基于声人工结构的声波调控研究
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摘要
声波和弹性波在声子晶体和声超常材料中的传播特性近年来引起了人们广泛的关注。声子晶体和声超常材料都是由人工结构构成的复合材料。声子晶体是指由两种或者两者以上的弹性材料按周期排列所组成的人工复合结构,其晶格结构的尺寸往往和波长可比拟。由于这类材料中存在声带隙,其中的声波／弹性波会表现出一些特殊的性质,从而使得声子晶体有望被用于声滤波器,声波导的制作和应用。声超常材料中人工结构的尺度一般远小于声波长,因而可以用等效参数来描述此类结构的声学性质。通过引入特殊的微结构单元可以实现一些天然材料无法实现的结构参数,比如密度各向异性、负质量密度、负弹性模量等,并产生许多新颖的声学现象,如声学隐身、声超透镜成像等。目前声超常材料的概念已不仅局限于具有单/双负参数的复合材料的范畴,而且涵盖了各种可以实现新颖声学现象的声学结构。因此声子晶体也可以被认为是超常材料的一个分支。
综上所述,对声子晶体和声超常材料中声传播特性的研究具有基础性的学术价值,对实际应用也具有一定的指导意义。本文对声子晶体与声超常材料中声传播行为进行了系统而深入的研究。主要包括以下内容：
第一章为绪论,回顾了声子晶体和声超常材料的研究背景,介绍了该领域的研究内容和最新进展,并针对本文的研究内容做了深入介绍,包括兰姆波型声子晶体,表面波型声子晶体,声单向传输,声梯度透镜。
第二章介绍了声人工结构的相关理论和计算方法。首先从固体物理理论出发,介绍了晶体结构的基础知识。然后给出了声人工结构中需要遵循的声波和弹性波方程。最后深入介绍了声人工结构的相关计算方法,包括平面波展开法、有限元方法和超常材料等效参数的反演方法。
第三章首先回顾了声单向结构研究领域的发展过程,然后介绍了当前研究中存在的两个重要难题：声单向结构的尺寸过大,以及正向出射波形混乱。为了解决这些难题,我们提出了两种新型的声单向结构。第一种是利用周期声栅和纯板构建的双层结构,在这个系统中,声单向效应是通过对平面波源的重建来实现的。通过该机理,可以实现小尺寸的声单向结构,通过合理地设计结构参数,出射束的方向可以被有效地控制。第二种是利用近零折射率材料设计的棱镜结构。利用这类材料对入射角度的高度选择性,声单向传输得以在该系统中实现。由于该类材料固有的隧穿效应,系统的正向出射波得以保持为平面波,其波形和入射波形几乎一致。
第四章首先介绍了声梯度透镜的发展历史。然后基于空间折叠的概念提出了一种新型的声学梯度透镜。通过在与透镜轴向相垂直的方向上使用不同大小的空间折叠材料,实现了声聚焦效应。由于空间折叠结构可以等效为高折射率的材料,该透镜的厚度可以被设计的很薄。同时我们发现在特定频域范围内,该结构的等效阻抗和背景介质的阻抗可以很好地匹配,进而使得该透镜的聚焦效果更加高效。
第五章首先回顾了表面波型声子晶体的研究背景,并介绍了前人工作中普遍存在的问题：均匀衬底的广泛采用将导致声表面波仅能在基底的体波声线之下被调控。针对该问题,我们提出了在有限厚度的声子晶体表面堆垛均匀/复合附加层的结构。研究结果表明,表面波会在体波声线之下和禁带之中出现,且这些频带中的表面波模式都可以通过添加均匀和复合层来有效操控,并得到表面波带隙。最后我们从表面波的衰减深度方面解释了该系统的能带结构随结构参数变化的物理机理。
最后在第六章,我们给出了本文的主要结论和对今后工作的展望。
In recent years, there is a growing interest in the studies of acoustic or elastic wave propagating in acoustic/phononic crystals and metamaterials, which are composite materials consisting of artificial structures. Acoustic/phononic crystals are composite materials, which are formed by periodical heterogeneous materials, and the geometrical parameters of the structure are comparable with the acoustic wavelength. Because of the existence of frequency band gaps, the acoustic or elastic waves in this kind of structure show some special properties such that the acoustic/phononic crystals are expected to be utilized as sound filter and waveguide materials, etc. The geometrical parameters of the units in metamaterials are much less than the acoustic wavelength. Through introducing different kinds of units, the acoustic metamaterials can be effectively regarded as effective medium with some unavailable parameter in nature, such as anisotropic mass density, negative mass density, negative modulus, etc. Some fascinating phenomena, such as acoustic cloaking, acoustic super lens, etc., can be realized through these parameters Actually, the structure, which can be utilized to realize some novel acoustic phenomenon, can also be regarded as metamaterials, such as unidirectional acoustic transmission, etc. In this point of view, the acoustic/phononic crystals can also be considered to be some special acoustic metamaterials.
