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

Using an exact Mie scattering solution, this paper investigates the mode conversions during the Mie scattering of a single bi- or one-component sphere in unbounded epoxy. Then the formation mechanism of the first complete gap in the corresponding tri- or bi-component phononic crystal is investigated by the multiple-scattering method. It is shown that the heavy density of the scatterer plays an essential role in the Mie resonance and the formation of the gaps for both types of the phononic crystals. For the tri-component phononic crystal, the gap is mainly induced by the Mie resonance of the single scatterer. For the bi-component phononic crystal, the transverse wave (by mode-conversion during the Mie scattering under a longitudinal wave incidence) is modulated by the periodicity and governed by the Bloch theory, which induces the gap cooperatively.