Calculation of the scattering coefficient of large scale periodic structure

The periodic structure is common used in engineering to improve the sound diffusion in room acoustics. It usually has large dimensions and it is difficult to calculate the scattering coefficient based on its original scale. In order to represent the scattering coefficients of a large scale periodic structure by those of a smaller one, the relations of the scattering coefficients of the periodic structures with different dimensions are analyzed in this paper. At first, a BMM (Boundary Meshless Method) for calculating the scattering coefficient is derived. The scattering coefficients of the periodic structures which have different numbers of sub-structures are calculated and compared. The computation results of different sub-structure numbers show that the periodic structure with 15 sub-structures can represent the samples which have more sub-structures. In addition, it can be proved that the square samples can be represented by those of the small and rectangular ones which have the same numbers of sub-periods. These conclusions not only greatly enhance the computational efficiency, but also show good prospect for fast evaluation of the periodic structures in engineering applications.