The problem of the non-uniform sliding of an indenter over a viscoelastic foundation with applications to the calculation of the dynamics of a movable contact

The problem of the non-uniform sliding of an indenter over a viscoelastic foundation, whose deformation properties are described by a simplified Kelvin model, is considered. An analytical solution is obtained, and it is established that it has a hereditary character, i.e., it depends on the past history of the interaction of the indenter with the foundation. The solution obtained is used to calculate the sliding dynamics of a massive body, i.e., the problem of braking of a massive indenter as it slides over a viscoelastic foundation and the problem of grasping a massive viscoelastic body by a pair of indenters sliding over its sides. The influence of the viscoelastic parameters and the shape of the indenter on the dynamic characteristics of the massive body is studied. In particular, it is shown that the type of dependence of the deformation friction force on the sliding velocity has a significant influence on the braking mode of the indenter. The possibility of controlling the braking process is demonstrated.