【作者】 黄小益；

【导师】 彭景翠；

【作者基本信息】 湖南大学 ， 材料物理与化学， 2006， 博士

【摘要】 近年来,电磁波在周期结构电介质材料即光子晶体的传播引起人们的极大关注,尤其令人感兴趣的是频率禁带的存在。对电磁波通过光子晶体频率带隙的研究可以类比推广到弹性波在声子晶体中的传播,尽管弹性波在周期性复合介质中的传播是一个经典的凝聚态和声学问题,但当前对该问题的研究主要集中在如何设计周期性复合介质的声子频率带隙。在声子频率带隙范围,声音和声子的传播被禁止,声子晶体的这种基本特征被广泛应用于声波滤波、为高精密仪器提供无振动环境,或者被设计为一种新的传感器。本文首先对声子晶体的基本概念、基本特征、基本结构及声子晶体带结构的计算方法进行了阐述。选择铝和聚合物构成的二维声子晶体,周期排列的圆柱体垂直于声子晶体表面嵌入基质材料中,我们从理论上研究了表面波和彻体波的声子频率带隙分布,计算了呈三角形排列的声子晶体表面波模和彻体波模随波矢变化的色散关系曲线。计算得到的禁带分布曲线与超声波试验结果符合得很好。本文对声子晶体带结构以及物理参数和结构参数对声子晶体带结构的影响进行了较深入的研究,研究发现,较高的声速比,有利于带隙的产生。对声子晶体中的弹性波传播,高密度的圆柱体嵌入低密度的基质材料,比较容易产生完全带隙;相反,对声子晶体中的声波传播,则低密介质嵌入高密基质中,容易产生完全带隙。另外,填充比和周期拓扑形式也是影响声子晶体带结构的重要因素,而且填充比只有在一定的范围内,声子晶体才有可能出现完全带隙。研究不同结构的声子频率带结构,找出决定带隙结构的各种因素,有着非常重要的意义。在理论研究上,可以让人们对声子带隙形成的物理过程有更深一步的理解,在应用上,可以指导人们根据不同的需要设计制作出具有不同带结构的声子晶体,使声子晶体器件的制作更简便、更具目的性。我们研究了一种新的几何结构的二维声子晶体带结构:类似于氮化硼结构。这种结构是两种不同半径的圆柱体位于规则的六角形的角顶,三角结构和六角结构是这种几何结构的两种特殊情况。填充体或基质取两种液体或两种固体,我们选择了水和水银以及碳(或钨)和环氧树脂。我们研究了BN带结构,尤其是完全频率带隙作为两种圆柱体半径比的函数的变化情况,讨论了这些带隙的出现与相关物理参数的关系。并把计算结果与正方形和三角排列结构进行了比较。选取无限长钢圆柱体按正方形排列插入空气基质中构成的二维周期性复合系统,采用超元胞计算方法和平面波展开法,我们研究了声子晶体带隙内出现的缺陷更多还原

【Abstract】 During the last few years, the propagation of electromagnetic waves in artificial periodic structures of dielectric materials, known as photonic crystals, has received a great deal of attention, of particular interest is the existence of forbidden frequency bands. This search for band gaps in photonic crystals and the mathematical analogy between electromagnetic waves and vibrations has spurred a renewed interest in the propagation of elastic waves in the so-called phononic crystals. The propagation of elastic waves in periodic or random composite materials is an old topic in condensed matter physics and/or acoustic. The present research activities focus on the design of band gap in the acoustic spectrum of composite media. Acoustic gap being frequency domains in which propagation of sound and phonons are forbidden, one can imagine for these phononic crystals numerous engineering applications such as frequency filters,vibrationless environments for high-precision mechanical systems or the design of new transducers.Spatial and frequency distributions of forbidden bands of both surface and bulk acoustic waves are studied theoretically for two-dimensional (2D) periodic elastic structures consisting of aluminum and polymer. The surface is perpendicular to the 2D periodic arrays of circular cylinders embedded in a background material. The dispersion relations of the surface and bulk modes with wave vectors parallel to the surface are calculated for triangular Lattice and the stop band distributions are plotted in a form relevant to the comparison with ultrasound imaging experiments.The band structure and its dependence on the physical parameters and structured parameters need further physical interpretations. The higher velocity ratio between the two components of the composite, the more favorable the condition for gaps. Similarly, the density contrast is very important. However, for elastic waves(EL),high-density scatters favor gaps,while for acoustic waves(AC), low-density inclusions in a high-density matrix is the preferable setup. The topology and volume fraction occupied are the important factors influenced the band structure of phononic crystal. The volume fraction occupied must be in a certain range for gaps to exist. It is very significant for us to work on phononic band structures, such work can result in further step on theoretic area and provides instruction to fabricate phononic devices.We present elastic band-structure results for a new geometry of two-dimensional更多还原