二维正方晶格多点缺陷声子晶体实验研究

基于超声浸水透射技术, 实验研究了有限尺寸二维正方晶格钢/水声子晶体多点缺陷模态性质. 利用COMSOL Multiphysics软件建立该声子晶体有限元计算方法, 求解了9×9超胞多点缺陷声子晶体能带结构, 把缺陷局域模态频率与数值仿真和实验结果进行对比, 结果表明: 实验数据和理论值能够很好符合. 进一步分析发现, 点缺陷数量影响声波局域效应、本征模态和传播特性, 为设计有限尺寸声波器件提供理论依据. 关键词： 声子晶体 多点缺陷 实验研究 有限元     

二维蜂窝结构声子晶体的负折射成像研究*

为了得到分辨率更好的平板透镜,对此进行了研究。利用有限元的方法研究了由水/水银材料组合的二维蜂窝结构声子晶体平板透镜的负折射成像特性,通过数值仿真计算了声子晶体的能带结构、等频色散曲线,模拟了点源成像,并且利用高斯波束验证了声子晶体平板透镜的负折射现象,得到了有效折射率neff =-1的成像。对比相同材料的正方晶格和三角晶格而言,该模型的成像效果更佳。为了改善成像分辨率,还在原来的模型上进行了改进,得到了分辨率约为0.37λ的亚波长像。     

三组元声子晶体中的缺陷态

运用基于平面波的超元胞方法，研究作为缺陷引入的第三组元材料(四氯化碳、水)对二维二组元声子晶体(水/水银，四氯化碳/水银)带结构的影响.结果表明，二组元声子晶体在引入第三组元点缺陷/线缺陷后，在原来的带结构中会出现缺陷态/带，原带隙的位置、宽度变化不大；缺陷态/带频率主要受第三组元材料物性参数的影响；这些缺陷态都是局域化的.因此，在具有宽带隙的二组元体系中引入适当的第三组元点缺陷/线缺陷，让缺陷态/带频率落在二组元体系的带隙中，就可以形成特殊的滤声态/波导态.声子晶体的这一特性对于声波/弹性波的传播和新的声学应用具有重要意义. 关键词： 声子晶体 三组元 点缺陷 线缺陷     

二维正方晶格各向异性光子晶体缺陷模

为了得到对TM和TE模具有相同缺陷模的共振微腔,通过在完整各向异性碲介质柱二维正方光子晶体中,引入各向同性的介质圆柱作为点缺陷,利用超胞平面波展开法计算该光子晶体的缺陷模,系统计算了在同时改变点缺陷介质柱介电常数和半径两种情况下的两种偏振缺陷模的变化规律。结果表明,在完全禁带中,缺陷介质柱介电常数从5.44变化到38.44、半径与晶格常数的比从0.05变化到0.50的整个区域,均会出现对TM和TE模具有相同缺陷模,且随着介电常数的减小,缺陷模随着缺陷半径的变化趋于缓慢,归一化共振频率在0.241 8~0.243 2之间可调,在引入ε_e＜ε_o的各向异性介质柱缺陷时,亦可得到对TM和TE模具有相同缺陷模,且共振频率的可调范围增大,该研究为光子晶体器件的设计提供了理论依据。     

二维声子晶体同质位错结缺陷态特性

利用平面波展开法结合超原胞的方法研究了二维声子晶体同质位错结的缺陷态.分别研究了横向位错和纵向位错两种情况，研究结果表明：横向位错效应与线缺陷相似，它可以使处于禁带频率范围内的声波沿位错通道进行传播，形成声波导；纵向位错效应则类似于点缺陷，位错线两边三个最接近的散射子形成腔，因而能够产生局域模.另外，横向位错距离和纵向位错距离的大小将影响缺陷带的位置和数量，因此，可以通过调节横向位错距离或纵向位错距离来人为的控制同质位错结中的缺陷带. 关键词： 声子晶体 同质位错结 缺陷态     

研究一维掺杂声子晶体缺陷模的解析方法

为了对一维掺杂声子晶体的缺陷模进行解析研究,利用多波束干涉原理和布洛赫定理,推导出一维掺杂声子晶体的缺陷模频率的解析公式.利用它对一维掺杂声子晶体的缺陷模进行了解析研究,得到了缺陷模频率的变化规律.该方法克服了其他方法不能对缺陷模进行解析研究的不足,是一种研究一维掺杂声子晶体的缺陷模的精确、有效方法. 关键词： 声子晶体 声波 缺陷模 解析方法     

