Theoretical Design And Numerical Analysis Of Phononic Crystals Lens Based On The Rotating Scatterer

Phononic crystals are acoustic artificial structures consisting of different elastic media arranged periodically.Due to the effect of periodic potential field,the band structure of phononic crystals is similar to that of electronic systems: Acoustic or elastic waves at forbidden band can not propagate into phononic crystals,while acoustic or elastic waves at passband with specific structures would show the novel physical phenomena such as imaging,focusing and directional transmission.Therefore,phononic crystals have wide application prospects in the vibration and noise reduction,acoustic waveguide,industrial non-destructive testing,medical examination and other fields.With the development of nondestructive testing and medical treatment,the design and research of phononic crystal lenses have attracted wide attention.At present,the gradient refractive index method is mainly used to construct the acoustic lens.The design of the lens is mainly realized by changing the lattice size of phononic crystals,the filling ratio of the scatterer and the material of the scatterer.In this paper,a phononic crystal lens with the constant filling ratio,the constant lattice constant and the constant scatterer material is designed,and numerical analysis is carried out.The main work and conclusions are as follows:(1)In this paper,a rotating three-petal scatterer is used to design the phononic crystal lens.By calculating the first and second band structures of the phononic crystals,the influence of the rotating angle of the scatterer on the band structure of the phononic crystal is analyzed.The results show that the first band structure and the second band structure change linearly with the rotation of the scatterer.The two band structures correspond to the effective positive refractive index and the effective negative refractive index.Therefore,different effective refractive indices can be achieved by rotating a three-petal scatterer and used to design the distribution of gradient refractive index.Compared with the traditional gradient lens,there is no need to change the filling index,material parameters or lattice size of the scatterer,so it is more convenient to manufacture and apply.(2)In this paper,a gradient positive refractive index phononic crystal lens is designed with a rotating three-petal scatterer.The phononic crystal is composed of epoxy resin scatterers arranged in a honeycomb lattice in a steel matrix.The relationship between the effective positive refractive index and the rotation angle of the scatterer is obtained by calculating the first band structure of the phononic crystal.A gradient phononic crystal lens with hyperbolic secant distribution effective refractive index is designed.The effects of different reduced frequencies on the focusing effect of the lens are studied by numerical calculation and analysis.The calculation results show that the focusing effect of the lens is obvious,and the focal length is consistent with the theoretical predicted result.Compared with the traditional lens,the simplified frequency range(??=0.18)of the focusing operation of the lens in this paper is obviously improved,showing the better focusing effect.(3)Based on the variation of the second band structure of the rotating three-petal scatterer,a gradient negative refractive index phononic crystal lens is designed.The phononic crystal consists of a steel scatterer arranged in a honeycomb lattice in the air matrix.By calculating and analyzing the variation law between the effective negative refractive index and the rotation angle of the scatterer,the gradient rotation angle distribution satisfying the equivalent path theory is designed,and the numerical analysis is carried out.The focusing effect of phononic crystal is studied,and the influence of acoustic frequency and lens size on the focusing effect of the lens is analyzed.The calculation results show that the lens can achieve negative refractive focusing of acoustic waves.The focal position of the lens is consistent with the theoretical predicted result.The range of the reduced frequency is 0.19,which is about twice the working frequency of the traditional negative refractive index gradient lens.The method of rotating scatterer provides a new method for the design of phononic crystals with high performance and easy processing.