The band gap of 1D viscoelastic phononic crystal

The band gap of one dimensional (1D) phononic crystal with viscoelastic host material is studied in this paper. The standard solid model is used to simulate the viscoelastic behavior of the host material and the fillers embedded in the host material are still assumed elastic material. The band gap problem in 1D phononic crystal leads to an eigenvalue problem by using the plane wave expansion method and the Bloch–Floquet wave theory in a periodic structure. An iterative algorithm is designed to obtain the band gap structure due to the dependence of elastic constants on frequency for the viscoelastic host material. A numerical example is given for steel/epoxy phononic crystal. The band gap of 1D phononic crystal is evaluated for different viscoelastic constants, namely, relaxation time, initial and final state elastic modulus. It is found that the viscoelastic constants of host material affect not only the location but also the width of band gaps.     

声子晶体中弹性波带隙与散射

声子带隙产生条件是声子晶体研究的一个重要问题,首先对钢圆柱体嵌入空气基质组成的声子晶体散射截面进行计算,然后用平面波方法计算了弹性波带结构。结果表明声子带隙将出现在两个完全分离的共振态之间。因此,声子晶体产生完全带隙的条件是弹性波在基质材料中的传播被禁止并远离共振。     

基于辛数学方法的一维声子晶体禁带计算

将一维声子晶体的原胞简化为有限多个自由度的弹簧振子结构,在辛对偶变量体系下探讨晶格振动,引入辛数学方法确定波矢与本证值的色散关系。通过本证值计数法计算特征频率,从而得到禁带区间。与传统集中质量法相比,该算法的计算结果与之吻合很好,且提高了计算精度和计算效率,更重要的是在低频处收敛性更好。     

一维功能梯度材料声子晶体弹性波带隙研究

应用平面波展开法研究了由功能梯度材料周期复合而成的一维声子晶体中存在的弹性波带隙特征,并得到第一阶带隙归一化起始频率、截止频率和宽度随功能梯度材料表面材料常数、指数因子和组分比变化的关系图。并对功能梯度材料声子晶体与常规材料声子晶体帯隙特征进行了比较,结果表明,功能梯度材料声子晶体较常规材料声子晶体在相同范围内能够出现更多阶带隙结构。这些结果为功能梯度材料声子晶体在工程实际中的广泛应用提供了理论依据和指导。     

Boundary element method for band gap calculations of two-dimensional solid phononic crystals

A boundary element method (BEM) is developed to calculate the elastic band gaps of two-dimensional (2D) phononic crystals which are composed of square or triangular lattices of solid cylinders in a solid matrix. In a unit cell, the boundary integral equations of the matrix and the scatterer are derived, the former of which involves integrals over the boundary of the scatterer and the periodic boundary of the matrix, while the latter only involves the boundary of the scatterer. Constant boundary elements are adopted to discretize the boundary integral equations. Substituting the periodic boundary conditions and the interface conditions, a linear eigenvalue equation dependent on the Bloch wave vector is derived. Some numerical examples are illustrated to discuss the accuracy, efficiency, convergence and the computing speed of the presented method.     

Three-dimensional phononic band gap calculations using the FDTD method and a PC cluster system

This paper aims at studying the band gap phenomena of three-dimensional phononic crystals using the finite difference time domain (FDTD) method and a PC cluster system. In the paper, Bloch's theorem is applied to the wave equation and to the boundary conditions of the periodic structure. We calculate the variations of displacements and take discrete Fourier transform to acquire the resonances of the structures. Then, the dispersion relations of the bulk acoustic wave can be obtained and the band gaps are predicted accordingly. On the other hand, because of larger data calculation in three-dimensional phononic crystals, we introduce the PC cluster system and parallel FDTD programs written with respect to the architecture of a PC cluster system. Finally, we discuss the numerical calculation of two-dimensional and three-dimensional phononic crystals consisting of steel/epoxy and draw conclusions regarding the band gap phenomena between these phononic crystals.     

