Comparison of the mechanism of gap formation for tri- and bi-component phononic crystal

Using an exact Mie scattering solution, this paper investigates themode conversions during the Mie scattering of a single bi- orone-component sphere in unbounded epoxy. Then the formationmechanism of the first complete gap in the corresponding tri- orbi-component phononic crystal is investigated by themultiple-scattering method. It is shown that the heavy density ofthe scatterer plays an essential role in the Mie resonance and theformation of the gaps for both types of the phononic crystals. Forthe tri-component phononic crystal, the gap is mainly induced by theMie resonance of the single scatterer. For the bi-component phononiccrystal, the transverse wave (by mode-conversion during the Miescattering under a longitudinal wave incidence) is modulated by theperiodicity and governed by the Bloch theory, which induces the gapcooperatively.