二维声子晶体的Schoch效应及其调控
发布时间：2018-10-18 18:26
【摘要】：经过二十多年的发展,一种存在弹性波带隙特性、结构呈现周期性排列的复合声学材料或结构,即声子晶体,引起了越来越多的国内外学者的广泛关注。这主要得益于声子晶体拥有丰富的物理内涵以及广阔的潜在应用前景。它的基本特征为:其一是存在声子带隙,这是其最显著的物理特性,即声子带隙内频率对应的弹性波/声波传播将受到抑制,在声子晶体里会呈现指数衰减,而不能传播,而其在通带范围内频率对应的弹性波/声波将可以实现无损耗地传播;其二是具有缺陷态特性,当声子晶体内部存在点缺陷、线缺陷或面缺陷时,则带隙频率范围内的弹性波/声波会被局域在点缺陷,或沿着线缺陷或面缺陷处传播。这些特性使得声子晶体可以设计成各式各样的新型声学器件,在机械振动、集成声学及声通信等领域有着广阔的应用前景。声子晶体作为一种新型人工周期性结构功能材料,已观测并证实具有许多独特的物理现象,如声聚焦,自准直,负折射,Schoch效应。本文主要对声子晶体Schoch效应展开研究,通过有限元方法,研究自准直声波在二维三组元声子晶体表面和声学超表面上(以下简称超表面)的反射,实现了对声子晶体的正向Schoch效应和超表面的负向Schoch效应的研究。本论文的内容安排如下:第一章首先介绍声子晶体的概念及其基本特点,然后讨论了声子晶体国内外的研究现状,最后叙述声子晶体的几个重要特性。第二章介绍了理想弹性介质条件中的弹性波波动方程,并利用散度和旋度算子分离出横波和纵波。介绍二维声子晶体三种常见的排列结构和声子晶体带隙的各种计算方法及其优缺点,从弹性力学基本原理出发着重地介绍了有限元方法。第三章针对二维三组元声子晶体Schoch效应进行了研究。本章设计了一种二维三组元声子晶体-表面-水结构,通过有限元方法仿真了自准直声波束在声子晶体-表面层界面的反射情况,观察到了声子晶体表面的Schoch效应,并获得反射波束产生Schoch位移与结构的关系。同时,利用模型超胞的能带结构,分析了这一现象的原因,发现由于类波导模与体模的干涉作用,导致反射波束的非镜面反射,即Schoch效应的产生是类波导模与体波模相互耦合的结果。另外,通过改变表面层包层的半径,得到Schoch位移与包层的半径的依赖关系。最后通过增加表面层层数,调控两层相同核圆柱的包层半径,实现了对Schoch位移的增强,达到了对Schoch效应调控的目的。第四章主要研究声波在超表面上反射的负向Schoch效应。通过在水中设计材料结构,实现水中负相位梯度超表面,进而研究超表面上声波反射的负向Schoch效应。研究结果表明在设计的超表面上能够明显的观测到声波的负向Schoch效应。进一步我们研究了表面的厚度其对Schoch位移的影响。第五章阐述了本文的主要结论。
[Abstract]:With the development of more than 20 years, a kind of composite acoustic material or structure with elastic band gap and periodic structure, namely phonon crystal, has attracted more and more attention from scholars at home and abroad. This is mainly due to the rich physical connotations of phononic crystals and their wide potential applications. Its basic characteristics are as follows: one is the existence of phonon band gap, which is the most remarkable physical property, that is, the elastic wave / acoustic wave propagation corresponding to the frequency in phonon band gap will be restrained, and the propagation of elastic wave / acoustic wave in phonon crystal will be exponentially attenuated rather than propagated. The elastic wave / acoustic wave corresponding to the frequency in the passband range can propagate without loss. Secondly, it has the characteristic of defective state, when there is a point defect, line defect or plane defect in the phonon crystal, The elastic wave / acoustic wave in the band gap frequency range will be propagated locally at the point defect or along the line defect or the plane defect. These characteristics enable phononic crystals to be designed into a variety of novel acoustic devices, which have a broad application prospect in the fields of mechanical vibration, integrated acoustics and acoustic communication. As a new type of artificial periodic functional materials, phononic crystals have been observed and proved to have many unique physical phenomena, such as acoustic focusing, autocollimation, negative refraction and Schoch effect. In this paper, the Schoch effect of phonon crystals is studied, and the reflection of self-collimating sound waves on the surface of two-dimensional three-component phonon crystals and on acoustic supersurfaces (hereinafter referred to as supersurface) is studied by finite element method. The forward Schoch effect and the negative Schoch effect on the supersurface of the phonon crystal are studied. The contents of this thesis are as follows: in the first chapter, the concept and basic characteristics of phonon crystal are introduced, then the research status of phonon crystal at home and abroad is discussed, and several important characteristics of phonon crystal are described. In chapter 2, the wave equation of elastic wave in ideal elastic medium is introduced, and the S-wave and P-wave are separated by using divergence and curl operators. This paper introduces three kinds of common arrangement structure of two-dimensional phonon crystal, various calculation methods of band gap of phonon crystal and their advantages and disadvantages. The finite element method is emphatically introduced from the basic principle of elastic mechanics. In chapter 3, the Schoch effect of two-dimensional three-component phonon crystals is studied. In this chapter, a two-dimensional three-component phonon crystal surface-water structure is designed. The reflection of the self-collimated acoustic beam at the interface between the phonon crystal and the surface layer is simulated by finite element method, and the Schoch effect on the surface of the phonon crystal is observed. The relation between the Schoch displacement and the structure is obtained. At the same time, by using the energy band structure of the model supercell, the causes of this phenomenon are analyzed. It is found that the interference between waveguide mode and bulk mode leads to the non-mirror reflection of the reflected beam. That is to say, the generation of Schoch effect is the result of the coupling of wave-like mode and bulk mode. In addition, by changing the radius of the surface cladding, the dependence of the Schoch displacement on the cladding radius is obtained. Finally, by increasing the number of surface layers and adjusting the cladding radius of two layers of the same nuclear cylinder, the Schoch displacement is enhanced and the Schoch effect is adjusted. In chapter 4, the negative Schoch effect of acoustic wave reflected on supersurface is studied. By designing the material structure in water, the negative phase gradient supersurface is realized, and the negative Schoch effect of acoustic reflection on the supersurface is studied. The results show that the negative Schoch effect of acoustic waves can be observed obviously on the designed supersurface. Furthermore, the influence of the thickness of the surface on the Schoch displacement is studied. The fifth chapter describes the main conclusions of this paper.
