A plane problem of rolling contact in linear viscoelasticity theory

The plane problem of a rigid cylinder rolling with constant velocity over a linear viscoelastic half space is treated within the limits of quasistatic theory. Tangential surface tractions are considered sufficiently small to be neglected, so that the contact deformation is due to a normal pressure distribution. The boundary-value problem is formulated for a general viscoelastic material, and is reduced to two pairs of dual integral equations. These are solved by infinite series expansions, and a numerical example is given to show that truncated series produce adequate results.