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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G. V. Aronovich, “The theory of automotive and aircraft shimmy revisited,” Prikl. Mat. Mekh., 13, No. 5, 477–488 (1949).
N. N. Bautin, Behavior of Dynamic Systems near the Stability Boundaries [in Russian], Nauka, Moscow (1984).
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).
V. G. Verbitskii and M. Ya. Sadkov, “Approximate analysis of a self-oscillating system,” Dop. NAN Ukrainy, No. 10, 48–52 (2001).
V. S. Gozdek, “Influence of various parameters on the stability of motion of aircraft’s swivel wheels,” Tr. TsAGI, 917, 1–30 (1964).
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).
V. F. Zhuravlev and D. M. Klimov, “The causes of the shimmy phenomenon,” Dokl. Phys., 54, No. 10, 475–478 (2009).
V. F. Zhuravlev and D. M. Klimov, “Theory of the shimmy phenomenon,” Mech. Solids, 45, No. 3, 324–330 (2010).
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.
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).
Yu. I. Neimark and N. A. Fufaev, Dynamics of Nonholonomic Systems [in Russian], Nauka, Moscow (1967).
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).
N. P. Plakhtienko and B. M. Shifrin, “Transverse elastic–friction vibrations of a running aircraft,” Int. Appl. Mech., 37, No. 5, 692–699 (2001).
J. M. Besselink, Shimmy of Aircraft Main Landing Gears, PhD thesis, Delft University of Technology (2000).
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).
H. B. Pacejka, The Wheel Shimmy Phenomenon, PhD thesis, Delft University of Technology (1966).
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).
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).
G. Somieski, “Shimmy analysis of a simple aircraft nose landing gear model using different mathematical methods,” Aerospace Sci. Technol., 8, 545–555 (1997).
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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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DOI: https://doi.org/10.1007/s10778-013-0606-6