Elastic wave localization in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity

The band structures of in-plane elastic waves propagating in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity are analyzed in this paper. The localization of wave propagation is discussed by introducing the concept of the localization factor, which is calculated by the plane-wave-based transfer-matrix method. By treating the random disorder and aperiodicity as the deviation from the periodicity in a special way, three kinds of aperiodic phononic crystals that have normally distributed random disorder, Thue-Morse and Rudin-Shapiro sequence in one direction and translational symmetry in the other direction are considered and the band structures are characterized using localization factors. Besides, as a special case, we analyze the band gap properties of a periodic planar layered composite containing a periodic array of square inclusions. The transmission coefficients based on eigen-mode matching theory are also calculated and the results show the same behaviors as the localization factor does. In the case of random disorders, the localization degree of the normally distributed random disorder is larger than that of the uniformly distributed random disorder although the eigenstates are both localized no matter what types of random disorders, whereas, for the case of Thue-Morse and Rudin-Shapiro structures, the band structures of Thue-Morse sequence exhibit similarities with the quasi-periodic (Fibonacci) sequence not present in the results of the Rudin-Shapiro sequence.     

Band structures of Fibonacci phononic quasicrystals

The paper studies the band structures of a two-component Fibonacci phononic quasicrystal which is considered as a phononic crystal disordered in a special way. Oblique propagation in an arbitrary direction of the in-plane elastic waves with coupling of longitudinal and transverse modes is considered. The transfer matrix method is used and the well-defined localization factors which are used to study the ordered and disordered phononic crystals are introduced to describe the band gaps of the phononic quasicrystals. The transmission coefficients are also calculated and the results show the same behaviours as the localization factor does. The results show the merits of using the localization factors. The band gaps of the phononic quasicrystal and crystals with translational and/or mirror symmetries are presented and compared to the perfect phononic crystals. More band structures are exhibited when symmetries are introduced to the phononic quasicrystals.     

Propagation in one-dimensional crystals with positional and compositional disorder

Propagation in perturbed one-dimensional phononic or photonic crystals, with bothcompositional and positional disorder, is considered. The coherent potential approximationis used to obtain the band structure and the Floquet normal form of theperiodic-on-average perturbed crystal, which is modified differently with respect to thetwo kinds of disorder. For finite size crystals, the transmission amplitude is calculatedand compared to direct numerical simulations and to an estimate based on localizationlength. The transmission spectrum is found to be better described using the fullexpression of the Floquet modes of the disordered, but periodic on average, medium.     

Influence of temperature on the properties of one-dimensional piezoelectric phononic crystals

The current study investigates the influence of temperature on a one-dimensional piezoelectric phononic crystal using tunable resonant frequencies. Analytical and numerical examples are introduced to emphasize the influence of temperature on the piezoelectric phononic crystals. It was observed that the transmission spectrum of a one-dimensional phononic crystal containing a piezoelectric material(0.7 PMN-0.3 PT) can be changed drastically by an increase in temperature.The resonant peak can be shifted toward high or low frequencies by an increase or decrease in temperature, respectively.Therefore, we deduced that temperature can exhibit a large tuning in the phononic band gaps and in the local resonant frequencies depending on the presence of a piezoelectric material. Such result can enhance the harvesting energy from piezoelectric materials, especially those that are confined in a phononic crystal.     

弹性波通过一维复合材料系统的透射性质

提出了不同结构的一维弹性波复合材料系统模型,包括一维周期结构声子晶体、标准Fibonacci准周期结构声子晶体、广义Fibonacci准周期结构声子晶体以及完全无序结构的复合材料系统. 采用模式匹配理论法,数值计算了弹性波通过一维复合材料系统的透射系数. 计算结果表明,利用特殊的准周期结构声子晶体可获得比周期结构声子晶体更宽的带隙范围,准周期结构排列的复合材料系统相当于在周期结构中引入了缺陷体一样,带隙内出现了丰富的局域模式. 对弹性波/声波在复合材料系统中局域态性质的研究有助于弹性波/声波滤波器、导波器 关键词： 弹性波复合材料 局域化     

