On the Stability of the Uniformly Accelerated Motion of an Elastic Cylinder on an Inclined Flat Surfaceстатья
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Дата последнего поиска статьи во внешних источниках: 8 апреля 2022 г.
Аннотация: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 delta 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 delta. 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