Periodic Contact Problem for a Surface with Two-Scale Waviness

Abstract

An analytical solution of a periodic contact problem on the penetration of a rigid wavy surface represented by two cosine harmonics into an elastic half-plane without accounting for the frictional forces is obtained. It is shown that the presence of cosine harmonics of the second scale for moderate and large loads causes oscillations of the pressure distributions, which depend linearly on its amplitude and nonlinearly on its period. The presence of the oscillations of the contact characteristics—the nominal and maximal pressures—is discovered.