Investigation of a silicon-based one-dimensional phononic crystal plate via the super-cell plane wave expansion method

The super-cell plane wave expansion method is employed to calculate band structures for the design of a silicon-based one-dimensional phononic crystal plate with large absolute forbidden bands. In this method, a low impedance medium is introduced to replace the free stress boundary, which largely reduces the computational complexity. The dependence of band gaps on structural parameters is investigated in detail. To prove the validity of the super-cell plane wave expansion, the transmitted power spectra of the Lamb wave are calculated by using a finite element method. With the detailed computation, the band-gap of a one-dimensional plate can be designed as required with appropriate structural parameters, which provides a guide to the fabrication of a Lamb wave phononic crystal.     

Complete band gaps of phononic crystal plates with square rods

Much of previous work has been devoted in studying complete band gaps for bulk phononic crystal (PC). In this paper, we theoretically investigate the existence and widths of these gaps for PC plates. We focus our attention on steel rods of square cross sectional area embedded in epoxy matrix. The equations for calculating the dispersion relation for square rods in a square or a triangular lattice have been derived. Our analysis is based on super cell plane wave expansion (SC-PWE) method. The influence of inclusions filling factor and plate thickness on the existence and width of the phononic band gaps has been discussed. Our calculations show that there is a certain filling factor (f = 0.55) below which arrangement of square rods in a triangular lattice is superior to the arrangement in a square lattice. A comparison between square and circular cross sectional rods reveals that the former has superior normalized gap width than the latter in case of a square lattice. This situation is switched in case of a triangular lattice. Moreover, a maximum normalized gap width of 0.7 can be achieved for PC plate of square rods embedded in a square lattice and having height 90% of the lattice constant.     

平板二维声子晶体声波能带结构研究

利用超元胞法,研究由钢板上生长有限长度的钢柱体形成的散射体嵌入环氧树脂基体中所构成的平板二维声子晶体的声波能带结构,分析散射体的几何参数如柱体的高、半径和板的厚度对声波带隙的影响。研究结果表明:(1)这种新型的声子晶体具有很宽的带隙,且带隙出现在低频范围内;(2)散射体的几何参数对带隙的宽度有很大的影响,它们是控制带隙宽度的主要因素。     

基于平面波算法的二维声子晶体带结构的研究

介绍了平面波算法计算声子晶体带结构的分析过程，计算了二维双组分液相体系声子晶体的带结构.结果表明，四氯化碳/水银体系比水银/四氯化碳体系更容易产生带隙.随分散相填充分数f的增加，四氯化碳/水银体系声子晶体带隙宽度ΔΩ先增加，后减小，当f=0229时，有最大值ΔΩ=0549；水银/四氯化碳体系的带隙宽度一直增大，当f=0554时，有最大值ΔΩ=0515；f一定时，改变分散相单元的几何尺寸和点阵常数，带隙宽度ΔΩ保持不变. 关键词： 声子晶体 声子带隙 平面波算法 带结构     

晶格中心插入体的对称性及取向对二维声子晶体带隙的影响

以二维钢/气体系声子晶体为模型,采用平面波法研究了圆柱正方及六角晶格中心添加插入体的对称性及取向与带隙的关系,给出了四方、六方、八方及圆柱插入体结构的带隙分布图及带隙随柱体取向的变化关系图.发现在低填充率条件下,插入体的截面形状与晶格类型相同时最有利于能带简并态的分离而获得带隙,但填充率较高时,采用高对称性的插入体可以获得最宽的带隙.正方晶格中心插入体取向对带隙的影响要比在六角晶格中更为显著.对四方柱正方晶格声子晶体的研究表明,仅旋转原柱体要比在其中心插入柱体后旋转更容易获得低频宽带隙,单独运用添加柱体或旋转非圆柱体来降低晶格对称性以获取低频带隙的方法要比同时使用两种方法效果更好.此外,从机理上对计算结果进行了解释.     

The Brillouin zones and band gaps of a two-dimensional phononic crystal with parallelogram lattice structure

We present a detailed theoretical study on the acoustic band structure of two-dimensional(2D)phononic crystal.The 2D phononic crystal with parallelogram lattice structure is considered to be formed by rigid solid rods embedded in air.For the circular rods,some of the extrema of the acoustic bands appear in the usual high-symmetry points and,in contrast,we find that some of them are located in other specific lines.For the case of elliptic rods,our results indicate that it is necessary to study the whole first Brillouin zone to obtain rightly the band structure and corresponding band gaps.Furthermore,we evaluate the first and second band gaps using the plane wave expansion method and find that these gaps can be tuned by adjusting the side lengths ratio R,inclined angleθand filling fraction F of the parallelogram lattice with circular rods.The results show that the largest value of the first band gap appears atθ=90°and F=0.7854.In contrast,the largest value of the second band gap is atθ=60°and F=0.9068.Our results indicate that the improvement of matching degree between scatterers and lattice pattern,rather than the reduction of structural symmetry,is mainly responsible for the enhancement of the band gaps in the 2D phononic crystal.     

正方点阵上Fibonacci超元胞声子晶体的带结构

用平面波展开方法研究了水柱体作为填充物, 按照二维Fibonacci排列成超元胞填充在Hg基体中构成的声子晶体的声频带结构. 结果发现, 随着超元胞中准晶格常数的变化, 各个能带均出现三分裂. 对声场分布的研究发现了居间态的存在. 这些现象体现了准周期结构的特征. 关键词： Fibonacci排列 声子晶体 能带结构     

二维复式声子晶体中基元配置对声学能带结构的影响

研究了二维复式声子晶体中基元配置对其声学能带结构的影响,发现当声子晶体的基元配置改变时,声子晶体的不可约布里渊区也会改变,而且部分能带的极值不再在高对称线上.特别地,在某些基元配置下,不可约布里渊区扩大为整个第一布里渊区.因此,对于对称性较高的复式晶格声子晶体,可用通常的方法得到能带结构,而对于对称性较低的复式晶格结构声子晶体,只有采用对整个第一布里渊区进行研究的方法,才能获得可信的能带结构及带隙.     

