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     

液氦表面准一维电子气体的集体激发

采用子能带模型,研究了有限温度情况下能带耦合对形成于液氦表面的准一维电子气体的集体激发的两类散射———带内散射和带间散射的影响。首先重点讨论了影响集体激发的重要因子———能量传播函数,得到了长波近似条件下的能量传播函数的普适表达式,然后在此基础上具体计算了三个子能带模型时的耦合散射谱,最后讨论了波矢、温度对耦合散射的影响。     

二维声子晶体带结构的多散射分析及解耦模式

利用多散射方法研究了二维声子晶体中的带结构，通过对柱散射波各阶分波之间的耦合分析，发现在带隙边缘的模式存在与对称性相关的解耦现象. 由此在低阶带隙边缘出现独立的自洽的零阶多散射模式. 通过引入周期结构因子和Mie散射因子，得到表征低阶带隙起始频率的解析公式. 利用该公式，采用图解法，定量地说明了带隙起始频率随周期性和单散射体Mie散射特性变化的规律. 关键词： 声子晶体 多散射     

流固耦合声子晶体管路冲击振动特性研究

流固耦合管路系统广泛应用于各种装备中,通常用来传递物质和能量或者动量.由于流固耦合效应,管壁在流体作用下易产生强烈的振动与噪声,对装备安全性、隐蔽性产生严重影响,甚至造成严重破坏.流固耦合管路振动抑制需求迫切,意义重大.声子晶体可以利用其带隙特性抑制特定频率范围内弹性波的传播,在减振降噪领域具有广泛的应用前景.本文基于声子晶体理论,研究了流固耦合条件下的布拉格声子晶体管路冲击振动传递特性.将传递矩阵法和有限元法相结合,计算了能带结构与带隙特性,重点考虑了流固耦合效应下,不同冲击激励条件下声子晶体管路振动特性,分析了流固耦合对声子晶体管路振动传递特性的影响.研究结果为流固耦合条件下管路系统的振动控制提供了技术参考.     

周期性加隔板有限长圆柱壳声散射

研究内部真空周期性加隔板圆柱壳在水中的声散射特性.壳体振动用薄壳理论的Donnell方程描述,隔板振动用相互独立的薄板纯弯曲振动和平面应力状态下的振动方程描述.考虑轴向、切向、径向三个方向的力和弯矩共同作用导出了散射声场的解析表达式.数值计算给出远场收发合置情况下的角度-频率谱图,并据此进行机理分析.通过与内部周期性加环肋圆柱壳声散射的角度-频率谱图比较发现,除周期加肋产生的Bragg散射波与弯曲Bloch-Floquet波外,加隔板的情况还存在明显的隔板共振亮线,并且发生隔板共振与壳体弹性波、Bragg散射波、弯曲Bloch-Floquet波耦合的现象.通过实验对理论进行了验证,在实验的频率范围内,Bragg散射亮线与理论符合得很好,部分Bloch-Floquet波散射亮线和隔板共振散射亮线也与理论符合.     

局部固体填充的水中复杂目标声散射计算与实验

利用二维有限元方法研究水中局部填充的带球冠柱体目标声散射特性,所采用的数值方法可高效地实现精细化、宽带、复杂轴对称模型散射声场计算.根据数值结果解释壳体、填充物以及入射方位对目标散射远场的影响,确定复杂目标散射研究中所必须考虑的重要物理和几何构成.完成水中悬浮目标自由场声散射实验,收发合置条件下将目标旋转360?接收并测量不同传播路径回波到达时刻得到距离-角度伪彩色图像.以表面环绕波和"回廊波"产生理论为基础,解释内真空和局部填充模型正横入射时目标散射信号中几何回波和各种弹性波成分产生的机理.由于固体填充与弹性壳的耦合作用,频率-角度谱的正横方向两侧呈现外八字"碗"形共振曲线.通过对比,理论计算和实验得到的散射函数关键频谱峰值特性符合较好.     

局域共振型声学超材料机理探讨

本文以二维固体薄板中的弹性波传播为例, 对基于共振子结构的声学超材料带隙机理进行了探讨, 证明在声学超材料中带隙形成既与共振子对波的散射相位有关, 也与波在共振体之间的几何传播相位有关. 通过调节散射相位和几何传播相位均能实现对色散关系的调控. 基于这一理解, 探究了弹性波超材料中的次波长缺陷态和负折射现象的实现条件.     