Wave localization in two-dimensional periodic systems with randomly disordered size

The expression of the localization factor in the two-dimensional periodic systems is derived based on the plane-wave expansion, transfer matrix and matrix eigenvalue methods. A comprehensive study is performed for the wave localization in the phononic crystal which is composed of steel cylinders embedded in epoxy matrix with the randomly disordered rod size. From the results, it can be observed that with the increase of the disorder degree, the localization phenomenon is strengthened. Furthermore, the filling fraction has significant effects on the wave localization characteristics.     

Localisation of elastic waves in two-dimensional randomly disordered solid phononic crystals

Combined with the supercell technique, the plane wave expansion method is used to calculate the band structures of the two-dimensional solid–solid phononic crystals with the random disorders in either radius or location of the scatterers. Phononic systems with plumbum scatterers embedded in an epoxy matrix are calculated in detail. The influences of the disorder degree on the band structures for both anti-plane and in-plane wave modes are investigated. It is found that, with increase of the disorder degree, the band gaps become narrower with more flat bands appearing in the gaps. Both displacement distribution and response spectra show that at the flat bands, elastic waves are localised due to the presence of the disorder. Wave localisation is more pronounced at the flat bands near the lower/upper edge for the radius/location disorder. Wave propagation and localisation in a randomly disordered system with a point defect is also studied. The influence of the disorder on the point-defect state is discussed. The results show that the disorder can tune the frequencies of the defect states. It is particularly noticed that the double degenerate mode appearing within the gap of the mixed in-plane waves is split up into two separated ones when the random disorder is introduced into the system. Generally, the influence of the disorder is more pronounced for the mixed in-plane modes than the anti-plane modes. The analysis of this paper is relevant to the assessment of the influences of manufacture errors on wave behaviours in phononic crystals as well as the possible control of wave propagation by intentionally introducing disorders into periodic systems.     

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.     

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     

Effect of Fabry‐Perot resonances in disordered one‐dimensional array of alternating dielectric bi‐layers

We study numerically and analytically the role of Fabry‐Perot resonances in the transmission through a one‐dimensional finite array formed by two alternating dielectric slabs. The disorder consists in varying randomly the width of one type of layers while keeping constant the width of the other type. Our numerical simulations show that localization is strongly inhibited in a wide neighborhood of the Fabry‐Perot resonances. Comparison of our numerical results with an analytical expression for the average transmission, derived for weak disorder and finite number of cells, reveals that such expression works well even for medium disorder up to a certain frequency. Our results are valid for photonic and phononic one‐dimensional disordered crystals, as well as for semiconductor superlattices.     

一维长程关联无序系统的局域性

研究了在紧束缚近似下,由de Moura和Lyra提出的一维长程关联无序模型的局域性. 分布在［-W/2,W/2］区间的格点位能,其关联函数〈ε_iεj〉的傅里叶变换满足S(k)∝k^-α,其中关联强度α>0. 利用participation ratio不仅证实了在α>2和W<4 关键词： 安德森局域化 长程关联 扩展态     

The effect of random variations of structure parameters on photonic band gaps of one-dimensional plasma photonic crystals

The electromagnetic properties of one-dimensional plasma photonic crystals influenced by random perturbation of structure parameters are studied through transfer matrix method in the paper. The random perturbation of thicknesses of layers as well as plasma frequency of layers can influence the electromagnetic properties of one-dimensional plasma photonic crystal. The random perturbation of thicknesses of layers tremendously impacts the band structure of one-dimensional plasma photonic crystals in high frequency domain. The random perturbation of plasma frequency, however, contributes to the moving of a cutoff frequency in the low frequency domain. The position of the defect mode of one-dimensional plasma photonic crystal randomly moves due to the random perturbations. The effect of random perturbation of plasma frequency is more significant than that of random perturbation of thickness of layers, which alters not only the transmittance but also the position of the defect mode. An improved quality factor and a shortened moving distance of the defect mode are both acquired by increasing the period number. And then this work may provide a crude but useful instrument in analyzing disordered 1DPPCs.     