局域共振型声子晶体中的缺陷态研究

本文以二维固体局域共振声子晶体为例,对次波长区域缺陷态的实现机理及其特点进行了探讨.众所周知,工作于次波长区域的声子晶体可以用有效媒质理论来描述,其色散关系对其构成单元的排列结构并不敏感,因而使得共振型声子晶体的带结构难以被其构成单元的局域空间无序所打破.本文发现共振型声子晶体在其带隙附近的色散关系可由共振单元间的长程相互作用来理解.基于这一理解,对目前文献中提出的两种实现局域态的方法进行了研究,结果表明缺陷态的引入正是通过打破这种长程相互作用来实现的.另外,在此理解的基础上,通过引入非各向同性"缺陷"共振单元,实现了纵波与横波导波模式的分离.     

二维点缺陷声子晶体中缺陷填充率对能带的影响

用超元胞的平面波展开法,计算了存在点缺陷的二维水/水银声子晶体的能带结构和压强分布。通过改变5×5超元胞中心圆柱体的半径而引入缺陷,发现缺陷填充率（F_d）小于或大于正常柱体填充率（F₀）一定数值时（如当F₀=0.35,F_d<0.10或F_d>0.50）,都将出现缺陷态,且F_d对缺陷态的频率有重要影响。还比较了当F_d=0.03和F_d=0.90两种情况下缺陷态的压强分布,计算结果表明压强分布均具有局域性,F_d的大小对单模缺陷态的局域程度有影响,而对二重简并模无显著影响。     

新型二维压电声子晶体板带隙可调性研究

设计了一种由涂有硬质材料涂层的柱状压电散射体周期性连接在四个环氧树脂薄板上构成的具有大带宽的新型二维压电声子晶体板,并利用有限元方法计算了该声子晶体板的能带结构、传输损失谱和位移矢量场.研究表明：与二组元材料构成的传统声子晶体板相比,新设计的声子晶体板的第一完全带隙频率更低,并且带宽扩大了5倍;通过在压电体表面上施加不同的电边界条件,可以实现多条完全带隙的主动调控;压电效应对能带结构有很大的影响,并且有利于完全带隙的扩大与形成.基于带隙的可调谐性,分析了可切换路径的压电声子晶体板波导,结果表明可以通过改变电边界条件来限制弹性波能量流.     

N重旋转对称的二维准晶电子态与声子态的简并性

通过相似变化矩阵,对具有N重旋转对称的二维准晶系统的哈密顿量和动力学矩阵进行对角约化。当N为偶数时,电子态与声子态中有(N-2)/(N+2)是双重简并,而4/(N+2)是非简并;当N为奇数时,电子态与声子态中有(N-1)/(N+1)是双重简并,而2/(N+1)是非简并。利用群论方法得到相同的结论。 关键词：     

Low frequency phononic band structures in two-dimensional arc-shaped phononic crystals

The low frequency phononic band structures of two-dimensional arc-shaped phononic crystals (APCs) were studied by the transfer matrix method in cylindrical coordinates. The results showed the first phononic band gaps (PBGs) of APCs from zero Hz with low modes. Locally resonant (LR) gaps were obtained with higher-order rotation symmetry, due to LR frequencies corresponding to the speeds of acoustic waves in the materials. These properties can be efficiently used in a structure for low frequencies that are forbidden, or in a device that permits a narrow window of frequencies.     

Effective velocity of 2D phononic crystals with rectangular lattice

The effective velocity of elastic waves for two-dimensional (2D) phononic crystals with rectangular lattice in the long-wavelength limit is studied by numerical simulations. It is demonstrated that, for all three propagating modes, not only the modes polarized in-plane (L wave and SV wave), but also the mode polarized out-plane (SH wave), the effective velocities are distinctly anisotropic and the slowness curves exhibit twofold symmetry. The anisotropy increases as the filling fraction increases or as the width to length ratio of the lattice decreases, and high anisotropy can be obtained in phononic crystals with large contrast between material parameters, which is much higher in rectangular lattice than in square lattice with the same material parameters. Owing to these dependences, the effective velocity can be controlled in engineering.     

