Abstract

Reflection and transmission coefficients in the problems of normal plane wave incidence on the system of finite and infinite periodic arrays of cracks in an elastic body are analyzed. A method permitting to solve the scalar diffraction problem for both single crack and any finite number of cracks with arbitrary lattice geometry was proposed. In one-mode frequency regime the problem was reduced to a discretization of the basic integral equation holding on the boundary of the scatterers located in one horizontal waveguide. A semi-analytical method developed for diffraction problems on infinite periodic crack arrays permits to present a comparative analysis of the properties of the main external parameters for a finite periodic system of cracks, where the solution of the boundary integral equations is constructed numerically, what leads to the explicit analytical representations for the wave field at the boundary of the obstacles. The analysis of the properties of the scattering coefficients depending on the physical parameters is carried out for three diffraction problems: a finite periodic system in a scalar formulation, an infinite periodic system in a scalar formulation, an infinite periodic system in a plane problem of the elasticity theory.

Keywords: Diffraction problem; One-mode frequency regime; Semi-analytical method; Periodic crack array; Reflection and transmission coefficients; Metamaterials