【作者】 钟会林；

【导师】 吴福根；

【作者基本信息】 广东工业大学 ， 材料物理与化学， 2005， 硕士

【摘要】 声子晶体的研究是在天然晶体和光子晶体研究的基础上提出的新课题,是对天然晶体概念的延伸和超越。声子晶体的特点之一就是具有弹性波带隙,在带隙频率范围内,弹性波(声波)是不允许通过的。基于这一原理,声子晶体具有广泛的应用前景,例如新型的隔声降噪材料、弹性波滤波器、波导等等。因此,声子晶体带隙结构的人工设计和优化对推动声子晶体的应用具有重要意义。 首先,本文介绍了声子晶体带结构计算的基本理论和方法。从弹性波波动方程出发,本文详细地介绍了计算声子晶体带结构的平面波展开方法。 其次,本文研究了二维声子晶体中对称性对声子晶体带隙的影响。分别讨论了晶格排列的对称性、填充体的对称性以及旋转效应对声子晶体带隙的影响,探讨了二维不同类型晶格排列和填充体类型的组合,在各种填充率和旋转角度情况下所具有的最大带隙宽度,并与光子晶体的相关结论进行了比较。 第三,本文将遗传算法引入到声子晶体的研究中。介绍了遗传算法的基本原理,探讨了将遗传算法应用到解决声子晶体带隙优化问题的一般方法。我们通过二维铅-环氧树脂声子晶体单元结构的优化的具体实例,显示了遗传算法对优化声子晶体带隙是可行的。 第四,研究了基于局域共振机制的声子晶体的带隙优化问题。共振单元由三种组元构成,通过数值计算,发现了这类局域共振结构的最大完全带隙所对应的参数规律。 最后,本文研究了周期性结构的缺陷态和缺陷模。运用超元胞方法,研究了三维声子晶体点缺陷的缺陷态。本文也研究了在二维正方形排列的周期性水底中,引入深度和半径点缺陷所引起的物理效应。通过数值计算,发现在水波中也能产生缺陷态和局域现象,从而进一步将能带理论、局域现象推广到水波系统中。更多还原

【Abstract】 The phononic crystals are the new research hotspots on the basis of traditional natural crystals and photonic crystals in the recent years. It extends and exceeds the concept of traditional natural crystals. A physical character of phononic crystals is the existence of phononic band gaps in which the sound and elastic waves are all forbidden. Base on this theory, the phononic crystals will have a broad foreground of engineering applications such as new sound insulation materials, elastic or acoustic filters, etc. Therefore, that the artificial design and optimization of the phononic band structure is meaningful for applications of phononic crystals.First, the basic theory and methods of phononic band structure are introduced in this paper. And the equations of plane-wave expansion (PWE) method are given in detail.Then, the influences of symmetry to phononic band gaps are investigated in two-dimensional systems. The lattice’s and unit cell’s symmetry and rotation effect are discussed in the paper, and the widest phononic band gaps are found for different symmetry compounding.Third, the popular genetic algorithm (GA) is introduced to optimization of phononic band gaps, and the combination of GA theory and the study of phononic crystals are discussed in the paper. Two examples reveal the GA’s advantage in the design of band structures, and GA method is effective to find out excellent topology of unit cell with a widest absolute band gaps.Firth, we study the band gaps optimization in locally resonant phononic crystal. It is a three-component composite. We get the parameters of this kind of structure with maximum phononic band gaps.Finally, we study the defect states and defect modes. The defect modes of three-dimensional phononic crystal are studied. The localized defect modes of water waves over two-dimensional periodic bottoms with a point defect are investigated by supercell calculations and plane-wave expansion method. Two kinds of defects are introduced, one is a radius defect created by changing radius of cylinder, and another更多还原