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.     

局域共振复合单元声子晶体结构的低频带隙特性研究

本文提出了一种新型局域共振复合单元声子晶体结构, 并结合有限元方法对结构的带隙机理及低频共振带隙特性进行了分析和研究. 共振带隙产生的频率位置由所对应的局域共振模态的固有频率决定, 并且带隙宽度与局域共振模态的品质因子及其与基体之间的耦合作用强度有关. 采用局域共振复合单元结构可以实现声子晶体的多重共振, 在低频范围能打开多条共振带隙, 但受到共振单元排列方式的的影响. 由于纵向和横向局域共振模态的简并, 复合单元结构能在200 Hz以下的低频范围打开超过60%宽度的共振带隙, 最低带隙频率低至18 Hz. 这为声子晶体结构获得低频、超低频带隙提供了一种有效的方法. 关键词： 局域共振 低频带隙 复合单元 声子晶体     

二维声子晶体带结构研究

声子晶体是近十年来提出的新课题，对声子晶体带结构的研究具有理论和应用价值。论文介绍了用平面波展开法计算二维正方点阵的固体／固体声子晶体带隙的方法，并应用于各向同性的铅柱体填充物以正方点阵排列于各向同性的环氧树脂基体中所形成的二维双组分复合体系。计算了柱体横截面是长方形时晶体的带隙，结果发现随着长方形截面的长宽比（l1／l2≥1时）的增加，带隙宽度逐渐减小，最后消失。     

Transverse wave band gaps and longitudinal wave band gaps in solid phononic crystals

Based on the properties of transverse (divergenceless) waves and longitudinal (irrotational) waves, we divided the transverse wave modes and longitudinal wave modes from the mixed eigen modes in solid phononic crystals. By investigating the transverse wave and longitudinal wave band structures at low frequency, we found that transverse bands and longitudinal bands exhibit different behaviors in solid systems including spherical scatterers. Phononic crystal with a large density ratio of solid spheres to the background can guarantee both the large longitudinal and large transverse band gap, but solid spheres with a small ratio of longitudinal wave velocity to transverse wave velocity can only help to enlarge the longitudinal band gap, and do not help to enlarge the transverse band gap.     

Large Lamb wave band gap in phononic crystals thin plates

We suggest that Lamb wave band gaps in one-dimensional phononic crystals can be substantially enlarged by using multiple heterostructures which consist of several pieces of phononic crystal with different ratios of the thickness to the lattice period. This is possible because each substructure shows a different band gap and the band structure of a Lamb wave is strongly affected by the ratio of the plate thickness to the lattice period. This effect has been demonstrated by using finite element simulations on two different one-dimensional systems. PACS 63.20.-e; 62.65.+k; 41.20.Jb; 43.20.+g     

The influence of the micro-topology on the phononic band gaps in 2D porous phononic crystals

The phononic band structures of two-dimensional metal porous phononic crystals consisting of different lattices (the lattice structures transformed from square to triangle), and pores of various shapes (circle, square, and triangle) and sizes are studied numerically by using Finite Difference Time Domain (FDTD) scheme. It is found that for x-y mode waves, the absolute phononic band gaps (PBGs) rely more on the pore shapes. For triangular pores, the PBG is opening in the whole process of the lattice transformation, and for circular ones, the PBG is closed after a certain lattice structure. No PBG forms in the crystals with square pores. The PBG can be varied by adjusting the size of the pores. But a critical porosity exists for the opening of the PBG.     

The influence of pore shapes on the band structures in phononic crystals with periodic distributed void pores

The influence of the pore shapes on the band structures in phononic crystals with periodic distributed void pores are investigated in this paper. By using finite difference time domain (FDTD) scheme, the dispersion properties of the in-plane x-y mode waves in the materials with triangular, circular or square pores are discussed respectively. The influence of the pore shapes and the porosity on the band gap structures is analyzed. The results show that for x-y mode waves, the stop bands are easily formed in the materials with triangular pores, but hard for square ones. Moreover, a critical porosity exists for the formation of the absolute band gaps. Along with the increase of the porosity, the width of the absolute band gap is increased, but the centre frequency is dropped.     

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.     

Two-dimensional locally resonant phononic crystals with binary structures

The lumped-mass method is applied to study the propagation of elastic waves in two-dimensional binary periodic systems, i.e., periodic soft rubber/epoxy and vacuum/epoxy composites, for which the conventional methods fail or converge very slowly. A comprehensive study is performed for the two-dimensional binary locally resonant phononic crystals, which are composed of periodic soft rubber cylinders immersed in epoxy host. Numerical simulations predict that subfrequency gaps also appear because of the high contrast of mass density and elastic constant of the soft rubber. The locally resonant mechanism in forming the subfrequency gaps is thoroughly analyzed by studying the two-dimensional model and its quasi-one-dimensional mechanical analog. The rule used to judge whether a resonant mode in the phononic crystals can result in a corresponding subfrequency gap or not is found.     

