声子晶体缺陷态的温度控制及兰姆波禁带的低频调节

发布时间：2018-08-08 13:06

【摘要】：由于拥有丰富的物理内涵以及广阔的潜在应用前景,声子晶体的研究工作在近二十年来越来越多地引起了国内外学者的广泛关注。声子晶体是指具有声波/弹性波带隙特性的周期性复合材料或者结构。它的基本特征主要有两个：一是具有缺陷态特性,当周期性复合结构中存在缺陷时,缺陷态频率范围内的声波/弹性波将被局域在点缺陷处或沿缺陷传播；二是具有声子带隙,这使得声波/弹性波在带隙频率范围内会被抑制,而其它频率范围(通带范围)内的声波/弹性波在色散关系的作用下将可以无损耗地传播。声子晶体是一种新型人工周期性结构功能材料,通过人为设计可以调节声波的频率,从而控制声波的传播。因此,在现实生活中存在许多潜在的应用,例如：用于设计声滤波器或声波导,还可用于设计新型的声子二极管等。因此,声子晶体的理论研究和完善在振动与噪声控制领域具有重要价值。本论文首先介绍了声子晶体的相关概念,阐述了声子晶体的研究意义,并讨论了声子晶体的国内外研究现状和声子晶体的一些相关特性。其次,介绍了各种声子晶体带隙计算方法及各自特点和二维声子晶体的常见排列方式,从布洛赫定理和弹性力学基本原理出发着重地介绍了有限元法,并举例介绍了有限元法数值模拟的基本步骤。然后,详细地介绍了关于温度对二维声子晶体缺陷态影响的研究。我们提出了两个新颖的模型：第一个模型是通过改变中心柱子的温度得到,第二个模型是通过改变中心柱子温度同时将中心方柱旋转45度角得到。我们得到了一些非常重要的结论：对于模型一,当声子晶体温度大于居里温度、且缺陷柱体温度小于居里温度时,缺陷态将出现在宽带隙中,并且中心缺陷柱体温度越低,缺陷模频率越低；对于模型二,只要声子晶体温度大于缺陷温度,缺陷模就将出现在宽带隙中,并且缺陷模的条数和频率位置都会随着中心缺陷柱体温度的变化而受到影响。但是,当声子晶体的温度设置低于居里温度时,即使中心缺陷柱体的旋转已经打破了结构原有的几何对称性,宽带隙中依然不会出现任何缺陷模。我们还考虑并计算了中心缺陷柱体周围有热流影响的情况,计算结果表明中心缺陷柱体周围的热流产生的温度梯度对结果的影响非常小,几乎可以忽略。最后,详细叙述了兰姆波在由重圆柱体以正方晶格放置在复合板两侧而构成的二维声子晶体板中的传播特性的数值研究。我们的计算结果表明：两种结构得到的相对带宽在深度次波长范围内,明显的比二维二组元局域共振型声子晶体板高两个数量级,比二维三组元复合板杆结构和三组元简单板复合杆结构都要高出一个数量级。基于有效的有限元法,我们分析得到相对带宽的增宽是由板模和“双振子弹簧”模之间的耦合导致的,它有效地增强了局域共振机制。我们计算得到的弹性波位移场很好地阐明低频带隙打开和平带出现的物理机制。我们还发现带隙和平带都非常明显地依赖于重杆和复合板的几何参数。本文的创新之处在于提出了新颖的点缺陷模型和局域共振声子晶体板模型,在研究内容方面,在不改变晶格排列方式,散射体形状、填充率、组元材料等因素下,可以很容易地获得缺陷态,并发现了一些非常有意义的规律；在不改变声子晶体板结构材料组成的前提下,通过构造新的板杆模型而得到了具有更大相对带宽的带隙。
[Abstract]:Because of its rich physical connotation and broad potential application prospects, the research work of phononic crystals has attracted more and more attention of scholars both at home and abroad in the past twenty years. Phononic crystals are periodic composite materials or structures with sonic / elastic band gap characteristics. The basic characteristics of phononic crystals are mainly two: one is When there is a defect state characteristic, when there is a defect in the periodic composite structure, the acoustic / elastic wave within the frequency range of the defect state will be localized at the point defect or along the defect; two is a phonon band gap, which makes the sound wave / elastic wave suppressed in the band gap frequency range, and the sound / elasticity in the other frequency range (through the band range). The wave can be transmitted without loss under the effect of the dispersion relation. The phononic crystal is a new type of artificial periodic structural functional material, which can regulate the frequency of sound waves by human design and control the propagation of sound waves. Therefore, there are many potential applications in real life, for example, for the design of acoustic filters or acoustic waveguides, it can also be used in the design of sound waves. The theoretical research and improvement of phononic crystals are of great value in the field of vibration and noise control. This paper first introduces the related concepts of phononic crystals, expounds the research significance of phononic crystals, and discusses the research status of phononic crystals at home and abroad and some correlation of phononic crystals. Secondly, various methods for calculating the band gap of phononic crystals, their characteristics and the common arrangement of two-dimensional phononic crystals are introduced. The finite element method is introduced emphatically from the Bloch theorem and the basic principles of elastic mechanics, and the basic steps of the numerical simulation of the finite element method are introduced with examples. Then, the temperature pair is introduced in detail. We have proposed two novel models: the first model is obtained by changing the temperature of the central column, and the second model is obtained by changing the central column temperature and rotating the central square column at the 45 degree angle. We get some very important conclusions: for the model one, when the sound is sound When the temperature of the crystal is greater than the Curie temperature, and the defect column temperature is less than Curie temperature, the defect state will appear in the broadband gap, and the lower the temperature of the center defect column, the lower the frequency of the defect mode. For model two, the defect mode will appear in the wide band gap and the number and frequency of the defect mode as long as the phonon crystal temperature is larger than the defect temperature. However, when the temperature of the phononic crystal is lower than the Curie temperature, even if the rotation of the central defect column has broken the original geometric symmetry of the structure, there will still be no vacancy in the wide band gap. We also consider and calculate the central defect column. The results show that the temperature gradient produced by the heat flow around the center of the center is very small and can almost be ignored. Finally, the numerical value of the propagation characteristics of Lamb wave in a two-dimensional phononic plate, which is placed on both sides of the composite plate with a square lattice with a square lattice, is described in detail. Our calculation results show that the relative bandwidth of the two structures is two orders of magnitude higher than that of the two dimensional two component local resonant phononic crystal plate, which is two orders of magnitude higher than that of the two-dimensional three component composite plate rod structure and the three component simple plate composite rod structure. We find that the widening of the relative bandwidth is caused by the coupling between the plate mode and the "double vibrator spring" mode. It effectively enhances the local resonance mechanism. We calculate the elastic wave displacement field well to illustrate the physical mechanism of the low frequency band gap open zone. We also find that the band gap peace belt is very obvious. The innovation of this paper is to propose a novel point defect model and a local resonant phononic crystal plate model. In the field of research, the defect state can be easily obtained without changing the lattice arrangement, the shape of the scatterer, the filling rate, the component material and so on. It is often meaningful. On the premise of not changing the composition of the phononic crystal plate structure, the band gap with larger relative bandwidth is obtained by constructing a new plate model.
【学位授予单位】：广东工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB33

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