A non-stationary dynamical periodic contact problem for a homogeneous elastic half-plane

Abstract

The problem of determining the contact stresses under a periodic system of stamps located on the boundary of a homogeneous elastic half-plane and moving under the effect of a load, identical for all stamps, that is arbitrary in time, is investigated. The problem reduces to solving a Fredholm integral equation of the first kind for the Laplace transform of the contact stresses. The stresses are sought in the form of a double expansion in Chebyshev polynomials of the linear coordinate and Laguerre polynomials of time. The coefficients of the expansions are determined recursively from an infinite quasiregular system of linear algebraic equations. Despite the fact that the static periodic contact problems of the theory of elasticity, on the one hand (/1–6/, say), and dynamic problems for a finite number if stamps on the other (see the survey in /17/), have been studied repeatedly by different investigators, so far as we know, the plane non-stationary dynamical periodic contact problem has still not been examined at all.