Research On Two-Dimensional Phononic Crystals Defect States Characteristics

Phononic crystal is a material or structure with periodic distribution of elastic constants and density.It has the property of suppressing the propagation of elastic waves in a certain frequency range,that is,producing a bandgap;and the defect state formed by destroying the periodicity of a perfect phononic crystal can propagate elastic waves at specific frequencies in the bandgap,so the study of phononic crystal defect state is of great significance to the design and manufacture of acoustic filters,acoustic waveguides and other acoustic devices.In this paper,for two typical two-dimensional phononic crystal structures of hole type and cylinder type under bragg mechanism,the influencing factors of point defects and line defects are studied by finite element method.The main contents are as follows:Firstly,the related theoretical basis of phononic crystals is introduced,including elastic wave equations and Bloch theorem.According to the calculation methods for band structure and transmission characteristics of phononic crystals,the theoretical formula of finite element method is derived,and the simulation steps of band structure and transmission characteristics in Comsol5.4 finite element software are introduced in detail.Finally,the correctness of the finite element method is verified by a case.Then,the defect state characteristics of the hole-type phononic crystal are studied.Taking the two-dimensional air/tungsten-type flat phononic crystal as the research object,the effects of the central scatterer filling rate,material and shape on the single point defects of the phononic crystal are studied firstly.Then,the band gap characteristics of the two-point defects in the hole-type flat phononic crystal are studied,including the adjacent mode,the sub-adjacent mode and so on.Finally,the influencing factors of the phononic crystal line defects are studied,including the line defect width,the line defect position and the corner.The results show that the filling rate and shape of the central scatterer have great influence on the point defects,while the material of the central scatterer has no effect on the point defects.As for two-point defects,the adjacent mode is more likely to separate the defect film than the sub-adjacent mode;in the same mode,the horizontal and vertical alignments are more likely to separate the defect film than the oblique direction.It is found that the position of the line defects has no influence on the band structure;with the increase of line defect width,the range of theconduction band is different,and the width of the conduction band becomes larger and larger;while the effect of the corner on the line defect is not obvious.Finally,the defect characteristics of cylindrical phononic crystals are studied in this paper.Firstly,the basic model of epoxy/tungsten is proposed,and a wide bragg bandgap is achieved by introducing a circular hole into the substrate.Then,the influencing factors of single point defects,two-point defects and line defects are studied for the optimized model.Under the single point defect,the results show that the radius,material and height of the central scatterer have a great influence on the point defects.Under the two-point defect,it is found that the defect film can be separated obviously only when the radius of the defect is 3mm in the adjacent mode and the alignment is horizontal or vertical.Under line defects,the height,radius,material and shape of the central scatterer have a large impact on the distribution and number of line defects.