As mentioned above, the investigations of acoustic properties of acoustic/phononic crystals and metamaterials are of fundamental scientific significance, which has great application value in practice. This dissertation gives systematic studies on acoustic wave propagation in these artificial structures. The dissertation is divided into following sections:
In Chapter I, the previous theoretical and experimental works on acoustic/phononic crystals and metamaterials are reviewed that serve for the background of the research and the progress of the investigations on these topics is introduced. The main contents of the present study are briefly described, such as lamb wave, surface acoustic wave in phononic crystals, unidirectional acoustic transmission and acoustic gradient-index lens.
In Chapter II, we reviewed the related theories on the crystals in solid states physics, and the acoustic/elastic waves equations. More attention is paid to the discussion of numerical calculations and simulations of artificial structures, such as the plane wave expansion method, finite element method and the retrieving of effective parameters of metamaterials with complex structure.
In Chapter III, we reviewed the background of unidirectional acoustic transmission and present some problems in the previous works, such as the large size stemming from the employment of acoustic crystals and the disorder of the transmitting wavefront. In order to overcome this problem, we present two systems. One is double-layered structure consisting of periodic grating and uniform plate. The one-way transmission can be realized based on the reconstruction of plane wave source. It is found that the size of the one-way device can be modulated to the wavelength scale and the angles of transmitting beams can be tuned effectively by appropriate selection the geometrical parameters. The other is a prism with near zero refractive index. Unidirectional acoustic transmission can be achieved due to the highly angular selectively of near zero index materials. The transmitted wave in this system is still plane wave and the wavefront of the transmitting wave are almost consistent with the incident plane wave.
In Chapter IV, we firstly reviewed the background of the gradient-index lens. By appropriate selection of the size of the coiling structure along the direction perpendicular to the lens axis, the gradient-index lens is constructed to realize the acoustic focusing effect. Due to the high refractive index providing by the coiling structure, the lens can be designed with thinner thickness. Moreover, the more effective focusing effect can be observed due to the lower impedance mismatch.
In Chapter V, we reviewed the background of the surface acoustic waves (SAWs) in phononic crystals, and find that due to the existence of uniform substrate, the SAWs modes can only be modulated below the sound cone of the substrate. To overcome the problem, we present a system consisting of a finite thickness phononic crystal plate stubbed with uniform/composite layer. Numerical results show that SAWs modes can be obtained below the sound cone and in the band gaps of the bulk waves. By introducing the uniform/composite layer, the SAWs modes both below the sound cone and in the band gaps can be tuned effectively. The attenuation depth of SAWs modes is introduced to interpret the relationship between the variation of the band structures and the geometrical parameters
Finally, the main conclusions of the present study and the prospect for the future work are drawn in Chapter VI.
综上所述,对声子晶体和声超常材料中声传播特性的研究具有基础性的学术价值,对实际应用也具有一定的指导意义。本文对声子晶体与声超常材料中声传播行为进行了系统而深入的研究。主要包括以下内容：
第一章为绪论,回顾了声子晶体和声超常材料的研究背景,介绍了该领域的研究内容和最新进展,并针对本文的研究内容做了深入介绍,包括兰姆波型声子晶体,表面波型声子晶体,声单向传输,声梯度透镜。
第二章介绍了声人工结构的相关理论和计算方法。首先从固体物理理论出发,介绍了晶体结构的基础知识。然后给出了声人工结构中需要遵循的声波和弹性波方程。最后深入介绍了声人工结构的相关计算方法,包括平面波展开法、有限元方法和超常材料等效参数的反演方法。
第三章首先回顾了声单向结构研究领域的发展过程,然后介绍了当前研究中存在的两个重要难题：声单向结构的尺寸过大,以及正向出射波形混乱。为了解决这些难题,我们提出了两种新型的声单向结构。第一种是利用周期声栅和纯板构建的双层结构,在这个系统中,声单向效应是通过对平面波源的重建来实现的。通过该机理,可以实现小尺寸的声单向结构,通过合理地设计结构参数,出射束的方向可以被有效地控制。第二种是利用近零折射率材料设计的棱镜结构。利用这类材料对入射角度的高度选择性,声单向传输得以在该系统中实现。由于该类材料固有的隧穿效应,系统的正向出射波得以保持为平面波,其波形和入射波形几乎一致。
第四章首先介绍了声梯度透镜的发展历史。然后基于空间折叠的概念提出了一种新型的声学梯度透镜。通过在与透镜轴向相垂直的方向上使用不同大小的空间折叠材料,实现了声聚焦效应。由于空间折叠结构可以等效为高折射率的材料,该透镜的厚度可以被设计的很薄。同时我们发现在特定频域范围内,该结构的等效阻抗和背景介质的阻抗可以很好地匹配,进而使得该透镜的聚焦效果更加高效。
第五章首先回顾了表面波型声子晶体的研究背景,并介绍了前人工作中普遍存在的问题：均匀衬底的广泛采用将导致声表面波仅能在基底的体波声线之下被调控。针对该问题,我们提出了在有限厚度的声子晶体表面堆垛均匀/复合附加层的结构。研究结果表明,表面波会在体波声线之下和禁带之中出现,且这些频带中的表面波模式都可以通过添加均匀和复合层来有效操控,并得到表面波带隙。最后我们从表面波的衰减深度方面解释了该系统的能带结构随结构参数变化的物理机理。
最后在第六章,我们给出了本文的主要结论和对今后工作的展望。
