Theory for elastic wave scattering by a two-dimensional periodical array of cylinders: An ideal approach for band-structure calculations

We extend the multiple-scattering theory to elastic waves propagating in two-dimensional periodical composites. The formalism for the band-structure calculation is presented by taking into account the full vector character of the elastic waves. Besides the efficiency in conventional band structure calculation for elastic waves, the approach shows special advantages in handling the systems with mixing solid and fluid components, for which the conventional plane-wave approach fails. As the applications of the formalism, we calculate the band structure for systems with lead cylinders in epoxy matrix, steel cylinders in water, and water-filled cylindrical holes in steel matrix.