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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu


Sensitivity Analysis for the Shimmy Dynamics of an Airplane Main Landing Gear

Journal of Applied Nonlinear Dynamics 10(3) (2021) 513--529 | DOI:10.5890/JAND.2021.09.011

F. A. Romero

Department of Mathematics, Faculty of Engineering, Universidad de Buenos Aires, Paseo Col'{o}n 850, Buenos Aires Argentina

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Abstract

Landing gear shimmy is the name given to the wobbling motion due to torsional vibration and lateral flexing of a landing gear leg. Depending on the airplane requirements Main Landing Gears have different configurations. In this paper we analyze the sensitivity responses of the shimmy dynamics of a main landing gear for different geometric configurations. The dynamics are expressed in terms of three different degrees of freedom. We focus on the geometry of the main landing gear, specifically how the side-stay attachment point inclination angle affects shimmy.

Acknowledgments

I would like to thank to my director of thesis Prof. Mar\'{i}a In\'{e}s Troparevsky for her support and guidance in this publication

References

  1. [1]  Civil Aviation Accident and Incident Investigation Commission (CIAIAC) (2003), Accident of aircraft Fokker MK-100, registration IALPL, at Barcelona Airport (Barcelona), on 7 November 1999. Technical Report A-068/1999. https://www.fomento.gob.es/NR/rdonlyres/FB9914BB-A098-4F68-ABF4-3B5EF0C8AA54/2422/1999{\_}068{\_}A{\_}ENG.pdf (Accessed 26 July 2018)
  2. [2]  Howcroft, C., Krauskopf, B., Lowenberg, M., and Neild, S. (2013), Influence of variable side-stay geometry on the shimmy dynamics of an aircraft dual-wheel main landing gear, SIAM, Journal on Applied Dynamical Systems, 12, N$^\circ$ 3, pp. 1181-1209.
  3. [3]  Dengler, M., Goland, M., and Herrman, G. (1951), A bibliographic survey of automobile and aircraft wheel shimmy. Technical Report, WADC Technical Report 52-141, Midwest Research Institute, USA, 1951. {http://www.dtic.mil/dtic/tr/fulltext/u2/a076003.pdf} (Accessed 26 July 2018)
  4. [4]  Pritchard, J. (1999), An overview of landing gear dynamics, Technical Report, NASA / TM-1999-209143. {https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19990047095.pdf} (Accessed 26 July 2018).
  5. [5]  Pacejka, H.B. (1966), The wheel shimmy phenomenon: a theoretical and experimental investigation with particular reference to the non-linear problem, PhD thesis, Delft University of Technology, The Netherlands.
  6. [6]  Moreland, W (1951). Landing-gear vibration. A. F. Technical Report N$^\circ$ 6590. http://www.dtic.mil/dtic/tr/ fulltext/u2/a955967.pdf (Accessed 26 July 2018).
  7. [7]  Howcroft, C. (2013), A bifurcation and numerical continuation study of aircraft main landing gear shimmy. PhD Thesis, Department of Engineering Mathematics, University of Bristol, UK.
  8. [8]  Thota, P., Krauskopf, B., and Lowenberg, M. (2009), Bifurcation analysis of nose landing gear shimmy with lateral and longitudinal bending. Faculty of Engineering, University of Bristol, UK.
  9. [9]  Thota, P., Krauskopf, B., and Lowenberg, M. (2009), Interaction of torsion and lateral bending in aircraft nose landing gear shimmy, Nonlinear Dynamics, 57(3), 455-467.
  10. [10]  Stanley, L.G. (1999), Computational methods for sensitivity analysis with applications to elliptic boundary value problems, PhD Thesis, Faculty of the Virginia Polytechnic Institute and State University, Virginia, USA.
  11. [11]  Wolfram Research, Inc., Mathematica, Version 12.0.0.0, Champaign, Illinois, USA.
  12. [12]  Ran, S. (2015), Tyre models for shimmy analysis: from linear to nonlinear, PhD thesis, Eindhoven University of Technology, Eindhoven, The Netherlands.
  13. [13]  Podgorski, W.A., Krauter, A.I., and Rand, R.H. (1975), The wheel shimmy problem: Its relationship to wheel and road irregularities, Vehicle System Dynamics, 4, pp. 9-41.
  14. [14]  Dokeva, N. (2012), Parametric differential equations. In the Wolfram Technology Conference, Champaign, Illinois, USA.
  15. [15]  Serban, R. and Hindmarsh, A.C. (2003), CVODES: An ODE Solver with sensitivity analysis capabilities, Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, California, USA. {https://computation.llnl.gov/casc/nsde/pubs/cvs{\_}guide.pdf} (Accessed 26 July 2018).