含内部连接体的二维声子晶体弹性波宽频带隙特性

声子晶体的弹性波带隙特性使得它在开发用于减振降噪的新型功能材料方面具有广阔应用前景。为获得宽频大带隙,改进了一种含连接体的正方晶格声子晶体结构.利用有限元法计算并分析了不同结构配置下其能带特性和振动模态。数值结果表明,单胞中同时引入新的质量块以及连接体将对原连接体的自由振动模态产生抑制作用,可在原分离的两带隙频率范围内获得相对带宽超过100%的单一宽频带隙。此外,通过调整几何尺寸、连接体数目、结构对称性等参数可进一步调控结构带隙特性。     

声波在二维固/流声子晶体中的禁带特性研究

采用时域有限差分法(FDTD),分析了声波在二维四方点阵铝/空气组合声子晶体中的禁带特性,并利用实验测试验证了理论分析的正确性.在此基础上研究了两种不同声阻抗率比固(实心圆柱和空心圆管)/流系统声子晶体的禁带特性.对于实心圆柱体,分析了有限尺寸结构声子晶体在传播方向上的层数对声波传播特性的影响,得到了这两种系统在不同填充率下取得最大声波禁带宽度所需的最少层数.同时指出,在低声阻抗率比条件下,对于空心圆管填充物,通过选取适当的半径比,可以获得比实心柱体更宽的方向带隙.     

Enhanced acoustic localization in the two-dimensional phononic crystals with slit tube defect

In this paper, the acoustic localization characteristics of the two-dimensional phononic crystals with slit tube defect are investigated theoretically and experimentally. In contrast to the typical formation pattern of defect states, the proposed defect states are created by replacing a slotted tube in the center of perfect phononic crystal. Compared to perfect phononic crystal, the proposed structure can effectively localize waves of specific frequencies in the point defect and improve the acoustic pressure amplification. Then the effects of the geometric parameters of the slotted tube on the acoustic localization characteristics are studied. Numerical results show that the resonant frequency and acoustic pressure amplification amplitude could be effectively modulated by the geometric parameters of the slotted tube. Experimental results are in good agreement with the simulation results.     

Effects of Poisson's ratio on the band gaps and defect states in two-dimensional vacuum/solid porous phononic crystals

The effects of the Poisson’s ratio of the solid host on the band gaps and point defect states of the mixed elastic wave modes in two-dimensional vacuum/solid porous PNCs are studied by numerical simulations. Four typical systems are considered. The four systems are, respectively, (I) the system with a square lattice and circular pores, (II) the system with a hexagonal lattice and circular pores, (III) the system with a square lattice and square pores and (IV) the system with a hexagonal lattice and regular-hexagonal pores. In the latter two systems, with respect to the outer boundaries of the Wigner-Seitz unit cell, the pores rotate 45° and 30°, respectively. Some observable effects of the Poisson’s ratio are found in the numerical results. Especially, the variations of the band gap boundaries with the Poisson’s ratio exhibit relatively consistent behaviors. With the increase of the Poisson’s ratio, the normalized frequency of a band gap boundary generally increases, except that in system (III) the normalized frequency of the upper boundary of the first band gap remains almost unchanged. Detailed interpretations on this phenomenon are given.     

Effect of defect configuration on the localization of phonons in two-dimensional phononic crystals

Effects of defect location on the defect frequency and the localization of phonons are investigated in two novel kinds of model, created by moving the location of the native cylinder and inserting an ad-cylinder in the central cellular respectively. The results show that the defect frequency in Model 1 is only related to the distance, while in Model 2, is related not only to the distance, but also to the moving direction. From the pressure distribution, obvious localization phenomenon is found. The position and shape of the localized energy are varied with the position of the defect.     

Tuning the band-gap of phononic crystals with an initial stress

The mechanism for the shift of the band-gap in two kinds of finite phononic crystals (PCs) (steel/epoxy and aluminum/epoxy) with different initial stresses is studied experimentally and theoretically. The experimental results and theoretical analysis simultaneously indicate that the initial stress will efficiently tune the location and width of the band-gap. The current work provides a basis for tuning the band-gap of phononic crystals in engineering applications.