金属柱平板慢波系统高频特性研究

对于离散的金属柱结构构建的周期性平板慢波系统,本文利用3维FDTD方法结合HFSS仿真软件深入分析了该慢波系统的高频特性.研究了金属柱高度、周期长度对色散特性的影响,计算了耦合阻抗,并与传统光栅慢波系统特性进行了对比分析.分析表明金属柱慢波系统既有与传统光栅慢波系统相似的高频特性,又具有独自的特点,位于离散的金属柱周期间隙中的电子注互作用耦合阻抗具有对称性;金属柱结构用作真空电子器件的高频系统可增加发生有效互作用的电子注厚度,降低起振电流密度,提高器件效率.本文的分析结果为设计低电流密度工作的多电子注短毫 关键词： 金属柱平板慢波系统 3维FDTD算法 色散特性 耦合阻抗     

等离子体加载耦合腔慢波结构色散分析

利用磁化等离子体介电张量和纵向场分量法对任意大小轴向磁场中等离子体填充耦合腔慢波结构进行场分析，得到磁化等离子体填充电子注通道电磁波场分量的轴对称精确解.在此基础上，建立耦合腔分区模型、采用场匹配方法建立色散方程，并数值计算得出不同等离子体密度及磁场下的耦合腔色散曲线.对不同密度等离子体填充情况下的耦合腔色散特性、混合模式的形成机理以及等离子体空间电荷波进行了分析讨论. 关键词： 耦合腔慢波结构 等离子体 混合模式 色散特性     

水下三弹性柱壳耦合声散射特性研究

为研究3个并排无限长弹性圆柱壳受垂直于柱轴方向的平面声波作用的声散射特性,采用Fourier级数展开法建立了圆柱壳声散射数学物理模型,考虑了三圆柱壳弹性振动声辐射和刚性声散射,建立了3个壳体辐射声场和刚性散射声场的耦合作用关系,比对了等效散射强度的刚性散射分量与弹性散射分量,并分析了三壳体等效散射强度特性。计算结果表明:当ka₂>40,在频率f=3000 Hz以上频段,弹性分量对等效散射强度变化趋势的贡献可以忽略。当ka₂>30,在频率f=2400 Hz以上频段,弹性散射分量对等效散射强度影响不超过3 dB;三壳与单壳的等效散射强度在0°入射角方位相当,其它方位三壳体等效散射强度明显大于单壳体。本文的理论公式可推广到任意数量阻抗柱的声透射和声反射问题。      

Effective dynamic properties of 3D composite materials containing rigid penny-shaped inclusions

The propagation of time-harmonic plane elastic waves in infinite elastic composite materials consisting of linear elastic matrix and rigid penny-shaped inclusions is investigated in this paper. The inclusions are allowed to translate and rotate in the matrix. First, the three-dimensional (3D) wave scattering problem by a single inclusion is reduced to a system of boundary integral equations for the stress jumps across the inclusion surfaces. A boundary element method (BEM) is developed for solving the boundary integral equations numerically. Far-field scattering amplitudes and complex wavenumbers are computed by using the stress jumps. Then the solution of the single scattering problem is applied to estimate the effective dynamic parameters of the composite materials containing randomly distributed inclusions of dilute concentration. Numerical results for the attenuation coefficient and the effective velocity of longitudinal and transverse waves in infinite elastic composites containing parallel and randomly oriented rigid penny-shaped inclusions of equal size and equal mass are presented and discussed. The effects of the wave frequency, the inclusion mass, the inclusion density, and the inclusion orientation or the direction of the wave incidence on the attenuation coefficient and the effective wave velocities are analysed. The results presented in this paper are compared with the available analytical results in the low-frequency range.     

Homogenization of Three-Dimensional Periodic Solid-Solid Elastic Composites

We develop an approach to homogenize three-dimensional periodic solid-solid elastic composites with cubic lattice at low frequencies, by using plane wave expansion and perturbation theory with respect to the long wavelength limit. Based on the fact that the two shear waves propagating along lattice axis are degenerated, we derive formulae for effective velocities parallel and normal to the lattice axis, from which three independent effective elastic moduli are calculated, respectively. Theoretical results, which take into account the multiple scattering and the structure of the periodic medium, are in good agreement with the previous isotropic theory at high-symmetry directions.     

Effective velocity of 2D phononic crystals with rectangular lattice

The effective velocity of elastic waves for two-dimensional (2D) phononic crystals with rectangular lattice in the long-wavelength limit is studied by numerical simulations. It is demonstrated that, for all three propagating modes, not only the modes polarized in-plane (L wave and SV wave), but also the mode polarized out-plane (SH wave), the effective velocities are distinctly anisotropic and the slowness curves exhibit twofold symmetry. The anisotropy increases as the filling fraction increases or as the width to length ratio of the lattice decreases, and high anisotropy can be obtained in phononic crystals with large contrast between material parameters, which is much higher in rectangular lattice than in square lattice with the same material parameters. Owing to these dependences, the effective velocity can be controlled in engineering.     