In recent years, there is a growing interest in the studies of acoustic or elastic wave propagating in acoustic/phononic crystals and metamaterials, which are composite materials consisting of artificial structures. Acoustic/phononic crystals are composite materials, which are formed by periodical heterogeneous materials, and the geometrical parameters of the structure are comparable with the acoustic wavelength. Because of the existence of frequency band gaps, the acoustic or elastic waves in this kind of structure show some special properties such that the acoustic/phononic crystals are expected to be utilized as sound filter and waveguide materials, etc. The geometrical parameters of the units in metamaterials are much less than the acoustic wavelength. Through introducing different kinds of units, the acoustic metamaterials can be effectively regarded as effective medium with some unavailable parameter in nature, such as anisotropic mass density, negative mass density, negative modulus, etc. Some fascinating phenomena, such as acoustic cloaking, acoustic super lens, etc., can be realized through these parameters Actually, the structure, which can be utilized to realize some novel acoustic phenomenon, can also be regarded as metamaterials, such as unidirectional acoustic transmission, etc. In this point of view, the acoustic/phononic crystals can also be considered to be some special acoustic metamaterials.
As mentioned above, the investigations of acoustic properties of acoustic/phononic crystals and metamaterials are of fundamental scientific significance, which has great application value in practice. This dissertation gives systematic studies on acoustic wave propagation in these artificial structures. The dissertation is divided into following sections:
In Chapter I, the previous theoretical and experimental works on acoustic/phononic crystals and metamaterials are reviewed that serve for the background of the research and the progress of the investigations on these topics is introduced. The main contents of the present study are briefly described, such as lamb wave, surface acoustic wave in phononic crystals, unidirectional acoustic transmission and acoustic gradient-index lens.
In Chapter II, we reviewed the related theories on the crystals in solid states physics, and the acoustic/elastic waves equations. More attention is paid to the discussion of numerical calculations and simulations of artificial structures, such as the plane wave expansion method, finite element method and the retrieving of effective parameters of metamaterials with complex structure.
In Chapter III, we reviewed the background of unidirectional acoustic transmission and present some problems in the previous works, such as the large size stemming from the employment of acoustic crystals and the disorder of the transmitting wavefront. In order to overcome this problem, we present two systems. One is double-layered structure consisting of periodic grating and uniform plate. The one-way transmission can be realized based on the reconstruction of plane wave source. It is found that the size of the one-way device can be modulated to the wavelength scale and the angles of transmitting beams can be tuned effectively by appropriate selection the geometrical parameters. The other is a prism with near zero refractive index. Unidirectional acoustic transmission can be achieved due to the highly angular selectively of near zero index materials. The transmitted wave in this system is still plane wave and the wavefront of the transmitting wave are almost consistent with the incident plane wave.
In Chapter IV, we firstly reviewed the background of the gradient-index lens. By appropriate selection of the size of the coiling structure along the direction perpendicular to the lens axis, the gradient-index lens is constructed to realize the acoustic focusing effect. Due to the high refractive index providing by the coiling structure, the lens can be designed with thinner thickness. Moreover, the more effective focusing effect can be observed due to the lower impedance mismatch.
In Chapter V, we reviewed the background of the surface acoustic waves (SAWs) in phononic crystals, and find that due to the existence of uniform substrate, the SAWs modes can only be modulated below the sound cone of the substrate. To overcome the problem, we present a system consisting of a finite thickness phononic crystal plate stubbed with uniform/composite layer. Numerical results show that SAWs modes can be obtained below the sound cone and in the band gaps of the bulk waves. By introducing the uniform/composite layer, the SAWs modes both below the sound cone and in the band gaps can be tuned effectively. The attenuation depth of SAWs modes is introduced to interpret the relationship between the variation of the band structures and the geometrical parameters
Finally, the main conclusions of the present study and the prospect for the future work are drawn in Chapter VI.
引文
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