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Bifurcations of the Self-Exciting Oscillations of a Wheeled Assembly About Straight-Line Motion

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The effect of characteristic parameters of a system describing a wheeled assembly on the oscillatory-instability domain is analyzed. The influence of the accuracy of approximation of the lateral force and the heeling moment on the behavior of self-exciting oscillations is examined. A bifurcation set that divides the plane of parameters into domains with different number of limit cycles is constructed

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References

  1. G. V. Aronovich, “The theory of automotive and aircraft shimmy revisited,” Prikl. Mat. Mekh., 13, No. 5, 477–488 (1949).

    Google Scholar 

  2. N. N. Bautin, Behavior of Dynamic Systems near the Stability Boundaries [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  3. N. A. Vel’magina and V. G. Verbitskii, “Analysis of the self-exciting oscillations of a wheeled assembly in straight-line motion,” Mekh. Tverd. Tela, No. 41, 100–108 (2011).

  4. V. G. Verbitskii and M. Ya. Sadkov, “Approximate analysis of a self-oscillating system,” Dop. NAN Ukrainy, No. 10, 48–52 (2001).

  5. V. S. Gozdek, “Influence of various parameters on the stability of motion of aircraft’s swivel wheels,” Tr. TsAGI, 917, 1–30 (1964).

    Google Scholar 

  6. V. I. Goncharenko, “Canonical description of the control system in the shimmy problem for the landing gear wheels of an aircraft,” Int. Appl. Mech., 47, No. 2, 215–224 (2011).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  7. V. F. Zhuravlev and D. M. Klimov, “The causes of the shimmy phenomenon,” Dokl. Phys., 54, No. 10, 475–478 (2009).

    Article  ADS  MATH  Google Scholar 

  8. V. F. Zhuravlev and D. M. Klimov, “Theory of the shimmy phenomenon,” Mech. Solids, 45, No. 3, 324–330 (2010).

    Article  Google Scholar 

  9. M. V. Keldysh, “Shimmy of the front wheel in three-wheel landing gear,” in: Selected Works: Mechanics [in Russian], Nauka, Moscow (1985), pp. 491–530.

  10. L. G. Lobas, “Self-oscillations of a wheel on self-orientating strut of an undercarriage with nonlinear damper,” J. Appl. Math. Mech., 45, No. 4, 561–563 (1981).

    Article  MATH  Google Scholar 

  11. Yu. I. Neimark and N. A. Fufaev, Dynamics of Nonholonomic Systems [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  12. N. P. Plakhtienko and B. M. Shifrin, “On the motion stability of an airplane on a runway under wind loading,” Int. Appl. Mech., 35, No. 10, 1068–1075 (1999).

    Article  ADS  Google Scholar 

  13. N. P. Plakhtienko and B. M. Shifrin, “Transverse elastic–friction vibrations of a running aircraft,” Int. Appl. Mech., 37, No. 5, 692–699 (2001).

    Article  ADS  Google Scholar 

  14. J. M. Besselink, Shimmy of Aircraft Main Landing Gears, PhD thesis, Delft University of Technology (2000).

  15. Yi Mi-Seon, Jae-Sung Bae, and Jae-Hyuk Hwang, “Non-linear shimmy analysis of a nose landing gear with friction,” J. Korean Soc. Aeronaut. & Space Sci., 39, No. 7, 605–611 (2011).

    Google Scholar 

  16. H. B. Pacejka, The Wheel Shimmy Phenomenon, PhD thesis, Delft University of Technology (1966).

  17. Schlippe B. Von and Dietrich R. Das, Flattern eines bepneuten Rades, Bericht 140 der Lilienthal Gesellschaft (1941); English translation: NACA TM 1365, 125–147 (1954).

  18. R. S. Sharp and C. J. Jones, “A comparison of tyre representations in a simple wheel shimmy problem,” Vehic. Syst. Dynam., 9, 45–57 (1980).

    Article  Google Scholar 

  19. G. Somieski, “Shimmy analysis of a simple aircraft nose landing gear model using different mathematical methods,” Aerospace Sci. Technol., 8, 545–555 (1997).

    Article  Google Scholar 

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Correspondence to N. A. Vel’magina.

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Translated from Prikladnaya Mekhanika, Vol. 49, No. 6, pp. 113–119, November–December 2013.

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Vel’magina, N.A. Bifurcations of the Self-Exciting Oscillations of a Wheeled Assembly About Straight-Line Motion. Int Appl Mech 49, 726–731 (2013). https://doi.org/10.1007/s10778-013-0606-6

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