二维局域共振型声子晶体微腔结构的带隙特性研究

利用有限元法研究了含十字型所形成的二维局域共振型微腔声子晶体结构的声波带隙特性。同时计算了最低带隙带边对应模态的位移分布和结构的传输谱。研究结果表明,含微腔结构的声子晶体在较低频率域内出现了完全带隙且带隙边缘的起始频率低,然而对于无微腔结构的类四边形声子晶体板中,则无第二带隙出现,并且第一带隙频率宽度较窄。微腔结构是产生局域共振以及出现低频带隙的最主要的原因。该研究为声子晶体在低频减振和噪音控制的工程应用方面提供了有益的支持。     

声子晶体板复能带计算方法

声子晶体具有弹性波带隙,可以用于结构振动与噪声控制。声子晶体传统能带算法一般给定波矢k在不可约布里渊区边界取值,然后求解特征频率ω,得到ω-k曲线。因而,传统方法中波矢k只取实数,只能求解实能带。为了求解复能带,一般需要给定频率ω,求解特征波矢k,从而得到k-ω曲线。提出了一种参数变换方法,解决了特征波矢求解中复杂的非线性特征值问题,实现了复能带的快速求解。最后,采用两个算例对文中算法进行了验证,包括布拉格声子晶体板和局域共振声子晶体板,研究了带隙内衰减常数随波传播方向的变化和阻尼对带隙的影响。     

层状双周期结构声子晶体带隙特性研究

设计了一种层状五组元双周期结构声子晶体,并将其等效为一维声子晶体,采用传递矩阵法推导出了该结构的能带结构;在该带隙范围内弹性波或声波的传播能够得到有效抑制,实现对噪声的控制。同时,分析了取消内部周期以后第一带隙的变化以及改变硅橡胶层厚度对第一带隙的影响。结果表明,该结构与简单二元结构相比,在降低带隙频率的同时有效减轻了结构质量,且"内部周期"主要影响带隙宽度;当增加硅橡胶层的厚度时,带隙频率进一步降低。     

散射体的取向对二维声子晶体带隙的影响

声子晶体是一种具有声波带隙特性的新型功能材料。运用平面波展开法研究了二维声子晶体的带结构,二维声子晶体由横截面为正方形的散射体按正方形排列植入环氧树脂基体中形成。结果表明:通过改变散射体的取向可以调节系统的带隙,当填充率较低时,带隙宽度随散射体旋转角的增加先减小再增加,而填充率较高时,带隙宽度随散射体旋转角的增加而先稍有增加然后再减小。     

决定二维声子晶体带隙的关键材料参数

从弹性波动方程入手,获得决定二维声子晶体z模态带隙的关键材料参数是散射体对基体的质量密度比和剪切模量比.利用平面波展开法计算带隙结构,研究正方点阵、三角点阵以及不同填充率时材料参数对带隙的影响.发现质量密度比对带隙起决定作用.仅以声阻抗比或波速比的大小不能决定带隙的存在和大小.给出不同点阵形式下产生带隙的材料参数取值范围.给出材料参数-带隙图,对以材料参数设计带隙具有直观的指导作用.     

Band gap of piezoelectric/piezomagnetic phononic crystal with graded interlayer

The band gaps of a laminated piezoelectric/piezomagnetic phononic crystal with graded interlayer are studied in this paper. First, the transfer matrix method and the Bloch theorem are used to derive the dispersion equation. Next, the graded interlayer with different gradient profiles between the piezoelectric and the piezomagnetic materials is considered. The graded interlayer is modeled as a system of homogenous sublayers with both piezoelectric and piezomagnetic effects simultaneously. The effect of the graded interlayer on the band gap is introduced by inserting an additional interlayer transfer matrix in the calculation of the total transfer matrix. Finally, the dispersion equation is solved numerically, and the dispersive curves are shown in the Brillouin zone. The band gaps of the phononic crystal with graded interlayer are compared with that without graded interlayer. The influences of the graded interlayer with different gradient profiles on the band gap of a laminated piezoelectric/piezomagnetic phononic crystal are discussed based on the numerical results.     

Probing thermomechanics at the nanoscale: impulsively excited pseudosurface acoustic waves in hypersonic phononic crystals

High-frequency surface acoustic waves can be generated by ultrafast laser excitation of nanoscale patterned surfaces. Here we study this phenomenon in the hypersonic frequency limit. By modeling the thermomechanics from first-principles, we calculate the system's initial heat-driven impulsive response and follow its time evolution. A scheme is introduced to quantitatively access frequencies and lifetimes of the composite system's excited eigenmodes. A spectral decomposition of the calculated response on the eigemodes of the system reveals asymmetric resonances that result from the coupling between surface and bulk acoustic modes. This finding allows evaluation of impulsively excited pseudosurface acoustic wave frequencies and lifetimes and expands our understanding of the scattering of surface waves in mesoscale metamaterials. The model is successfully benchmarked against time-resolved optical diffraction measurements performed on one-dimensional and two-dimensional surface phononic crystals, probed using light at extreme ultraviolet and near-infrared wavelengths.     

