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     

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     

二维声子晶体带隙计算中的时域有限差分方法

通过将各向同性介质动态弹性方程转化为一阶双曲型波动方程，采用交错网格法改进了O(2,4)的时域有限差分算法. 进而将其应用于二维声子晶体带隙特性计算，理论计算结果和实验结果符合较好，证明该方法适用于声子晶体带隙特性的计算. 关键词： 声子晶体 声子带隙 时域有限差分 交错网格PACC：     

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     

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     

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。     

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     

薄板状周期栅格结构中弹性波传播特性研究

相位常数面可以描述特定频率、特定结构中波的传播方向及传播区域.将相位常数面这一分析方法应用于薄板状周期栅格结构中弹性波传播特性的研究，采用集中质量法计算了周期栅格结构的相位常数面，得到了直观的三维能带结构图.相位常数面可以用二维等高线图描述，通过计算等高线上每一点的法线方向，得到了在特定通带频率下弹性波的传播方向及传播区域.这些研究对于通带频率范围内的弹性波传播特性具有重要意义. 关键词： 声子晶体 弹性波带隙 集中质量法 相位常数面     

一维指数形变截面有限周期声子晶体的研究

本文利用集中质量法对弹性纵波在一维指数形截面有限周期声子晶体中的传播进行了研究, 得到了频率响应函数的表达式. 与一维等截面的声子晶体相比, 指数形变截面声子晶体带隙内的衰减值随着输出端截面积的增大而减小, 同时带隙的起始频率降低而截止频率升高, 也即带隙的宽度会得到拓展. 晶格常数和材料组份比变化时, 变截面声子晶体带隙的起始频率和截止频率的变化趋势与等截面时的声子晶体相同. 希望本文的研究能够推动声子晶体在减振降噪等领域中的应用.     

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     

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)     

Wave localization in two-dimensional porous phononic crystals with one-dimensional aperiodicity

The localization properties of in-plane elastic waves propagating in two-dimensional porous phononic crystals with one-dimensional aperiodicity are initially analyzed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method in this paper. The band structures characterized by using localization factors are calculated for different phononic crystals by altering matrix material properties and geometric structure parameters. Numerical results show that the effect of matrix material properties on wave localization can be ignored, while the effect of geometric structure parameters is obvious. For comparison, the periodic porous system and Fibonacci system with rigid inclusion are also analyzed. It is found that the band gaps are easily formed in aperiodic porous system, but hard for periodic porous system. Moreover, compared with aperiodic system with rigid inclusion, the wider low-frequency band gaps appear in the aperiodic porous system.     

Band structures of two dimensional solid/air hierarchical phononic crystals

The hierarchical phononic crystals to be considered show a two-order “hierarchical” feature, which consists of square array arranged macroscopic periodic unit cells with each unit cell itself including four sub-units. Propagation of acoustic wave in such two dimensional solid/air phononic crystals is investigated by the finite element method (FEM) with the Bloch theory. Their band structure, wave filtering property, and the physical mechanism responsible for the broadened band gap are explored. The corresponding ordinary phononic crystal without hierarchical feature is used for comparison. Obtained results show that the solid/air hierarchical phononic crystals possess tunable outstanding band gap features, which are favorable for applications such as sound insulation and vibration attenuation.     

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     

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.     

Theoretical and experimental investigations of flexural wave propagation in periodic grid structures designed with the idea of phononic crystals

The propagation characteristics of flexural waves in periodic grid structures designed with the idea of phononic crystals are investigated by combining the Bloch theorem with the finite element method. This combined analysis yields phase constant surfaces, which predict the location and the extension of band gaps, as well as the directions and the regions of wave propagation at assigned frequencies. The predictions are validated by computation and experimental analysis of the harmonic responses of a finite structure with 11× 11 unit cells. The flexural wave is localized at the point of excitation in band gaps, while the directional behaviour occurs at particular frequencies in pass bands. These studies provide guidelines to designing periodic structures for vibration attenuation.     

Control analysis of the tunable phononic crystal with electrorheological material

The elastic band structure of a two-dimensional phononic crystal (PC) with electrorheological (ER) material is investigated and the plane-wave-expansion (PWE) method is adopted to solve the problem in this paper. The ER material is used to act as a tunable elastic composite inserts and its material parameter can be changed by the applied electric fields. Variations of the band gaps for the phononic composite system are also calculated with various electric fields and it is found to have a significant effect on the band gaps of the phononic system with ER material inserts. The band gaps of the smart system can be controlled and the acoustic characteristics of the system are also changed by applied different electric fields.     

一维压电Fibonacci类准周期声子晶体传输特性

基于传输矩阵法研究了一维压电Fibonacci类准周期声子晶体的传输特性, 比较了一维Fibonacci序列压电准周期声子晶体与非压电准周期声子晶体以及压电周期性声子晶体的透射性. 计算结果表明:弹性波通过一维准周期结构压电声子晶体时与周期性声子晶体一样会有带隙的出现, 且发现具有压电性的Fibonacci序列准周期声子晶体禁带宽度发生了展宽. 进一步讨论了入射角度对固定频率下声子透射系数的影响,结果表明一维压电Fibonacci序列准周期结构声子透射性依赖于入射角度的选取.     

二维组合宽带隙材料的研究

运用FDTD(时域有限差分法)研究了弹性波/声波通过二维正方形排列的铁/水声子晶体的传播特性.发现铁/水声子晶体在高频范围存在完全带隙，软包层铁/水声子晶体在低频范围出现共振带隙，它们分别对应于不同的带隙形成机理.通过铁/水声子晶体和软包层铁/水声子晶体的组合，可以得到从高频到低频的组合宽带隙结构，从而达到在更宽频范围内控制弹性波传播的目的；而且通过调整包层的厚度、铁芯的大小、以及填充率等结构参数，可以有效地调节组合宽带隙的频率结构.