Band-structure results for elastic waves interpreted with multiple-scattering theory

The band-structure results for elastic wave propagating in a binary phononic crystal are analyzed by employing a multiple-scattering approach. It has been found that there are uncoupling effects at the high symmetry points of the Brillouin zone that open the spectral gaps. At the edge of the first band gap, a self-contained multiple scattering mode has been obtained which comprises only the zeroth-order cylindrical wave component. An analytic relationship for the beginning frequency of the first band gap has been obtained which comprises the periodic structural property and the Mie scattering of a single inclusion simultaneously. By graphic analytic method, the influence of these two properties were evaluated separately and combined.