Frequency-dependent localization length of SH-wave in randomly disordered piezoelectric phononic crystals

In this paper, the localization length that represents the distance of elastic waves propagating along the disordered periodic structures is defined as the reciprocal of the smallest positive Lyapunov exponent, i.e. the localization factor. The algorithm for determining all the Lyapunov exponents in continuous dynamic systems presented by Wolf et al. is employed to calculate those in discrete dynamic systems. Numerical results of the localization lengths of SH-wave are presented and discussed in ordered and disordered piezoelectric phononic crystals to identify the different effect degrees for the decay of electrical potential in the polymers and the randomness on the localization level. For the disordered case, disorder in the thickness of the polymers and disorder in the elastic constant of the piezoelectric ceramics are all considered. The results show that some parameters such as the incident angle of elastic wave, the randomness degree and the piezoelectricity of piezoelectric ceramics and so on have pronounced effects on the frequency-dependent localization length.     

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.     

一维准周期声子晶体中平面波的传播和局部化

本文研究了平面波在一维准周期声子晶体中的传播,引进局部化因子的概念研究了结构的带隙特性和局部化特征,利用Wolf方法给出了局部化因子的表达式并用传递矩阵法计算了局部化因子,考查了平面波垂直入射和斜入射的情形,并与相应的周期结构及随机失谐结构进行了比较。     

声波在一维声子晶体中共振隧穿的研究

通过从实验和理论方面对声波在一维声子晶体单晶体和被小的共振腔分开的双晶体中传播时发生的隧穿和共振隧穿现象的研究，观察到了声子晶体单晶体在带隙频率范围内发生的隧穿现象，而对于双晶体样品，在带隙频率范围内出现了很强的共振透射峰.共振发生时，实验测得的群时间很大，但是没有共振时，群速度却很快. 关键词： 声波 声子晶体 隧穿 共振     

Anomalous localization in low-dimensional systems with correlated disorder

This review presents a unified view on the problem of Anderson localization in one-dimensional weakly disordered systems with short-range and long-range statistical correlations in random potentials. The following models are analyzed: the models with continuous potentials, the tight-binding models of the Anderson type, and various Kronig–Penney models with different types of perturbations. Main attention is paid to the methods of obtaining the localization length in dependence on the controlling parameters of the models. Specific interest is in an emergence of effective mobility edges due to certain long-range correlations in a disorder. The predictions of the theoretical and numerical analysis are compared to recent experiments on microwave transmission through randomly filled waveguides.     

Eigenstate statistics and optical properties of one-dimensional disordered photonic crystals

Optical eigenstates in one-dimensional disordered photonic crystals were studied. The threshold disorder level was established below which the probability of appearance of an eigenstate at the photonic bandgap center is negligible. The threshold is reached when the relative fluctuation in the optical lengths of the structure periods becomes equal to the square root of one-third of the relative bandgap width. The dependence of the ensemble-averaged structure transmission coefficient on the fluctuation of the period optical length has a break corresponding to the threshold fluctuation.     

一维颗粒声子晶体的拓扑相变及可调界面态

基于Su-Schrieffer-Heeger模型,构造了一种一维非线性声子晶体,通过调控外加在声子晶体上的预紧力,可调控声子晶体的拓扑态,从而实现拓扑相变.利用这一效应,把该非线性声子晶体与另一线性声子晶体形成异质结构,可以实现一种新型声学开关:通过调节预紧力即调控非线性声子晶体的拓扑相,可以实现异质结构中界面态从无到有的转变,从而实现了开关效应.利用该效应可望开发新型声学器件,如可调谐振器、可调滤波器、可调隔振器等.