利用叠加理论研究固-液声子晶体纵波的能带结构

采用相干叠加原理推导出一种研究一维固-液有限周期声子晶体中纵波的透射率公式,建立了一种研究一维固-液有限周期声子晶体能带的新方法——波叠加理论。将波叠加理论和转移矩阵法进行了比较研究,结果表明波叠加理论和转移矩阵法得出的结果是一致的。波叠加理论不仅具有转移矩阵法的优点,而且又克服了转移矩阵法的不足。因此波叠加理论是一种研究一维固-液有限周期声子晶体中纵波能带的更为有效的方法。     

一维固-液掺杂声子晶体缺陷模的机理研究

建立了一维固-液掺杂声子晶体的谐振腔模型,利用谐振腔的共振条件推导出了缺陷模频率满足的解析公式,从理论上解释了产生一维固-液掺杂声子晶体缺陷模的物理机理.利用频率的解析公式研究了缺陷模的频率随入射角、杂质厚度、杂质波速的变化规律.结果表明:缺陷模的频率随入射角和杂质波速的增加而增加,缺陷模的频率随杂质厚度的增加而减少,圆满地解释了一维固-液掺杂声子晶体缺陷模的变化规律.在此基础上并与转移矩阵法的计算结果进行了比较,其结果吻合.     

固-液圆柱掺杂声子晶体中弹性波的缺陷模

利用一维固-液圆柱形掺杂声子晶体中弹性波横向受限的条件,推导出弹性波在一维固-液圆柱形掺杂声子晶体中各种模式满足的关系式,研究了各种模式弹性波的特性。利用转移矩阵计算出弹性波的缺陷模随模式量子数以及圆柱半径的变化规律,得到了一些一维固-液结构圆柱形掺杂声子晶体缺陷模的新特征。研究结果表明,缺陷模的频率和半高宽均与模式量子数和圆柱半径有关。     

固-固有限周期声子晶体中SH波全反射隧穿的机理

利用边界条件推导出SH波在一维固-固有限周期声子晶体中的转移矩阵,并用倏逝波的概念和多波束干涉理论,从理论上解释了一维固-固有限周期声子晶体全反射隧穿效应产生的物理机理,得出了全反射隧穿峰带波长满足的解析公式。利用解析公式和转移矩阵研究了一维固-固有限周期声子晶体中SH波的全反射隧穿效应,结果发现两种方法得出的结论是吻合的。     

固-固有限周期声子晶体中SH波全反射隧穿的机理

利用边界条件推导出SH波在一维固-固有限周期声子晶体中的转移矩阵,并用倏逝波的概念和多波束干涉理论,从理论上解释了一维固-固有限周期声子晶体全反射隧穿效应产生的物理机理,得出了全反射隧穿峰带波长满足的解析公式。利用解析公式和转移矩阵研究了一维固-固有限周期声子晶体中SH波的全反射隧穿效应,结果发现两种方法得出的结论是吻合的。     

固-固掺杂结构声子晶体中弹性波的缺陷模

为了研究弹性波在固-固掺杂结构声子晶体中缺陷模的特性,推导出弹性波斜入射固-固掺杂结构声子晶体的转移矩阵。利用它计算了固-固掺杂结构声子晶体中弹性波的透射系数,得到由于掺杂在禁带的中间出现了多条缺陷模透射峰带,缺陷模透射峰带随杂质厚度的变化呈周期性地出现,在同一缺陷模透射峰带上缺陷模的频率随杂质厚度增加近似呈线性减少。缺陷模的这些特征可以作为设计声子晶体滤波器的理论依据。     

一维声子晶体中声波能带的解析研究

为了对一维声子晶体的能带进行解析研究,采用一维声子晶体的色散法,推导出一维声子晶体禁带频率和通带频率的解析公式;并利用此式对一维声子晶体的能带结构进行了解析研究,得到了禁带和导带的频率中心、频率宽度分别随介质厚度和声阻抗两者的变化规律,并与转移矩阵方法的计算结果进行了比较.研究结果表明:两种方法得到的结论相同,但解析法能更准确、更深刻地反映出一维声子晶体的能带随介质厚度和声阻抗等因素的变化规律;并且解析法克服了转移矩阵法等其他方法不能对能带结构进行解析研究的不足,是一种研究一维声子晶体能带更有效的方法.     

SH波在局部非均匀声子晶体中的传播

使用传输矩阵法,研究了水平剪切波(SH波)在一维局部材料非均匀声子晶体中的传播。首先使用皮亚诺方程给出了SH波在特定非均匀梯度介质声场的传输矩阵。然后使用传输矩阵和布洛赫定律给出了该声子晶体的禁带结构和传输系数。通过具体计算,发现这种非均匀性能明显影响声子晶体的频散曲线和禁带结构。然后比较了幂指数取不同值时,禁带结构与归一化频率和填充比的关系。发现幂指数不同,声子晶体的禁带不同。     

镜像对称准周期固/液声子晶体的传输特性

以准周期Fibonacci序列为基础,构建了准周期镜像对称结构的一维固液介质声子晶体。利用转移矩阵法,研究了弹性波在所构建的声子晶体中的透射特性。结果表明:弹性波正入射时,转移矩阵与变介质的特性阻抗有关,由于声子晶体结构的局域失谐,在透射谱的中心频率附近对称出现谐振模;对于Q7序列的声子晶体,带隙内谐振模带宽小于10Hz,能实现超窄带声滤波;弹性波斜入射时,带隙向高频区移动;入射角为5°时,谐振模也向高频移动;入射角为10°时,由于谐振的增强,声子晶体结构对频率的选择性提高,使带隙内的谐振模消失。     

