Multiple-scattering theory for two-dimensional arbitrarily shaped acoustic composites

Multi-scattering theory (MST) is an analytical tool which allows for the resolution of the field dispersed (scattered) by an interfering medium after leaving a source. The basis of the method consists in determining the way each inhomogeneity (scatterer) in the medium affects the incident wave, something which ultimately depends on the shape and mechanical properties of the scatterer. Unlike previously reported MST implementations in acoustics, which only deal with cylindrical scatterers, we studied the effects of employing structures with different shapes (triangular, square, elliptical). The using of these scatterers to conform periodic composite materials (crystals) is further tested and the arising results are contrasted with predictions based upon the band structures of the corresponding crystals. Also, both the geometrical parameters of the scatterers (cross-section and size) and their orientations in the crystal with respect to the source are varied, giving rise to additional tools to manipulate th...