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IssuesArchive of Issues2010-3pp.324-330

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V.Ph. Zhuravlev and D.M. Klimov, "Theory of the Shimmy Phenomenon," Mech. Solids. 45 (3), 324-330 (2010)
Year 2010 Volume 45 Number 3 Pages 324-330
DOI 10.3103/S0025654410030039
Title Theory of the Shimmy Phenomenon
Author(s) V.Ph. Zhuravlev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, zhurav@ipmnet.ru)
D.M. Klimov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, klimov@ipmnet.ru)
Abstract The shimmy phenomenon is the appearance of angular self-excited vibrations of the carriage wheels. Such self-excited vibrations provide a serious safety hazard for motion, which explains the great interest of scientists in this phenomenon [1-6]. This problem is most serious for the aircraft fore wheels.

It is commonly agreed that the main cause of the shimmy phenomenon is the tyre deformation [2]. We do not doubt this thesis, but still we note that this cause is not unique. The shimmy phenomenon can be observed in everyday life in the case of various hand trucks with rigid wheels, where the reference to the elastic tyre is out of place.

In what follows, we show that the theory of polycomponent dry friction can completely explain the shimmy phenomenon for absolutely rigid wheels, and hence can be at least one of the causes of this phenomenon in the general case.

Dry friction has been ignored by the scientists in their explanations of the shimmy phenomenon, because this friction has not been fully investigated until now, and it has been impossible to explain the shimmy phenomenon in the framework of the former representations.
Keywords shimmy, polycomponent dry friction, Padé approximation
References
1.  V. S. Gozdek, "Reaction of the Ground on a Vibrating Rolling Wheel with an Elastic Tire," Dokl. Akad. Nauk SSSR 186 (5), 1031-1033 (1969) [Soviet Phys. Dokl. (Engl. Transl.) 14, 536 (1969)].
2.  M. V. Keldysh, "Fore Wheel Shimmy of a Three-Wheel Landing Gear," in Selected Works. Mechanics (Nauka, Moscow, 1985), pp. 491-530.
3.  K. S. Kolesnikov, Self-Excited Vibrations of Car Steering Wheels (Gostekhteorizdat, Moscow, 1955).
4.  J. Medzorian, "An Investigation of Landing Gear Shimmy: Tire Models, Tire Test Methodologies, Analysis and Parameter Studies," in 1999 World Aviation Conf. San Francisco, CA (1999), Docum. No. 1999-01-SS27.
5.  H. B. Pacejka, Tyre and Vehicle Dynamics (Butterworth-Heinemann, Oxford, 2002).
6.  Y. Rocard, Dynamique Général des Vibrations (Masson, Paris, 1949).
7.  J. Svendenius, "Tire Models for Use in Braking Applications," in Department of Automatic Control, Lund Institute of Technology (Lund, 2003).
8.  I. G. Goryacheva, Mechanics of Friction Interaction (Nauka, Moscow, 2001).
9.  V. Ph. Zhuravlev, "On the Model of Dry Friction in Problems of Rigid Body Dynamics," Uspekhi Mekh., No. 3 (2005).
10.  V. Ph. Zhuravlev and D. M. Klimov, "On the Dynamics of the Thompson Top (Tippe Top) on the Plane with Real Dry Friction," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 157-168 (2005) [Mech. Solids (Engl. Transl.) 40 (6), 117-127 (2005)].
11.  V. Ph. Zhuravlev and D. M. Klimov, "The Causes of the Shimmy Phenomenon," Dokl. Ross. Akad. Nauk 428 (6), 761-765 (2009) [Dokl. Phys. (Engl. Transl.) 54 (10), 475-478 (2009)].
Received 08 December 2009
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