Calculation of Band Structure in Two-dimensional Phononic Crystals with Arbitrary Scatters

With the discretization of one lattice with scatter in arbitrary shape inside two-dimensional phononic crystals,the integral problem in the calculation of structural functions is successfully solved with a numerical integral method.Thus,an improved plane-wave expansion method is proposed for the calculation of band structure in two-dimensional phononic crystals with lattice of scatters in arbitrary shape.Using traditional and improved plane-wave expansion method respectively,we calculate the band structures of same two-dimensional phononic crystals with regular unit structure.The two calculation results are in good agreement,which validates the correctness of our method.The special ability of the improved method will be especially helpful in the topological optimization of unit structure in phononic crystals.