椭圆柱三角晶格固态声子晶体的带隙结构

用平面波法研究了椭圆钢柱与环氧树脂组成的二维三角晶格声子晶体的带隙结构.结果表明,带隙的宽度和中心频率随填充率F或椭圆柱体横截面两半径之比T的变化表现出明显的变化规律;椭圆柱体横截面的对称性越高,带隙越宽;当F很小时,F对带隙中心频率的影响与T关系不大;椭圆柱体绕其中心轴旋转时,带隙的宽度呈现出与中心频率相反的变化规律,而且最小的带隙宽度及最高的中心频率均在柱体旋转60°左右出现.     

一种新型复合局域共振型声子晶体带隙特性

设计了一种新型复合局域共振型声子晶体,通过建立弹簧-质量块等效模型用于计算带隙的上下边界频率,同时结合有限元方法分析了该结构共振带隙的产生机理,根据带隙起止点频率处的位移模态研究了声子晶体的带隙特性。研究结果表明,该声子晶体结构在频率2 200 Hz附近产生三条完整带隙,其中一条是带宽达406.17 Hz的宽带隙。对于有限周期结构的声子晶体进行了传输特性仿真和隔声实验测试,在相同的频段内弹性波传播受到了阻碍。最后,对影响声子晶体带隙打开的几种因素进行分析,讨论了带隙上下边界调控机制。研究结果为声子晶体获得较宽的低频带隙提供了一种新的设计思路和方法。     

一类声子晶体角梁的振动带隙研究

针对声子晶体直梁的低维窄带减振特性的不足,提出了一类声子晶体角梁。采用传递矩阵法对角梁进行了理论分析和数值求解,并进行了有限元仿真验证。分析结果表明：声子晶体角梁能够通过纵向振动和弯曲振动的转化使得组成梁的两种带隙同时得以发挥减振作用,从而有效地实现了宽频多维减振;声子晶体角梁的构造角度对其减振性能有明显的影响,90度角梁减振能力明显优于45度和135度情况;当加载角由0度向90度变化时,角梁内的振动由纵向振动为主逐渐过渡到弯曲振动占主导地位,弯曲带隙内的衰减也随之更加显著,反之亦然;扭簧能够加强角梁的“弹簧-振子”效应,不仅可以增加总振动带隙的宽度和衰减量,而且提高了低频区减振能力。     

Tuning the band gap of ZnO nanoparticles by ultrasonic irradiation

In this present paper, we report the tunability of ZnO nanoparticles by ultrasonic irradiation. Different sized ZnO nanoparticles viz. 2.58–2.97 nm have been synthesized with variation of ultrasonic irradiation time 75–270 min in presence of Histidine as capping agent. UV and visible spectroscopy study revealed that as ultrasonic irradiation time increases, there is increase in amount of formed ZnO nanoparticles and also there is red shift in absorption edge. This confirms the tunability of bandgap of histidine capped ZnO nanoparticles with ultrasonic irradiation. Growth mechanism for controlling the size of ZnO nanoparticles are also discussed.     

椭圆柱三维简立方排列声子晶体的带隙结构

用平面波法研究了椭圆钢柱与环氧树脂组成的三维简立方晶格声子晶体的带隙结构.一般情况下,椭圆柱体的横截面形状对称性越高,带隙宽度极值和中心频率越大;带隙宽度随椭圆柱体绕其中心轴旋转角度的增大而增大,但带隙中心频率随旋转角度的增大而减小;无论柱体是否旋转,通过改变柱体横截面半径都比改变柱体高度更易获得宽带隙.     

Temperature dependence of AlInAs band gap energy and AlInAs/InP band offsets

Abstract

The temperature variations of the AlInAs photoluminescence (PL) transition energies and the AlInAs/InP interface staggered lineup luminescence (SLL) energy are reported. The S shape appearing from 4 to 90 K on the energy v. temperature curves of these PL energies are owing to extrinsic recombinations. In particular, the S shape of the SLL energy curve v. temperature is probably a result of acceptor impurities localised in AlInAs at the interface (on edge impurities). The band offsets were determined by solving the Schrödinger and Poisson equations with a self consistent calculation program. At 4.5 K, the conduction and valence band offsets are 0.384 and 0.295 eV respectively. Their temperature variation is shown to be important: 35 and 23 meV at 4.5 and 300 K respectively. The Van Vechten and Malloy model (following a thermodynamic approach) for the temperature variation of the band offsets is compared to the results in the present work.