shimmy oscillations, as well as transient quasiperiodic shimmy where both modes are excited.

Keywords

Aircraft dynamics Shimmy oscillations Mode interaction Quasiperiodic motion 

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References

  1. 1.
    Baumann, J.: A nonlinear model for landing gear shimmy with applications to the McDonnell Douglas G/A-18A. In: 81st Meeting of the AGARD Structures and Materials Panel (1995) Google Scholar
  2. 2.
    Besselink, I.J.M.: Shimmy of aircraft main landing gears. Dissertation, University of Delft, The Netherlands (2000) Google Scholar
  3. 3.
    Broulhiet, M.G.: La suspension de la direction de la voiture automobile—shimmy et dandinement. Bull. Soc. Ing. Civ. (France) 78 (1925) Google Scholar
  4. 4.
    Dengler, M., Goland, M., Herrman, G.: A bibliographic survey of automobile and aircraft wheel shimmy. Technical report, Midwest Research Institute, Kansas City, MO, USA (1951) Google Scholar
  5. 5.
    Doedel, E.J., Keller, H.B., Kernevez, J.P.: Numerical analysis and control of bifurcation problems, part II: bifurcation in infinite dimensions. J. Bifurc. Chaos Appl. Sci. Eng. 1(4), 745–772 (1991) MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Glaser, J., Hrycko, G.: Landing gear shimmy—De Havilland’s experience. In: 81st Meeting of the AGARD Structures and Materials Panel (1995) Google Scholar
  7. 7.
    Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer, New York (1983) MATHGoogle Scholar
  8. 8.
    Krabacher, W.E.: A review of aircraft landing gear dynamics. In: 81st Meeting of the AGARD Structures and Materials Panel (1995) Google Scholar
  9. 9.
    Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory. Springer, New York (1995) MATHGoogle Scholar
  10. 10.
    Pacejka, H.B.: Analysis of the shimmy phenomenon. Proc. Inst. Mech. Eng. 2A 180(10) (1965–1966) Google Scholar
  11. 11.
    Pacejka, H.B.: The wheel shimmy phenomenon: a theoretical and experimental investigation with particular reference to the nonlinear problem. Dissertation, Delft University of Technology (1966) Google Scholar
  12. 12.
    Pritchard, I.J.: An overview of landing gear dynamics. NASA Technical Reports, NASA/TM-1999-209143 (1999) Google Scholar
  13. 13.
    Smiley, R.F.: Correlation, evaluation, and extension of linearized theories for tyre motion and wheel shimmy. Report submitted to the National Advisory Committee for Aeronautics, Report 1299 (1957) Google Scholar
  14. 14.
    Somieski, G.: Shimmy analysis of a simple aircraft nose landing gear model using different mathematical methods. Aerosp. Sci. Technol. 8, 1270–9638 (1997) Google Scholar
  15. 15.
    Stépán, G.: Delay, Nonlinear Oscillations and Shimmying Wheels, Kluwer, Dordrecht (1998) Google Scholar
  16. 16.
    Stépán, G.: Chaotic motion of wheels. Veh. Syst. Dyn. 20(6), 341–351 (1991) CrossRefGoogle Scholar
  17. 17.
    von Schlippe, B., Dietrich, R.: Shimmying of a pneumatic wheel. Report submitted to the National Advisory Committee for Aeronautics, NACA TM 1365 (1947) Google Scholar
  18. 18.
    Takács, D., Stépán, G.: Experiments on quasi-periodic wheel shimmy. In: Proc. IDETC/CIE. DETC2007-35336 (2007) Google Scholar
  19. 19.
    Thota, P., Krauskopf, B., Lowenberg, M.: Shimmy in a nonlinear model of an aircraft nose landing gear with nonzero rake angle. In: Proceedings of ENOC (2008) Google Scholar
  20. 20.
    Woerner, P., Noel, O.: Influence of nonlinearity on the shimmy behaviour of landing gear. In: 81st Meeting of the AGARD Structures and Materials Panel (1995) Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Phanikrishna Thota
    • 1
  • Bernd Krauskopf
    • 1
  • Mark Lowenberg
    • 2
  1. 1.Department of Engineering MathematicsUniversity of Bristol, Queen’s BuildingBristolUK
  2. 2.Department of Aerospace EngineeringUniversity of BristolBristolUK

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