Propagation of elastic waves through two-dimensional lattices of cylindrical empty or water-filled inclusions in an aluminum matrix.

The layer-multiple-scattering method is developed to study wave propagation through two-dimensional lattices of cylindrical inclusions in an elastic medium. The lattices are a series of periodically spaced infinite one-dimensional periodic gratings (or rows) of inclusions. The layer-multiple-scattering method allows the analysis of the reflection and transmission properties of the two-dimensional lattice, provided those of each row are known. These are later determined by means of an exact multiple scattering formalism based on modal series developments. A new characteristic equation is obtained that describes the Bloch wave propagation into the infinite lattice. Lattices with empty and fluid-filled inclusions are compared. The comparison shows the existence of pass and stop bands due to the resonances of the fluid-filled inclusions. Resonant inclusions allow the opening of narrow pass bands inside phononic stop band, which is an interesting phenomenon for demultiplexing problems. It is worth noting that inclusion resonances have nothing to do with resonances due to defects, as they involve the whole lattice. In addition, it is shown that stop bands, at an oblique incidence, due to a strong coupling between longitudinal and transverse waves, are related to dispersive guided waves that propagate in the direction of the reticular planes of the lattices.