| Abstract: | Solutions are presented of certain plane and axisymmetric contact problems on the frictionless impression of a rigid stamp into a two-layered ageing viscoelastic foundation. It is assumed that the upper layer is thin relative to the contact domain, and inhomogeneously ageing. The rheological properties of the lower layer are described by the equations of linear creep theory for ageing materials. The layers are mutually rigidly adherent. The contact domain does not change with time. Depending on the relationships between the moduli of the instantaneous elastic strains of the layers, the mixed problems reduce to integral equations of the first or second kinds containing Fredholm and Volterra operators. An analytic method is proposed for solving such equations which enables an expansion to be obtained for the fundamental characteristics of the contact interaction for a force varying with time in an arbitrary manner and acting on the stamp. Cases are investigaged for the artificial and natural ageing of a two-layer foundation. |
