 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
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| V.Ph. Zhuravlev, "On Plane Self-Excited Vibrations of a Cantilever Suspended Wheel," Mech. Solids. 47 (2), 155-159 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
2 |
Pages |
155-159 |
| DOI |
10.3103/S002565441202001X |
| Title |
On Plane Self-Excited Vibrations of a Cantilever Suspended Wheel |
| 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) |
| Abstract |
Torsional vibrations of a wheel about its leg axis arising in the carriage rectilinear motion were dubbed the shimmy phenomenon. Because of insufficient understanding of dry friction laws in the case of point contact, the causes of the shimmy phenomenon were explained by specific features of tyre deformation [1-3].
But this phenomenon is also observed in the case of rigid (for example, metallic) wheels. The recently developed theory of polycomponent dry friction [5-11] was used to explain the shimmy phenomenon in [4]. It was discovered there that the shimmy phenomenon arises if sliding friction prevails over rolling
friction.
In the present paper, it is shown that self-excited vibrations are also possible if, conversely, rolling friction prevails over sliding friction, but these vibrations then occur in the rolling plane. Such self-excited vibrations are close in their physical meaning to the vibrations studied in textbooks on the theory of oscillations in the problem called an oscillator with dry friction on an infinite belt [12]. In contrast to this problem, the order of the system considered below is greater, and, in addition to sliding friction, rolling friction is present as well. |
| Keywords |
pseudo-shimmy, dry friction, self-excited vibrations of the wheel cantilever suspension, averaging method |
| References |
| 1. | M. V. Keldysh,
"Fore Wheel Shimmy of a Three-Wheel Landing Gear,"
in Selected Works. Mechanics
(Nauka, Moscow, 1985)
[in Russian],
pp. 491-530. |
| 2. | 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)]. |
| 3. | H. B. Pacejka,
Tyre and Vehicle Dynamics
(Butterworth-Heinemann, Oxford, 2002). |
| 4. | V. Ph. Zhuravlev and D. M. Klimov,
"Theory of the Shimmy Phenomenon,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 22-29 (2010)
[Mech. Solids (Engl. Transl.)
45 (3), 324-330 (2010)]. |
| 5. | V. V. Andronov and V. Ph. Zhuravlev,
Dry Friction in Problems of Mechanics
(NITz "Regular and Chaotic Dynamics," Moscow-Izhevsk, 2010)
[in Russian]. |
| 6. | V. Ph. Zhuravlev,
"Friction Laws in the Case of Combination of Slip and Spin,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 81-88 (2003)
[Mech. Solids (Engl. Transl.)
38 (4), 52-58 (2003)]. |
| 7. | V. Ph. Zhuravlev,
"The Model of Dry Friction in the Problem of the
Rolling of Rigid Bodies,"
Prikl. Mat. Mekh.
62 (5), 762-767 (1998)
[J. Appl. Math. Mech. (Engl. Transl.)
62 (5), 705-710 (1998)]. |
| 8. | V. Ph. Zhuravlev and A. A. Kireenkov,
"Padé Expansions in the Two-Dimensional Model of
Coulomb Friction,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 3-14 (2005)
[Mech. Solids (Engl. Transl.)
40 (2), 1-10 (2005)]. |
| 9. | A. A. Kireenkov,
"On the Motion of a Homogeneous Rotating
Disk along a Plane in the Case of Combined Friction,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 60-67 (2002)
[Mech. Solids (Engl. Transl.)
37 (1), 47-53 (2002)]. |
| 10. | P. Contensou,
"Couplage Entre Frottenment de Glissement et Frottement de Pivotement Dans la
Theórie de la Toupie,"
in Kreiselprobleme Gyrodynamics, IUTAM Symp. Celerina
(Springer, Berlin etc., 1962; Mir, Moscow, 1967),
pp. 201-216 (60-77). |
| 11. | R. I. Leine and Ch. Glocker,
"A Set-Valued Force Law for Spatial
Coulomb-Contensou Friction,"
Europ. J. Mech. A. Solids
22, 193-216 (2003). |
| 12. | V. Ph. Zhuravlev and D. M. Klimov,
Applied Methods in Vibration Theory
(Nauka, Moscow, 1988)
[in Russian]. |
| 13. | D. M. Klimov,
"On One Type of Self-Excited Vibrations in
a System with Dry Friction,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 6-12 (2003)
[Mech. Solids (Engl. Transl.)
38 (3), 1-7 (2003)]. |
|
| Received |
25 January 2011 |
| Link to Fulltext |
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