Dynamics of the Motion of an Elastic Cylinder Along an Elastic Foundation

The quasi-static plane-parallel motion of an infinite elastic cylinder along a horizontal foundation made of the same material is studied (the cylinder axis is horizontal). The distribution of normal and tangential stresses in the region of contact interaction between the cylinder and plane is derived from the solution to the problem of the theory of elasticity, where the Amontons-Coulomb dry friction model is used in the slip area and the presence of a stick area is taken into account. The analytic solution to the problem is obtained and the phase portrait of the system is drawn. We compare this with the problem of the motion of a perfectly rigid cylinder along a rigid surface with dry friction and without slip.