One-Mode Propagation of Elastic Waves through a Doubly Periodic Array of Cracks

Abstract

The article is devoted to the derivation of analytical expressions for the reflection and propagation coefficients, when a plane longitudinal wave falls on a system of a finite number of consecutively located identical flat gratings, each of which consists of a periodic array of rectilinear cracks in an elastic isotropic medium. The problem is solved in a flat statement. In the mode of single-mode frequency range, the problem is reduced to a system of hypersingular integral equations, the solution of which gives the reflection and propagation coefficients, as well as the representation of the wave field inside the medium.