Axisymmetric Contact Problem for a Punch and Nonuniform Foundation with Rough Surfaces

The axisymmetric contact problem for a viscoelastic foundation with a radially nonuniform elastic (surface nonuniform) coating and a rigid punch is considered. It is assumed that the nonuniformity and shape of the coating and the shape of the punch surface can be described by different rapidly changing functions. We obtain basic mixed integral equation with three different rapidly changing functions and two different integral operators (a compact self-adjoint positively defined operator with respect to the coordinate and the non-self-adjoint integral Volterra operator with respect to time) for this problem and additional condition. A projection method is developed for this problem. It allows one to obtain the solution of the equation with high accuracy that cannot be done by known methods.