Effect of compressible liquid on the contact between an elastic body and a rigid base with a periodic array of quasielliptic grooves

Abstract

The frictionless contact between an elastic body and a rigid base in the presence of a periodically arranged quasielliptic grooves with in interface gaps in the presence of a compressible liquid is modeled. The contact problem formulated for the elastic half-space is reduced to a singular integral equation (SIE) with Hilbert kernel for a derivative of a height of the interface gaps, which is transformed to a SIE with Cauchy kernel that is solved analytically, and a transcendental equation for liquid’s pressure, which has been obtained from the equation of compressible barotropic liquid state. The dependences of the pressure of the liquid, shape of the gaps, average normal displacement and contact compliance of the bodies on the applied load and bulk modulus of the liquid are analysed.