Influence Of Geometry And Material On The Band Gap Structure And Defect States Of Two Dimensional Solid-solid Phononic Crystals

Phononic crystals are medium structures or materials with artificial periodic distribution of elastic waves or phononic band gaps.Because of the interaction between the elastic wave and the periodic structure,only the elastic wave in the partial frequency range can pass through the phononic crystal,while the elastic wave in the other frequency range could not pass through the so-called elastic wave band gap.In order to control the propagation range and direction of the elastic wave,the defects were introduced in the phononic crystal based on the dopant principle of semiconductors.Therefore,by adjusting the geometrical or material parameters of the periodic structure,the width,position and suppression of the wave propagation can be artificially controlled.This provides a new idea for the vibration and noise reduction of the traditional engineering structure,which means the engineering structure is designed as a special artificial cycle structure,so that it has band gap characteristics,which could control the spread of the wave in the structure,so as to achieve the purpose of vibration and noise reduction.Based on the introduction of the basic concepts,the research status,the characterization of acoustic features,the calculation method of band structure of phononic crystals and the band structure method under different modules in finite element software,the effects of geometrical shape and material on the bandgap and defect states of phononic crystals are studied in this paper.The main contents are as follows:The influence of the geometrical structure of the two-dimensional solid-solid phononic crystals on the defect state under the superlattice was studied by applying the finite element method.This paper analyzed the impact of the geometric structure of the central scatterer,the ratio of the semi-major axis to the semi-minor axis of the asymmetric and elliptical scatterer,and the aspect ratio of the rectangular scatterer on the defect band of the two-dimensional solid-solid phononic crystals transmission spectrum and other characteristics.Through the calculation,there are following findings.When the geometrical shape of the central scatterer is elliptic,the smaller the ratio of the semi-minor axis to the half-major axis,the defect frequency of the ellipse is moved to the center of the band gap.When the geometrical shape of the central scatterer is rectangular,the smaller the ratio of the width to the long,the defect frequency is also moving to the center of the band gap.When the geometry of the central scatterer is a regular polygon,with the increase of it's edges,it's shape is closer to the cylindrical scatterer,the less appearance of the defects.When the difference between the geometry of the central scatterer and other scatterers are larger and asymmetrical,the more prone of the defect frequency is.When the geometrical shape of the central scatterer is radian and symmetrical,the frequency of the defect is prone to occur,and the vibration local is in the surface of the defect scatterer with the phase between adjacent scatterers.The influence of the material parameters on the bending state of the two-dimensional phononic crystal thin plate under the superlattice was studied by adopting the finite element method.The influence on defect state is calculated by replacing the central scatterers.Besides,the influence on defect state is calculated by changing the density and Young's modulus in material parameters.The result shows that the defect band is generated when the elastic constant of central scatterer is same with other scatterers but their density are different.As the density increases,the number of defect band is different.The defect band moves toward the lower edge of the bandgap with the increase of density.And some of the defect bands disappear with the increase of the density.When the Young's modulus of the central scatterer is different from other scatterers,but their density and shear modulus are the same and when their Young's modulus difference is small,there is no defect.With the Young's modulus of the center scatterer becomes smaller,a defect band appears on the upper edge of the bandgap,and the defect band gradually moves toward the lower edge of the bandgap.When the Young's modulus of the central scatterer is different from the Young's modulus of the other scatterers by more than four orders of magnitude,the defective band no longer moves.This paper studies the defects of phononic crystals and the localization of elastic waves,and it is of great significance in the preparation of acoustic devices such as tunable acoustic filters and the vibration and noise reduction of precision instruments.