【学位授予单位】：广东工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O735
本文编号：2279993
[Abstract]:With the development of more than 20 years, a kind of composite acoustic material or structure with elastic band gap and periodic structure, namely phonon crystal, has attracted more and more attention from scholars at home and abroad. This is mainly due to the rich physical connotations of phononic crystals and their wide potential applications. Its basic characteristics are as follows: one is the existence of phonon band gap, which is the most remarkable physical property, that is, the elastic wave / acoustic wave propagation corresponding to the frequency in phonon band gap will be restrained, and the propagation of elastic wave / acoustic wave in phonon crystal will be exponentially attenuated rather than propagated. The elastic wave / acoustic wave corresponding to the frequency in the passband range can propagate without loss. Secondly, it has the characteristic of defective state, when there is a point defect, line defect or plane defect in the phonon crystal, The elastic wave / acoustic wave in the band gap frequency range will be propagated locally at the point defect or along the line defect or the plane defect. These characteristics enable phononic crystals to be designed into a variety of novel acoustic devices, which have a broad application prospect in the fields of mechanical vibration, integrated acoustics and acoustic communication. As a new type of artificial periodic functional materials, phononic crystals have been observed and proved to have many unique physical phenomena, such as acoustic focusing, autocollimation, negative refraction and Schoch effect. In this paper, the Schoch effect of phonon crystals is studied, and the reflection of self-collimating sound waves on the surface of two-dimensional three-component phonon crystals and on acoustic supersurfaces (hereinafter referred to as supersurface) is studied by finite element method. The forward Schoch effect and the negative Schoch effect on the supersurface of the phonon crystal are studied. The contents of this thesis are as follows: in the first chapter, the concept and basic characteristics of phonon crystal are introduced, then the research status of phonon crystal at home and abroad is discussed, and several important characteristics of phonon crystal are described. In chapter 2, the wave equation of elastic wave in ideal elastic medium is introduced, and the S-wave and P-wave are separated by using divergence and curl operators. This paper introduces three kinds of common arrangement structure of two-dimensional phonon crystal, various calculation methods of band gap of phonon crystal and their advantages and disadvantages. The finite element method is emphatically introduced from the basic principle of elastic mechanics. In chapter 3, the Schoch effect of two-dimensional three-component phonon crystals is studied. In this chapter, a two-dimensional three-component phonon crystal surface-water structure is designed. The reflection of the self-collimated acoustic beam at the interface between the phonon crystal and the surface layer is simulated by finite element method, and the Schoch effect on the surface of the phonon crystal is observed. The relation between the Schoch displacement and the structure is obtained. At the same time, by using the energy band structure of the model supercell, the causes of this phenomenon are analyzed. It is found that the interference between waveguide mode and bulk mode leads to the non-mirror reflection of the reflected beam. That is to say, the generation of Schoch effect is the result of the coupling of wave-like mode and bulk mode. In addition, by changing the radius of the surface cladding, the dependence of the Schoch displacement on the cladding radius is obtained. Finally, by increasing the number of surface layers and adjusting the cladding radius of two layers of the same nuclear cylinder, the Schoch displacement is enhanced and the Schoch effect is adjusted. In chapter 4, the negative Schoch effect of acoustic wave reflected on supersurface is studied. By designing the material structure in water, the negative phase gradient supersurface is realized, and the negative Schoch effect of acoustic reflection on the supersurface is studied. The results show that the negative Schoch effect of acoustic waves can be observed obviously on the designed supersurface. Furthermore, the influence of the thickness of the surface on the Schoch displacement is studied. The fifth chapter describes the main conclusions of this paper.
【学位授予单位】：广东工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O735
【参考文献】
相关期刊论文 前1条
1 诸国桢,刘亮,傅德永;液-固界面上非镜面反射的波束位移的实验研究[J];中国科学(A辑);2000年07期
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