 | | 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: | | 11262 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3251 |
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| A.A. Zobova and I.G. Goryacheva, "On the Stability of the Uniformly Accelerated Motion of an Elastic Cylinder on an Inclined Flat Surface," Mech. Solids. 56 (8), 1559-1568 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
8 |
Pages |
1559-1568 |
| DOI |
10.3103/S0025654421080197 |
| Title |
On the Stability of the Uniformly Accelerated Motion of an Elastic Cylinder on an Inclined Flat Surface |
| Author(s) |
A.A. Zobova (Moscow State University, Moscow, 119991 Russia, alexandra.zobova@math.msu.ru)
I.G. Goryacheva (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119256 Russia, goryache@ipmnet.ru) |
| Abstract |
Rolling with the slipping of an infinite elastic cylinder with a horizontal axis in the gravity
field on a flat surface made of the same material is considered. The angle between the nondeformed
boundary of the surface and the horizon is nonzero. Based on solution of the corresponding contact
problem in Carter’s quasi-static formulation, the reaction of the flat surface in dynamic equations is
determined. It is shown that if the tangent of the inclination angle does not exceed the product of the
friction coefficient and the coefficient that depends on the elastic properties of the material and the
mass distribution, motion with constant relative slip δ and a constant acceleration of the center of mass
is possible; there is a region in the contact area where the materials stick together. This motion is found
to be asymptotically stable with respect to δ. The dependence of the cylinder-axis acceleration on the
mechanical properties of the material and the friction coefficient is examined. The results obtained are
compared with those of the classical problem of rigid-disk motion along an inclined straight line. |
| Keywords |
rolling with slipping, elastic cylinder, dry friction, partial stability, inclined plane |
| Received |
01 February 2021 | Revised |
01 March 2021 | Accepted |
15 March 2021 |
| Link to Fulltext |
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