The band structures of a new two-dimensional triangle-shaped array geometry of 4340 steel cylinders of square cross section in an epoxy resin were studied by the plane-wave expansion and supercell calculation method. The band gaps of this type of phononic crystals with different defects were calculated such as defect-free, 60 • crystal linear defect states, 120 • crystal linear defect states, and 180 • crystal linear defect states. It was found that the band gap will emerge in different linear defects of the phononic crystals and the bandwidth of linear defect states is larger than that of the free-defect crystal by about 2.14 times within the filling fraction F = 0.1-0.85. In addition, the influence of the filling fraction on the relative width of the minimum band gap is discussed.

The band gaps of a two-dimensional phononic crystal are studied by using the plane-wave expansion method and the supercell calculations. The two-dimensional phononic crystal is formed by square-shape arrangement of 4340 steel inserted into epoxy resin. The band gaps of different structures are calculated such as defect-free, 45 crystal defect states, 90 crystal defect states, 135 crystal defect states and 180 crystal defect states. It is found that the bandwidth of defect state is about 31 times larger than that of the defect-free crystal; with F=0.10.9 the band gaps occur in different defect structures and increase with defect state angle increasing. In addition, the influences of filling fraction on the band gap number and the relative width of the minimum band gap are also discussed.