Locally resonant phononic crystals made of hollow spheres or cylinders

The acoustic properties of three- and two-dimensional phononic crystals consisting of hollow spheres or cylinders are studied by means of numerical calculations by the layer-multiple-scattering and the finite-difference--time-domain methods. The frequency band structure of these crystals is analyzed in conjunction with relevant transmission spectra, and the nature and physical origin of the different modes is elucidated. The building units of these crystals exhibit localized resonance states which can lead to almost dispersionless bands within an otherwise absolute gap. A feature that makes such systems potentially useful in the way of practical applications as efficient frequency filters. The influence of different geometric and material parameters on the position of these resonances is systematically examined. Such an optimized system made of a polymer material is proposed and studied in detail.