A comparative analysis of wave properties of the finite and infinite doubly periodic arrays of volumetric and thin defects

A two-dimensional problem on wave propagation through doubly periodic arrays of defects located in an elastic material is studied. The incident wave is longitudinal and the defects may be thin (cracks) or volumetric (voids). For both the types of defects the main aim is to compare the wave properties of the structure whose geometry may be either finite or infinite in the transversal periodic direction with respect to the direction of the incident wave. The physical parameters under consideration are the reflection and the transmission coefficients, which are studied versus frequency parameter in the one-mode regime.