On deforming of a linear viscoelastic orthotropic half-space under the turning rigid cylindrical roller

In this paper we consider the problem of rigid cylinder turning on a linear viscoelastic orthotropic half-space with Coulombʹs friction acting along the contact area. Results for extents of contact area and pressure under the cylinder are obtained using Volterraʹs principle. The obtained functions of viscoelastic operators are interpreted by a method based on expansion of such functions in operator continued fractions. A solution is given for the general type of resolvent viscoelastic operators expressing rheological properties of half-space material. Algebra of resolvent Volterrian operators is used to facilitate the calculations. An example is given to illustrate the results for real viscoelastic material with the rheological properties expressed by the operators of Yu.N. Rabotnov.