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.     

超元胞方法研究平移群对称性对声子带隙的影响

采用基于超元胞的平面波展开法，计算了由水银(水)正四棱柱体按正方格子排列于水(水银)基体中所组成的两种声子晶体的能带结构.通过改变两相邻的柱体底面边长之比来改变声子晶体的平移群对称性.结果发现，改变相邻柱体的底面边长之比，具有很好的调节声学带隙的作用.研究表明，声子晶体的平移群对称性对于其带隙的形成具有重要影响,同时还表明,超元胞方法也是研究声子晶体平移群对称性影响声子带隙形成的一种有效方法. 关键词： 声子晶体 带隙 对称性     

X形超阻尼局域共振声子晶体梁弯曲振动带隙特性

以声子晶体理论为基础,设计了一种具有超阻尼特性的X形局域共振结构,分析了周期性附加X形局域共振的梁弯曲振动传播特性.利用拉格朗日方程分析了X形局域共振结构动力学等效特性,揭示了该结构的阻尼放大的机理,分析了几何结构参数对于带隙特性的影响,并利用有限元法验证了X形局域共振结构的超阻尼特性.研究结果表明,周期性附加X形局域结构能够有效地抑制低频弯曲振动在梁中的传播,产生超阻尼特性,实现低频、宽带的减振效果,为结构的低频减振提供了一个新的设计方案.     

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     

一维准周期结构声子晶体透射性质的研究

提出了一维准周期结构的声子晶体模型.对弹性波通过该一维准周期结构声子晶体的透射系数进行了数值计算，并与周期结构的透射系数进行了比较.计算结果表明，弹性波通过一维准周期结构声子晶体时，同样会有带隙的出现，且带隙所在频率范围与周期结构的情形完全一样，不同的是在准周期结构声子晶体中，带隙内有很强的局域共振模.对此局域模性质的研究有助于声波或弹性波滤波器的制作. 关键词： 准周期结构 声子晶体 局域化     

Hybrid phononic crystal plates for lowering and widening acoustic band gaps

We propose hybrid phononic-crystal plates which are composed of periodic stepped pillars and periodic holes to lower and widen acoustic band gaps. The acoustic waves scattered simultaneously by the pillars and holes in a relevant frequency range can generate low and wide acoustic forbidden bands. We introduce an alternative double-sided arrangement of the periodic stepped pillars for an enlarged pillars’ head diameter in the hybrid structure and optimize the hole diameter to further lower and widen the acoustic band gaps. The lowering and widening effects are simultaneously achieved by reducing the frequencies of locally resonant pillar modes and prohibiting suitable frequency bands of propagating plate modes.     

复合兰姆波声子晶体中超宽部分禁带

兰姆波在声子晶体薄板中的传播特性因其在无损检测、 减振技术和传感器件等领域的潜在应用价值而受到越来越多的关注. 本文采用超原胞平面波展开法和有限元法系统地研究了复合对称结构声子晶体薄板中的兰姆波超宽部分禁带. 结果表明: 对于在薄板侧面对称地嵌入双层矩形空气柱构成的复杂系统, 低阶兰姆波部分带隙结构极为丰富. 将晶格常数(L)和板厚(H) 比值具有匹配关系的兰姆波声子晶体衔接构成复合结构, 低阶兰姆波部分禁带宽度因各组分结构的部分禁带交叠而得到显著拓宽, 可在低频超宽频带内实现对特定低阶兰姆波模式良好的模式选择功能. 该研究结果对兰姆波缺陷无损检测中模式优化选择及兰姆波单向导通器件设计等方面具有重要意义.     

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.     

Lamb wave band gaps in locally resonant phononic crystal strip waveguides

Using finite element method, we have made a theoretically study of the band structure of Lamb wave in a locally resonant phononic crystal strip waveguide with periodic soft rubber attached on the two sides of epoxy main plate. The numerical results show that the Lamb wave band gap based on local resonant mechanism can be opened up in the stub strip waveguides, and the width of the local resonant band gap is narrower than that based on the Bragg scattering mechanism. The results also show that the stub shape and width have influence on the frequency and width of the Lamb wave band gap.     

Zone folding induced tunable topological interface states in one-dimensional phononic crystal plates

In previous literature, the realization of topological interface state in one-dimensional periodic system is strongly relied on the tedious parameter adjustment to search for the Dirac cone. In this paper, based on a strategy of zone folding, multiple topological interface modes for the shear horizontal guided waves in one dimensional phononic crystal plate are investigated by using finite element method and eigenmode matching theory, in which the Dirac points are formed by simply making the unit cell double. Significantly, by simply contracting or expanding the stubs can bring the topological phase transition. Furthermore, the topological phase transition is further achieved by varying the height of the stubs. The proposed designs will be more convenient to be applied in real engineering.     

广义Fibonacci准周期结构声子晶体透射性质的研究

提出了一维广义Fibonacci准周期结构的声子晶体模型. 对弹性波通过该一维准周期结构声子晶体的透射系数进行数值计算,并与周期结构和标准Fibonacci准周期结构声子晶体的透射系数进行比较. 结果表明,利用一维广义Fibonacci准周期结构的声子晶体可获得比周期结构和标准Fibonacci准周期结构声子晶体更大的带隙范围,同时在带隙内有更丰富的局域模式存在. 对局域模性质的研究有助于声波或弹性波滤波器的制作. 关键词： 广义Fibonacci准周期结构 声子晶体 局域化     

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