Using coupling slabs to tailor surface-acoustic-wave band structures in phononic crystals consisting of pillars attached to elastic substrates

The propagation of surface acoustic waves (SAWs) in two-dimensional phononic crystals (PnCs) with and without coupling-enhancement slabs was theoretically investigated using a three-dimensional finite element method. Different piezoelectric substrates, for example, lithium niobate (LiNbO₃), gallium nitride (GaN), and aluminium nitride (AlN), were taken into account. Compared to the PnCs without coupling-enhancement slabs, the coupling between each pillar and its nearest neighbor was largely enhanced in the presence of slabs. The bandwidth of the first directional band gap increased markedly compared with its initial value for the PnCs without a slab (within square symmetry). In addition, with increasing thicknesses of the slabs bonded between neighboring pillars, the first directional band-gap and second directional band gap of the PnCs tend to merge. Therefore, the structure with coupling-enhancement slabs can be used as an excellent electrical band elimination filter for most electro-SAW devices, offering a new strategy to realize chip-scale applications in electroacoustic signal processing, optoacoustic modulation, and even SAW microfluidic devices.     

Accurate evaluation of lowest band gaps in ternary locally resonant phononic crystals

Based on a better understanding of the lattice vibration modes, two simple spring--mass models are constructed in order to evaluate the frequencies on both the lower and upper edges of the lowest locally resonant band gaps of the ternary locally resonant phononic crystals. The parameters of the models are given in a reasonable way based on the physical insight into the band gap mechanism. Both the lumped-mass methods and our models are used in the study of the influences of structural and the material parameters on frequencies on both edges of the lowest gaps in the ternary locally resonant phononic crystals. The analytical evaluations with our models and the theoretical predictions with the lumped-mass method are in good agreement with each other. The newly proposed heuristic models are helpful for a better understanding of the locally resonant band gap mechanism, as well as more accurate evaluation of the band edge frequencies.     

Wavelet-based method for computing elastic band gaps of one-dimensional phononic crystals

A wavelet-based method was developed to compute elastic band gaps of one-dimensional phononic crystals. The wave field was expanded in the wavelet basis and an equivalent eigenvalue problem was derived in a matrix form involving the adaptive computation of integrals of the wavelets. The method was then applied to a binary system. For comparison, the elastic band gaps of the same one-dimensional phononic crystals computed with the wavelet method and the well-known plane wave expansion (PWE) method are both presented in this paper. The numerical results of the two methods are in good agreement while the computation costs of the wavelet method are much lower than that of PWE method. In addition, the adaptability of wavelets makes the method possible for efficient band gap computation of more complex phononic structures. Supported by the National Natural Science Foundation of China (Grant No. 10632020)     

二维复式格子声子晶体带隙结构特性

借助于平面波展开法分析了二维复式格子声子晶体能带结构，计算了铝合金柱体按周期性结构排列在空气中形成的二维固/气复合体系的声子晶体，给出了复式蜂窝格子和复式Kagome格子的能带结构，进而对比分析了复式格子和简单格子的能带结构特性.结果表明，与简单格子相比，复式格子的带隙出现在频率相对较低的位置；在f=0.091—0.6046范围内，将声子晶体排列为复式格子要优于简单格子，可以得到更宽带隙.此外，引入了带隙分布图，讨论了填充系数f对带隙数目、带隙宽度以及带隙上下边界频率的影响. 关键词： 声子晶体 复式格子 带隙 平面波算法     

遗传算法在二维声子晶体带隙优化中的应用

运用自适应遗传算法对二维声子晶体的带隙宽度进行优化设计，并与平面波展开法相结合，研究了由正方形排列的铅-环氧树脂构成的声子晶体的带隙宽度优化问题，发现自适应遗传算法可以有效地搜索到具有较宽完全声子带隙的优化单胞形式. 关键词： 声子晶体 声子带隙 遗传算法     

二维8重固-流型准周期声子晶体带隙特性研究

针对二维8重固-流型(钢-水)准周期声子晶体,通过实验方法测试得到了不同大小准周期系统的透射谱,并利用有限元方法计算了准周期体系的频散曲线和透射谱.结果显示,实验与有限元方法所得透射谱结果基本符合,但有限元方法得到的透射谱显示的带隙特性更为明显;二维固-流型8重准周期声子晶体选用包含其中心拼图在内的最小超元胞可以近似计算整个准周期结构的频带结构.     

Band structures and localization properties of aperiodic layered phononic crystals

The band structures and localization properties of in-plane elastic waves with coupling of longitudinal and transverse modes oblique propagating in aperiodic phononic crystals based on Thue-Morse and Rudin-Shapiro sequences are studied. Using transfer matrix method, the concept of the localization factor is introduced and the correctness is testified through the Rytov dispersion relation. For comparison, the perfect periodic structure and the quasi-periodic Fibonacci system are also considered. In addition, the influences of the random disorder, local resonance, translational and/or mirror symmetries on the band structures of the aperiodic phononic crystals are analyzed in this paper.     

基于集中质量法的一维声子晶体弹性波带隙计算

通过将一维声子晶体中的原胞简化为有限多个自由度的弹簧振子结构，引入了一种基于集中 质量法的一维声子晶体弹性波带隙计算方法.与传统平面波展开法相比，该方法的计算结果 与之相符合，而且在收敛性方面较之有很大改善.通过使用集中质量法，可在得到同样计算 精度的条件下，显著降低计算量，提高计算速度. 关键词： 声子晶体 弹性波带隙 集中质量法 平面波展开法     

Hypersonic phononic crystals

In this Letter we propose the use of hypersonic phononic crystals to control the emission and propagation of high frequency phonons. We report the fabrication of high quality, single crystalline hypersonic crystals using interference lithography and show that direct measurement of their phononic band structure is possible with Brillouin light scattering. Numerical calculations are employed to explain the nature of the observed propagation modes. This work lays the foundation for experimental studies of hypersonic crystals and, more generally, phonon-dependent processes in nanostructures.