 | | 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 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| << Previous article | Volume 48, Issue 5 / 2013 | Next article >> |
| G.M. Rozenblat, "On a Disk Sliding on a Rough Inclined Plane under an Arbitrary Law of Normal Stresses," Mech. Solids. 48 (5), 573-580 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
5 |
Pages |
573-580 |
| DOI |
10.3103/S0025654413050130 |
| Title |
On a Disk Sliding on a Rough Inclined Plane under an Arbitrary Law of Normal Stresses |
| Author(s) |
G.M. Rozenblat (Moscow State Automobile and Road Technical University, Leningradskii pr-t 64, Moscow, 125319 Russia, gr51@mail.ru) |
| Abstract |
The paper deals with the problem of a disk sliding on a rough inclined plane under the action of an arbitrary (symmetric) law of normal stress distribution and the classical differential Euler-Coulomb dry friction law. Some qualitative results concerned with the global dynamics of motion of such a disk are obtained. In several cases where the Galin distribution of normal stresses and the corresponding Zhuravlev formulas for friction forces and moments are used, one can succeed in obtaining the first integrals for the corresponding equations of motion of an annular disk. The limit cases concerned with the well-posedness of transition from a disk to a material point, which is directly related to the problem of justification of the point contact with sliding friction or a nonholonomic constraint, are also discussed. |
| Keywords |
disk, dry friction, normal stress, inclined plane |
| References |
| 1. | A. Yu. Ishlinskii, B. N. Sokolov, and F. L. Chernousko,
"On Motion of Plane Bodies with Dry Friction,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 4, 17-28 (1981)
[Mech. Solids (Engl. Transl.)]. |
| 2. | S. Goyal, A. Ruina, and J. Papadopoulos,
"Planar Sliding with Dry Friction. Pt. 2: Dynamics of Motion,"
Wear
143, 331-352 (1991). |
| 3. | Z. Farkas, G. Bartels, T. Unger, and D. Wolf,
"Frictional Coupling between Sliding and Spinning Motion,"
Phys. Rev. Lett.
90 (24), 248302 (2003). |
| 4. | G. M. Rozenblat,
Dynamical Systems with Dry Friction
(NITs "Regular and Chaotic Dynamics," Moscow-Izhevsk, 2006)
[in Russian]. |
| 5. | N. N. Dmitriev,
"Motion of Disk and Ring on a Plane with Anisotropic Friction,"
Trenie i Iznos 23 (1), 10-15 (2002)
[J. Frict. Wear (Engl. Transl.)]. |
| 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. | G. M. Rozenblat,
"Integration of the Equations of Motion of a Disk on a Rough Plane,"
Izv. Akad. Nauk, Mekh. Tverd. Tela,
No. 4, 65-71 (2007)
[Mech. Solids (Engl. Transl.)
42 (4), 552-557 (2007)]. |
| 9. | L. A. Galin,
Contact Problems of Elasticity and Viscoelasticity
(Nauka, Moscow, 1980)
[in Russian]. |
| 10. | V. V. Andronov and V. Ph. Zhuravlev,
Dry Friction in Problems of Mechanics
(NITs "Regular and Chaotic Dynamics," Moscow-Izhevsk, 2010)
[in Russian]. |
| 11. | A. P. Ivanov,
"A Dynamically Consistent Model of the Contact Stresses in the Plane Motion of a Rigid Body,"
Prikl. Mat. Mekh.
73 (2), 189-203 (2009)
[J. Appl. Math. Mech. (Engl. Transl.)
73 (2), 134-144 (2009)]. |
| 12. | T. V. Sal'nikova, D. V. Treshchev, and S. R. Gallyamov,
Motion of a Free Hollow Disk on a Rough Horizontal Plane,"
Nelin. Din.
8 (1), 83-101 (2012). |
| 13. | O. B. Fedichev and P. O. Fedichev,
"Deceleration and Stop of Plane Bodies Sliding on a Rough Horizontal Plane,"
Nelin. Din.
7 (3), 549-558 (2011). |
| 14. | A. V. Karapetyan and A. M. Rusinova,
"A Qualitative Analysis of the Dynamics of a Disc on an Inclined Plane with Friction,"
Prikl. Mat. Mekh.
75 (5), 731-737 (2011)
[J. Appl. Math. Mech. (Engl. Transl.)
75 (5), 511-516 (2011)]. |
| 15. | V. Ph. Zhuravlev and G. M. Rozenblat,
Theoretical Mechanics in Solutions of Problems from I. V. Meshcherskii's Collection
(LIBROKOM, Moscow, 2013)
[in Russian]. |
|
| Received |
27 May 2013 |
| Link to Fulltext |
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