Schoch Effect Of Two Dimensional Acoustic Metamaterials Based On Near Zero Refractive Index

After more than 20 years of development,a synthetic composite acoustic material or structure(phononic crystals)with periodic structure arrangement has attracted more and more attention from scholars at home and abroad.Phononic crystals have rich physical connotations and broad application prospects because of their elastic wave or acoustic band gap characteristics.To its acoustic control mainly has: one is the phononic band gap exists,this is one of the most significant physical characteristics,namely the phononic frequency range corresponding to the elastic wave band gaps or sound waves will be reined in,and the macro performance is banned in the phononic band gaps frequency range,and in other frequency range can be lossless transmission;The existence of defect state is the second characteristic of phononic crystals.When there is a defect,line defect or surface defect inside the phononic crystals,the elastic wave or sound wave propagating inside the phononic crystals will be locally propagated at the correct defect or along the line defect or surface defect.Therefore,a variety of new acoustic devices can be invented through manual design,that is,different lattice arrangement,scatterer radius,different kinds of materials,introducing defects and so on.Phononic crystals,as a new kind of artificial composite periodic material,have been proved to have many novel and unique physical properties,such as acoustic focusing,acoustic stealth,acoustic imaging,negative refraction,zero refraction,Schoch effect,etc.Phononic crystals whose refractive index is close to or equal to zero is called a near-zero refractive index acoustic material.In this paper,the negative Schoch effect of acoustic materials with near-zero refractive index was studied by using the effective media theory method and the finite element method based on the inversion method,and the relationship between the maximum negative Schoch displacement and various parameters of acoustic metamaterial(hereinafter referred to as metamaterial)model was obtained.The writing framework of this article is as follows:In the first chapter,some basic definitions of phononic crystals are described in detail,and some basic characteristics of phononic crystals are introduced emphatically.Then,the research achievements and the progress of phononic crystals at home and abroad are described in detail.Finally,the main concepts of acoustic metamaterials and the current research achievements are introduced.The following chapter starts with the derivation of the elastic wave equation in ideal medium in detail,and then by introducing curl and divergence into the equation,the P-wave and S-wave are finally separated.We then introduce three common arrangements of phononic crystals and the theory of effective media based on the inversion method.In the following chapter,we describe in detail the large negative Schoch displacement of a near zero refractive index acoustic material based on this theory.Finally,the common finite element methods in simulation are introduced.In chapter three,the negative Schoch displacement of two-dimensional near zero refractive index acoustic materials is investigated.This chapter proposes a two-dimensional mercury-water-acoustic metamaterial structure,using the finite element method to simulate the limited width of gaussian sound waves from the mercury in the solution to the acoustic metamaterial in condition of oblique incidence,acoustic metamaterial interface in the huge negative Schoch displacement,and maximum negative displacement of Schoch and model the relationship between different parameters,and at the same time the acoustic metamaterial can combined with the above content,found that negative Schoch displacement excitation frequency of sound waves incident,near the border on the band structure of the first gap frequency on the band gap border take negative Schoch displacement take maximum.In chapter four,we study the positive or negative Schoch displacement at the interface caused by the difference of incident frequency when acoustic waves incident into a particular acoustic metamaterial.Thus a positive or negative Schoch displacement can be obtained by adjusting the frequency of the incident sound wave.Inspired by the single pole and double throw switch in the circuit,an acoustic switch based on acoustic Schoch displacement is designed.In the fifth chapter,the main conclusions of the paper are summarized,and the further studies on Schoch displacement of acoustic waves are prospected in detail.