方形固-液声子晶体的全反射隧穿及其多通道滤波

为了研究一维固-液结构方形声子晶体中弹性波的全反射隧穿效应,利用传输矩阵法计算了弹性波在大于全反射角入射一维固-液结构方形声子晶体的透射率。在透射波中发现了全反射隧穿效应,并且全反射隧穿峰具有优良的多通道滤波特性。得出了一维固-液结构声子晶体的全反射隧穿的滤波特性随周期数、模式量子数、边长的变化规律。为设计性能优良的多通道声子晶体滤波器提供了理论依据。     

局域共振型声子晶体板缺陷态带隙及其俘能特性研究

设计了一种由圆柱形散射体嵌入环氧树脂基体而组成的周期阵列局域共振型声子晶体板结构, 分析了其平直带区域以及缺陷态的能量集中特性, 并研究了其振动能量采集特性. 首先基于超元胞法结合有限元方法分析了5 $\times$ 5完美声子晶体结构和缺陷态声子晶体结构的能带曲线和能量传输特性; 考虑点缺陷局域共振声子晶体结构的能量集中特性, 利用压电材料代替超元胞中某点的散射体材料引入点缺陷, 分析其振动能量采集特性, 结果表明单个5 $\times$ 5点缺陷超胞结构共振频带较窄; 为提升俘能效率, 提出两种由3个具有不同缺陷态数量和构型的5 $\times$ 5超元胞结构并联而成的5 $\times$ 15声子晶体板结构, 机电耦合特性分析结果表明: 所提出的局域共振型声子晶体板结构克服了单个点缺陷超胞结构缺陷模过少、共振频带过窄的局限性, 拓宽了俘能器的工作频带, 提高了输出电压; 此外, 引入不同的缺陷态数量和构型, 可以进一步拓宽俘能带宽, 实现更好的俘能效果.      

Simulation of elastic wave diffraction by multiple strip-like cracks in a layered periodic composite

The problem of numerical simulation of the steady-state harmonic vibrations of a layered phononic crystal (elastic periodic composite) with a set of strip-like cracks parallel to the layer boundaries is solved, and the accompanying wave phenomena are considered. The transfer matrix method (propagator matrix method) is used to describe the incident wave field. It allows one not only to construct the wave fields but also to calculate the pass bands and band gaps and to find the localization factor. The wave field scattered by multiple defects is represented by means of an integral approach as a superposition of the fields scattered by all cracks. An integral representation in the form of a convolution of the Fourier symbols of Green’s matrices for the corresponding layered structures and a Fourier transform of the crack opening displacement vector is constructed for each of the scattered fields. The crack opening displacements are determined by the boundary integral equation method using the Bubnov-Galerkin scheme, where Chebyshev polynomials of the second kind, which take into account the behavior of the solution near the crack edges, are chosen as the projection and basis systems. The system of linear algebraic equations with a diagonal predominance of components arising when the system of integral equations is discretized has a block structure. The characteristics describing qualitatively and quantitatively the wave processes that take place under the diffraction of plane elastic waves by multiple cracks in a phononic crystal are analyzed. The resonant properties of a system of defects and the influence of the relative positions and sizes of defects in a layered phononic crystal on the resonant properties are studied. To obtain clearer results and to explain them, the energy flux vector is calculated and the energy surfaces and streamlines corresponding to them are constructed.     

Propagation of bending waves in phononic crystal thin plates with a point defect

In this paper, the band structures of bending waves in a phononic crystal thin plate with a point defect are studied using an improved plane wave expansion method combined with the supercell technique. In particular, a phononic crystal thin plate composed of an array of circular crystalline Al₂O₃ cylinders embedded in an epoxy matrix with a square lattice is considered in detail. Full band gaps are shown. When a point defect is introduced, the bending waves are highly localized at or near the defect, resulting in defect modes. The frequency and number of the defect modes are strongly dependent on the filling fraction of the system and the size of the point defect. The defect bands appear from the upper edge of the gap and move to the middle of the gap as the defect size is reduced. For a given defect, the frequencies of the defect bands increase as the filling fraction increases.     

Band structure properties of elastic waves propagating in the nanoscaled nearly periodic layered phononic crystals

The localization factor is used to describe the band structures for P wave propagating normally in the nanoscaled nearly periodic layered phononic crystals. The localization factor is calculated by the transfer matrix method based on the nonlocal elastic continuum theory.Three kinds of nearly periodic arrangements are concerned, i.e., random disorder, quasiperiodicity and defects. The influences of randomly disordered degree of the sub-layer's thickness and mass density, the arrangement of quasi-periodicity and the location of defect on the band structures and cut-off frequency are analyzed in detail.     

Wave localization in randomly disordered layered three-component phononic crystals with thermal effects

In this paper, the propagation and localization of elastic waves in randomly disordered layered three-component phononic crystals with thermal effects are studied. The transfer matrix is obtained by applying the continuity conditions between three consecutive sub-cells. Based on the transfer matrix method and Bloch theory, the expressions of the localization factor and dispersion relation are presented. The relation between the localization factors and dispersion curves is discussed. Numerical simulations are performed to investigate the influences of the incident angle on band structures of ordered phononic crystals. For the randomly disordered ones, disorders of structural thickness ratios and Lamé constants are considered. The incident angles, disorder degrees, thickness ratios, Lamé constants and temperature changes have prominent effects on wave localization phenomena in three-component systems. Furthermore, it can be observed that stopbands locate in very low-frequency regions. The localization factor is an effective way to investigate randomly disordered phononic crystals in which the band structure cannot be described.