Research On Band Gap Algorithm And Regularity Of Two Component Phononic Crystals

The important characteristic of the phononic crystals is the band structure of elastic wave,and its calculation method requires the characteristics of high precision, fast speed and good convergence. The calculation method and the regulation about the band structure of the phononic crystals are studied. The results have guiding significance for the design and fabrication of novel acoustic devices.Starting from the elastic wave equation of ideal medium, the theory and algorithm of plane wave expansion method and finite element method are studied in detail, combining with Fourier expansion and Bloch theorem of lattice periodic functions in solid theory. The eigenvalues of characteristic equation are obtained by a number of calculation and simulation through MATLAB and COMSOL.The results of the band gap calculated are different by the comparison of two algorithms. The two algorithms have overlapping regions through analyzing the causes of these differences, which proves that combination of plane wave expansion method and finite element method are more reasonable to calculate the band gap.On the basis of the discussing of algorithm, analysising the modulation laws of the band gap, the main factors influencing the band gaps are: parameters of group material, structure parameters and the thickness of phononic crystal plate. In terms of the parameters of material parameters, we found that the bigger the density of the scattering body to the matrix, the wider the width of band gap, Compared to the matrix, the impact of scatterers on the band gap is much bigger. The greater young's modulus of the scatterer, the greater upper boundary of band gap. While Young's modulus of matrix has no influence on band gap.The shear modulus of scatterer and matrix does little influence on band gap.In aspect of the structure parameters,we compared triangular lattice and tetragonal lattice, the conclusion is that thehigher the symmetry of the lattice, the wider the band gap width. In aspect of the fill rate,when the filling rate is increased, the band gap becomes wider and the filling rate is larger to a certain extent, and the band gap becomes narrow.In aspect of the shape of the scattering body, the elliptical shape is selected to compare with the circle shape. The conclusion is that the ratio of elliptical scatterer body short and long axes of T is smaller, the wider the band gap width.In aspect of the thickness of phononic crystal plate,the width of band gap broaden by the increase of the plate. The research provide theoretical guidance for the design of the phononic crystal.