Study On The Characteristics Of Acoustic Singular Index Metamaterials

Natural materials can control the propagation of classical waves such as light/electromagnetic waves,acoustic waves/elastic waves,and different materials have different electromagnetic and acoustic functions However,natural materials offer limited options.In recent years,scholars in various countries have devoted themselves to the research of a new type of artificial material,namely "metamaterials",to achieve the material functions that many natural materials do not have.The metamaterial consists of artificially composite local resonance unit that “operates at” the sub-wavelength scale,the structural unit is much smaller than the corresponding wavelength,Thus the interaction of meta-materials with classical waves can be described by effective material parameters such as effective dielectric constant,magnetic permeability,mass density,and bulk modulus.The effective material parameters of the metamaterial can change from positive to negative The Singular refractive index of meta-materials has attracted a lot of interest from scholars all over the world.In this dissertation,we will further study the interface acoustic mode in double negative acoustic metamaterials and further extend the concept of zero refractive index to the elastic wave system to explore the scattering problem of elastic waves in zero-index extraordinary materials.The main results of this dissertation are listed as follows:(1)Study on acoustic interface waves in acoustic meta-materials with double negative parametersThe supercell method is employed to study the dispersion relation and eigenfield distributions of the interface modes existing in the incomplete band gap in the double negative acoustic metamaterial.Acoustic meta-materials with double negative parameters are designed by placing square rubber cylinders in water.Further,with the application of the effective medium theory,we find that these interface modes are induced by the double-negative responses of acoustic metamaterials – negative effective mass density and bulk modulus.By means of the interface modes,an acoustic superlens for ultrasonic imaging can be obtained.(2)Study on the propagation properties of zero refractive index metamaterials with different combinations of effective material parametersSystematically discussing the simplified form of the elastic wave equation and the Christoffel equation when zero values of effective material parameters in the acoustic metamaterial,and exploring the general solutions of these equations,the propagation characteristics of the longitudinal/transverse waves,the occurrence of resonance modes,the scattering of the longitudinal/transverse waves,and the mode conversion.(3)Independent manipulation the propagation of longitudinal/transverse waves by using complicated obstaclesBy using lower symmetry scatter embedded in the elastic wave zero-index metamaterial,the resonance mode is degenerated in the x-axis direction and the y-axis direction,thereby we can separate and independent control propagation of the longitudinal/transverse waves to achieve the longitudinal wave transmission and transverse wave reflection,or the longitudinal wave reflection and transverse wave transmission,finally the numerical simulation method is used to verify the result.(4)Realizing the zero refractive index of Lamb waves in metamaterial plateOur research extends from the two-dimensional plane problem to the three-dimensional plate problem and studies the zero-refractive index of Lamb wave in the metamaterial plate,exploring the introduction of suitable effective parameters to achieve the effective zero-refraction in the metamaterial plate,the propagation characteristics of Lamb waves in a three-dimensional metamaterial plate with new effective parameters are theoretically studied.Using finite element software COMSOL Multiphysics to theoretical analyze numerical simulation result.