Study on bandgap extension and defect states of hybrid primitive structure phononic crystals

Abstract

Based on the two-dimensional square lattice phononic crystal of the steel-gas system, a hybrid primitive phononic crystal is constructed by replacing the single-cylinder primitive with a tangent double-cylinders primitive structure and inserting the tangent double-cylinders primitive in the center of the lattice. The plane wave expansion method is used to calculate the band structure according to the variation of the extremal positions of the band. It is found that compared with the simple single-cylinder primitive lattice structure, the new structure can significantly separate the degenerate states of the band, and obtain a huge bandgap with a width of 5 times the simple single-cylinder lattice at low filling ratios. Its mechanism can be revealed by the inconsistency of the sound pressure field in the boundary direction. Meanwhile, adding the double-cylinders primitive to the center of the simple single-cylinder lattice produces an effect similar to the interstitial impurity defect, which can excite high-quality localized states of defects in the bandgap. The filling ratio of the defect body mainly affects the position of the localized states and the locality of sound pressure, whereas the orientation of the defect body has almost no effect on the distribution of sound field and the position of defect states.