The band gap of 2D perfect and defect phononic crystal are calculated by using plane-wave expansion (PWE) and supercell plane wave method, which is consist of Al2O3 embedded in the epoxy resin with a square arrangement. Compared to the perfect, the gap of defect will become wider. As the size of defect length ld varied, the band structure changed. It is found that the acoustic wave only propagates along the path of defect when the propagation of acoustic wave is simulated on the 900 bending defect phononic crystals by matlab. It means that the waves are localized. So the defect mode of phononic crystal can be used as acoustic waveguide along the specific path.

The band gap of a new two-dimensional phononic crystal was studied by the plane-wave expansion method. The two-dimensional phononic crystal is formed by square-shape array geometry of iron cylinders with square cross section inserted in an epoxy resin. The band gaps of different structures were calculated such as defect-free, single cavity crystal point defect states, crystal point defect states with (10) direction coupling, crystal point defect states with (10) direction next-nearest-neighbor coupling, and crystal point defect states with (11) direction next-nearest-neighbor coupling. Compared with that of defect-free, it is conclude that point defect is beneficial to the production of band gaps. The bandwidth of point defect is about 5 times larger than that of the defect-free crystal with the filling fraction F=0.4. In addition, the maximum number of band gap is in the crystal point defect states with (10) direction next-nearest-neighbor coupling. It will provide a theoretical reference for the manufacture of phononic crystal.

The band gap of 2D perfect phononic crystal thin plate was investigated by plane-wave expansion (PWE), which is consist of copper embedded in the organic glass with a square arrangement. The band gap of straight linear defect, branching linear defect, and symmetrical linear defect are calculated by supercell plane wave method respectively. It is found that the bandwidth of defect structure will become narrow. Especially there is little band gap appearing for straight linear defect. As the filling fraction varied, the band gap width and the band gap number changed.