The Schoch Effect Mechanism Analysis And Its Regulation Of Two Dimensional Phononic Crystal

After 20 years of development,a kind of acoustic material or composite structure with elastic wave band gaps,periodic arrangement,namely the phononic crystal,has attracted more and more attention from domestic and foreign scholars thanks to the physical connotation and wide potential application prospects.Its basic characteristics are as follows:One is the presence of phononic bandgap,which is its most significant physical properties,that is,the elastic wave / acoustic wave propagation corresponding to the frequency in the phononic bandgap will be suppressed,and exponential decay will occur in the phononic crystal,and its frequency in the pass band corresponding to the elastic wave / acoustic wave in the dispersion relationship will be able to achieve lossless propagation.The other is a defective state,the bandgap frequency range of elastic wave / sound waves will be spread locally in the point defects or along the line defects or surface defects when the phononic crystal within the existence of point defects,line defects or surface defects.A variety of new type acoustic devices can be designed in wide potential applications for the unique characteristic of phononic crystal,such as mechanical vibration,integrated acoustics,sound communication.As a new type artificial periodic structural functional material,phononic crystal has a lot distinctive physical behaviors which have been observed and verified,for instance,sound focus,collimation,negative refraction,Schoch effect.In this paper,we focus on the Schoch effect of the phononic crystal.The finite element method is used to study the reflection of the collimated frequency acoustic wave on the surface of the two-dimensional three-element phononic crystal.The effects of the forward and negative Schoch effects on the phononic crystal are explored.The contents of this paper are arranged as follows:The first chapter introduces the concept of phononic crystal and its basic characteristics,then discusses the research status of phononic crystals both at home and abroad,and finally describes several important characteristics of phononic crystals.The second chapter introduces the elastic wave equation in the ideal elastic medium condition,and separates the shear wave and the longitudinal wave by the divergence and therotation operator.This paper introduces the calculation methods and advantages and disadvantages of two kinds of two-dimensional phononic crystals,and introduces the finite element method from the basis of elastic mechanics.Two-dimensional three components phononic crystal Schoch effect are studied in Chapter 3,a two-dimensional three element structure,that is phononic crystal-surface-water,is investigated by finite element method(FEM).Based on the proposed structure,the reflection situation of the self-collimation acoustic beam in phononic crystal has been studied on the interface of the phononic crystal and water.The Schoch effect has been observed,and the Schoch displacement data has been obtained.At the same time,using the energy band structure of the model,it is found that the non-specular reflection of the reflected beam is presented due to the coupling between the waveguide and the bulk mode.Through further studies,a curve about the Schoch displacement varied with the radius of the surface layer cladding is obtained.Finally,the cladding radius of two layers of the same nuclear cylinder keeps unchangeably,the enhancement of Schoch displacement is achieved by increasing the number of surface layers,which means that the Schoch effect can be manipulated by the number of the surface layer.The fourth chapter mainly studied the negative Schoch effect on a reflected acoustic metasurface.The reflected Schoch effect in water has been studied based on the gradient acoustic metasurface constructed by special designed structure in water.An obvious negative Schoch effect on the designed acoustic metasurface has been observed through finite element simulation,and the relationship between the displacement of Schoch effect and the thickness of the acoustic metasurface has been obtained.The last chapter presents the main conclusion of this article.