FREQUENCY DISPERSION CHARACTERISTICS OF PHASE VELOCITIES IN SURFACE WAVE FOR ROTATIONAL COMPONENTS OF SEISMIC MOTION

When rotational components of ground motion produced by seismic surface waves are computed, the phase velocities must always be dealt with in earthquake engineering. In this paper, appropriate methods are presented to obtain the calculation formulas for the phase velocities of surface waves by applying the theory of elastic wave propagation. Frequency dispersion characteristics of phase velocities are discussed. The rocking component around a horizontal axis and the torsional component around a vertical axis, which are generated, respectively, by the Rayleigh and Love waves, are reasonably given. A procedure is developed to calculate the time histories of these rotational components.     

Elastic waves in carbon 2D supracrystals

The elastic moduli and propagation velocities of elastic waves in 2D supracrystalline nanoallotropes of carbon have been calculated. It has been shown that these velocities in sp ² nanoallotropes are close to those in graphene and exceed the propagation velocities of elastic waves in single-crystal diamond by a factor of 2. The propagation velocities of both longitudinal and transverse elastic waves in carbon 2D supracrystalline sp ³ nanoallotropes are several times lower than those in sp ² nanoallotropes.     

The effect of a surface impedance load on the properties of quasi-Rayleigh waves

The propagation of quasi-Rayleigh waves along an impedance-loaded plane boundary of an isotropic elastic half-space is studied theoretically. The dispersion equation of these waves is derived with allowance for the fact that an impedance load has both normal and tangential components. The conditions for the existence of such waves are analyzed depending on the magnitude and nature of each of these components. Specific examples of calculating the quasi-Rayleigh wave velocities are considered: for the models of surface and bulk cracked media, for a fluid layer in an elastic medium, and for a resonant load.     

Scattering from very rough metallic and dielectric surfaces: a theory based on the modified Kirchhoff approximation

This paper presents a theory of scattering from very rough metallic and dielectric surfaces using the first- and second-order Kirchhoff approximations (KA) modified with the angular and propagation shadowing. The shadowing functions limit the single and double scattered waves which are illuminated and not shadowed by the surface. The theoretical results are compared with the Monte Carlo simulations showing the range of validity of the theory. The theory is applicable to the range where the RMS height is close to a wavelength and the RMS slope is close to unity, and the second medium is lossy. The second-order scattering includes two waves travelling in opposite directions on the surface, giving a physical explanation of the enhanced backscattering.     

非长波极限下二维光子晶体中横电模的等效介质理论

基于Mie散射理论, 推导、建立了适用于非长波极限的二维光子晶体中横电模的等效介质理论. 随后利用该理论探讨了二维光子晶体中横电模的负折射特性和零折射特性, 计算结果与相应的能带结构相符合, 验证了该理论在非长波极限条件下的适用性. 更进一步的是, 使用该理论能得到从能带结构中无法获取的额外信息.     

Characterization of single-crystalline GaAs by imaging with ballistic phonons

Ballistic phonon propagation in single-crystalline [001]-oriented gallium arsenide has been studied using low-temperature scanning electron microscopy for imaging. Deviations in the phonon focusing pattern due to dispersion effects were found by comparing the phonon images to theoretical calculations of the long-wavelength limit. The phonon propagation behavior in, samples cut from differently prepared wafers has been investigated. For highly impure crystals we found a pronounced increase of the diffusive signal component at the expense of the ballistic one. Samples with varying dislocation densities also showed a sensitive dependence, of the ballistic phonon propagation on these crystal defects. For focusing calculations considering elastic scattering processes the diffusivity of the phonons could be determined as a function of the mean scattering length. We have found phonon mean free paths of 0.35 mm to 0.80 mm for the various GaAs crystals.     

Time-domain numerical simulations of multiple scattering to extract elastic effective wavenumbers

Elastic wave propagation is studied in a heterogeneous two-dimensional medium consisting of an elastic matrix containing randomly distributed circular elastic inclusions. The aim of this study is to determine the effective wavenumbers when the incident wavelength is similar to the radius of the inclusions. A purely numerical methodology is presented, with which the limitations usually associated with low scatterer concentrations can be avoided. The elastodynamic equations are integrated by a fourth-order time-domain numerical scheme. An immersed interface method is used to accurately discretize the interfaces on a Cartesian grid. The effective field is extracted from the simulated data, and signal-processing tools are used to obtain the complex effective wavenumbers. The numerical reference solution thus obtained can be used to check the validity of multiple scattering analytical models. The method is applied to the case of concrete. A parametric study is performed on longitudinal and transverse incident plane waves at various scatterer concentrations. The phase velocities and attenuations determined numerically are compared with predictions obtained with multiple scattering models, such as the Independent Scattering Approximation model, the Waterman–Truell model, and the more recent Conoir–Norris model.