Nonlinear Dynamics

, Volume 70, Issue 2, pp 1675–1688 | Cite as

Multi-parameter bifurcation study of shimmy oscillations in a dual-wheel aircraft nose landing gear

  • Phanikrishna Thota
  • Bernd Krauskopf
  • Mark Lowenberg
Original Paper

Abstract

We develop and investigate a mathematical model of an aircraft nose landing gear with a dual-wheel configuration. The main aim here is to study the influence of a dual-wheel configuration on the existence of shimmy oscillations. To this end, we consider a model that describes the torsional and lateral vibrational modes and the non-linear interaction between them via the tyre-ground contact. More specifically, we perform a bifurcation analysis (with the software package auto) of the model in the two-parameter plane of forward velocity of the aircraft and vertical load on the nose landing gear. This two-parameter bifurcation diagram allows one to identify regions of different dynamics, and the question addressed here is how it depends on two key parameters of the dual-wheel configuration. Namely, we consider the influence of, first, the separation distance between the two wheels and, second, of gyroscopic effects arising from the inertia of the wheels. For both cases, we find that with increasing separation distance and wheel inertia, respectively, the lateral mode becomes more stable and the torsional mode becomes less stable. More specifically, we present associated bifurcation scenarios that explain the transitions between qualitatively different two-parameter bifurcation diagrams. Overall, we find that the separation distance and gyroscopic effects due to wheel inertia may have a significant influence on the quantitative and qualitative nature of shimmy oscillations in aircraft nose landing gears. In particular, the torsional and the lateral modes of a dual-wheel nose landing gear may interact in a quite complicated fashion.

Keywords

Aircraft ground dynamics Bifurcation analysis Shimmy oscillations Mode interaction Dual-wheel configuration Co-dimension-three bifurcation 

References

  1. 1.
    Besselink, I.J.M.: Shimmy of aircraft main landing gears. PhD Dissertation, University of Delft, The Netherlands (2000) Google Scholar
  2. 2.
    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. AGARD-R-800 (1995) Google Scholar
  3. 3.
    Glaser, J., Hrycko, G.: Landing gear shimmy—De Havilland’s experience. In: 81st Meeting of the AGARD Structures and Materials Panel. AGARD-R-800 (1995) Google Scholar
  4. 4.
    Krabacher, W.E.: A review of aircraft landing gear dynamics. In: 81st Meeting of the AGARD Structures and Materials Panel. AGARD-R-800 (1995) Google Scholar
  5. 5.
    Smiley, R.F.: Correlation, evaluation, and extension of linearized theories for tire motion and wheel shimmy. NACA-1299 (1957) Google Scholar
  6. 6.
    Broulhiet, M.G.: La suspension de la direction de la voiture automobile—shimmy et dandinement. Bull. Soc. Ing. Civ., France 78 (1925) Google Scholar
  7. 7.
    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
  8. 8.
    Van Der Valk, R., Pacejka, H.B.: An analysis of a civil aircraft main gear shimmy failure. Veh. Syst. Dyn. 22, 97–121 (1993) CrossRefGoogle Scholar
  9. 9.
    Pacejka, H.B.: Analysis of the shimmy phenomenon. Proc. IMECHE 180(2A)(10) (1965–1966) Google Scholar
  10. 10.
    Leve, H.L.: Designing stable dual wheel gears. In: AIAA Aircraft Design and Operations Meeting, Los Angeles, California (1969) Google Scholar
  11. 11.
    Pritchard, I.J.: An overview of landing gear dynamics. NASA/TM-1999-209143 (1999) Google Scholar
  12. 12.
    Thota, P., Krauskopf, B., Lowenberg, M.: Interaction of torsion and lateral bending in aircraft nose landing gear shimmy. Nonlinear Dyn. 57(3), 455–467 (2009) MATHCrossRefGoogle Scholar
  13. 13.
    von Schlippe, B., Dietrich, R.: Shimmying of a pneumatic wheel. Naca report 1365 (1947) Google Scholar
  14. 14.
    Doedel, E.J., Champneys, A.R., Fairgrieve, T., Kuznetsov, Yu., Sandstede, B., Wang, X.: Auto 97: continuation and bifurcation software for ordinary differential equations. http://indy.cs.concordia.ca/auto/ (May 2001)
  15. 15.
    Somieski, G.: Shimmy analysis of a simple aircraft nose landing gear model using different mathematical methods. Aerosp. Sci. Technol. 8, 545–555 (1997) CrossRefGoogle Scholar
  16. 16.
    Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer, New York (1983) MATHGoogle Scholar
  17. 17.
    Kuznetsov, Yu.A.: Elements of Applied Bifurcation Theory. Springer, New York (1998) MATHGoogle Scholar
  18. 18.
    Green, K., Krauskopf, B.: Bifurcation analysis of a semiconductor laser subject to non-instantaneous phase-conjugate feedback. Opt. Commun. 231(1–6), 383–393 (2004) CrossRefGoogle Scholar
  19. 19.
    Erzgräber, H., Krauskopf, B., Lenstra, D.: Bifurcation analysis of a semiconductor laser with filtered optical feedback. SIAM J. Dyn. Control Syst. 6(1), 1–28 (2007) MATHCrossRefGoogle Scholar
  20. 20.
    Krauskopf, B., Walker, J.: Bifurcation study of a semiconductor laser with saturable absorber and delayed optical feedback. In: Lüdge, K. (ed.) Nonlinear Laser Dynamics. From Quantum Dots to Cryptography. Wiley-VCH, New York (2012) doi:10.1002/9783527639823 Google Scholar
  21. 21.
    Green, K., Krauskopf, B.: Dynamics of patterns in lasers with delayed feedback. In: Dubbeldam, J., Green, K., Lenstra, D. (eds.) The Complexity of Dynamical Systems. A Multi-Disciplinary Perspective, pp. 37–62. Wiley-VCH, New York (2011) Google Scholar
  22. 22.
    Takacs, D., Stépán, G., Hogan, J.H.: Isolated large amplitude periodic motions of towed rigid wheels. Nonlinear Dyn. 52(1–2), 27–34 (2007) Google Scholar
  23. 23.
    Takacs, D., Stépán, G.: Experiments on quasi-periodic wheel shimmy. ASME J. Comput. Nonlinear Dyn. 4(3) (2009) Google Scholar
  24. 24.
    Sateesh, D., Maiti, D.: Non-linear analysis of a typical nose landing gear model with torsional free play. J. Aerospace Eng. 223(6), 627–641 (2009) Google Scholar
  25. 25.
    Sura, N., Suryanarayan, S.: Lateral response of nonlinear nose-wheel landing gear models with torsional free play. J. Aircraft 44(6) (2007) Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Phanikrishna Thota
    • 1
  • Bernd Krauskopf
    • 2
  • Mark Lowenberg
    • 3
  1. 1.Airbus, FiltonBristolUK
  2. 2.Department of Engineering MathematicsUniversity of BristolBristolUK
  3. 3.Department of Aerospace EngineeringUniversity of BristolBristolUK

Personalised recommendations