contact problems, viscoelasticity, coating, non-uniformity, rapid oscillation, system of mixed integral equations.

A contact problem of the interaction between a system of rigid punches and a viscoelastic foundation with a thin nonuniform elastic coating in the case of plane strain state is under research. Various versions of mathematical formulation are considered. A principal system of integral equations is obtained. It is reduced to an integral equation with a tensor kernel in a functional vector space. The effective projective spectral method is developed. A model problem is solved. Detailed calculations are performed. Qualitative conclusions are formulated.

Manzhirov, Alexander Vladimirovich Dr. Sci. Phys. & Math., Professor, Head of Department for Modeling in Solid Mechanics, Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow; Head of Branch Department of Applied Mathematics, Bauman Moscow State Technical University; Professor of Mathematics, Department of Higher Mathematics, Moscow State University of Instrument Engineering and Computer Science