Three-dimensional one-mode penetration of elastic waves through a doubly periodic array of cracks

The paper is devoted to the calculation of the reflection and transmission coefficients, when a plane wave is incident on a two-dimensional grating with an infinite doubly periodic array of rectangular cracks in the elastic material. In the one-mode frequency range the problem is reduced to an integral equation holding over the single chosen crack. The semi-analytical method previously introduced for scalar and elastic plane problems gives explicit representations for the wave field and the scattering parameters.