Analysis of sound absorption by periodic structures using a hybrid-boundary element/mode expansion method

An improved hybrid method is proposed for analyzing sound scattering by a periodic structure. Part of the scattered field formulated with the mode expansion method is combined with other components of the field formulated with the boundary integration method in one period of the structure. Structures treated by this method can have arbitrary periodic forms made of locally reactive boundaries and porous materials. The oblique incident absorption coefficient of the structure is obtained simply from the reflection factor calculated for each elemental wave of the scattered field. The accuracy of the method is demonstrated by the agreement between calculated and measured values of the normal absorption coefficient of some test structures.     

Electromagnetic wave scattering by large-scale inhomogeneities in a bragg cavity

We study the single scattering of a plane electromagnetic wave by random inhomogeneities in a plane periodically nonuniform layer with a reflecting rear boundary. It is shown that when the incident wave satisfies the condition of excitation of the fundamental Bragg cavity mode and its field is large in the layer depth, the average angular spectrum of the backscattered wave field at the cavity output has a narrow maximum proportional to the exponent of the quadruple optical thickness of the periodic structure. This maximum corresponds to the condition of excitation of the fundamental Bragg cavity mode by the scattered field. The other spectral maxima have small amplitudes and intensities. Such scattering takes place if the characteristic size of random inhomogeneities in the direction perpendicular to the layer boundary exceeds the scale of multiple scattering on a periodic structure. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 11, pp. 1342–1354, November, 1997.     

支撑介质对平面型电磁带隙结构带隙特性的影响

运用直线法对含有不同参数支撑介质的平面型电磁带隙（EBG）结构进行了分析.概述了算法的实现过程,使用周期边界条件隔离出一个结构单元作为计算区域,并利用直线法得到了位函数在各层介质界面间的传输方程.通过联立场分量与位函数的变换关系和界面处切向场分量的连续性条件,建立了本征方程, 得到了表征该EBG 结构表面波带隙的本征模频带图.同时,使用该方法对含有不同介电常数、不同厚度支撑介质的表面波带隙进行了计算.通过对计算结果的分析,得到了支撑介质对平面型EBG 结构带隙特性影响的六条结论,为平面型EBG 结构的设计 关键词： 超媒质 光子带隙 周期结构 表面波     

Propagation of acoustic waves in the woodpile sonic crystal with a defect

Acoustic wave propagation in a woodpile sonic crystal with a defect is studied theoretically and experimentally. The woodpile sonic crystal is composed of polymethyl methacrylate square rods which orthogonally stacked together, and it is embedded in air background. Defects are created by varying the width and positions of the middle rods in the periodic structure. Defect bands and transmission spectra are calculated by using the finite element method with the periodic boundary condition and the Bloch–Floquet theorem. Frequencies of defect bands are strongly dependent on the width and positions of the middle rods in the periodic structure. The experimental transmission spectra of the woodpile sonic crystals with a defect are also presented and compared with the numerical results. The defect mode properties of the woodpile sonic crystal with a defect can be applied to design novel acoustic devices for filtering sound and trapping sound in defects.     

基于波传播法的周期复合板振动带隙衰减特性研究

运用波传播法对有限和无限周期对边简支复合板的振动带隙衰减特性进行了研究.在建立相邻板结构边界连续方程的基础上, 分别运用传递矩阵和Bloch定理建立了有限和无限周期复合板的耦合运动方程, 并详细对比分析了有限和无限周期复合板带隙衰减特性的关联关系.研究表明: 周期板结构的振动带隙频率范围与激励方式和激励位置是相关的, 若周期复合板在宽度方向按某阶模态进行线激励, 则该激励下的振动带隙与无限周期复合板在该阶模态下的振动带隙是一致的; 若周期板在点激励作用, 则该点激励下的振动带隙是参与振动的各阶模态振动带隙的交集. 此外, 还进一步研究了结构阻尼对振动衰减带隙的影响. 关键词： 周期复合板 带隙衰减特性 波传播法 结构阻尼     

Periodically structured X‐ray waveguides

The properties of X‐ray vacuum‐gap waveguides (WGs) with additional periodic structure on one of the reflecting walls are studied. Theoretical considerations, numerical simulations and experimental results confirm that the periodic structure imposes additional conditions on efficient propagation of the electromagnetic field along the WGs. The transmission is maximum for guided modes that possess sufficient phase synchronism with the periodic structure (here called `super‐resonances'). The field inside the WGs is essentially given at low incidence angle by the fundamental mode strongly coupled with the corresponding phased‐matched mode. Both the simulated and the experimental diffraction patterns show in the far field that propagation takes place essentially only for low incidence angles, confirming the mode filtering properties of the structured X‐ray waveguides.     

Tunneling of electromagnetic waves through a barrier with a periodic structure

The propagation of an electromagnetic wave through a barrier with a periodic structure is considered. An interesting manifestation of electromagnetic wave tunneling through a barrier with a periodic structure is revealed. Specifically, it is theoretically and experimentally shown that, when an electromagnetic wave passes through a medium with a periodic structure in the diffraction mode within a photonic band gap, the field in the medium is localized near its boundaries. Theoretical calculations have been performed for a cholesteric liquid crystal layer of finite thickness and for a 1D photonic crystal. The experiment was carried out with perfect Si single crystals in reflection from the $ (2\bar 20)$ (2\bar 20) and $ (4\bar 40)$ (4\bar 40) planes using MoK _α X rays.     

管间界面特性对周向超声导波传播特性的影响

采用界面弹簧模型对圆管结构的管间界面特性进行描述, 推导出含弱界面的圆管结构中声波沿周向传播时的位移场及应力场的数学表达式. 在此基础上采用导波的模式展开分析方法, 给出了与管间界面特性及激励源密切相关的周向超声导波模式展开系数的解析表达式. 数值分析了管间界面特性的变化对周向超声导波的频散和声场产生的影响. 理论与数值分析结果表明, 通过选择适当的驱动频率及周向导波模式, 可使周向超声导波的相速度及圆管外表面的位移场随管间界面特性的变化表现出非常敏感且单调的性质. 这一结果有助于采用周向超声导波方法准确定征圆管结构的管间界面特性.     

Coupled THz Waveguide Utilizing Surface Plasmon Polaritons on Thin Dielectric Slab Sandwiched between Two Corrugated Metallic Claddings

We present a comprehensive experimental study of terahertz （THz） wave propagation utilizing surface plasmon polaritons （SPPs） on the interfaces of a thin dielectric core layer sandwiched between two corrugated metallic claddings. THz wave impinges on the structured surfaces at normal incidence. Long-lasting oscillation propagation features are observed in the temporal waveform after traveling through the periodic arrays. The enhanced THz transmission can be achieved due to the coupling between incident waves to SPPs at the bottom and top interfaces. The finite element method is used to simulate the field distribution and the transmission mode in the waveguide. The hybrid waveguide with low absorption has great potential applications in THz integrated devices.     

合成冷/热射流控制超声速边界层流动稳定性

为了探究超声速边界层流动稳定性及其转捩控制机理,提出基于合成冷/热射流的边界层速度-温度耦合控制方法,并通过数值模拟研究了Ma=4.5超声速平板边界层不稳定波的传播,采用线性稳定性理论中的时间模式分析了壁面吹吸、射流温度、扰动频率、扰动振幅等对不稳定波控制效果的影响.结果表明:无射流控制时,边界层内同时存在不稳定的第一模态扰动波和第二模态扰动波,且二维波形式的第二模态占主导地位;壁面吹吸作用下,仅出现更加不稳定的第二模态,第一模态被抑制;速度-温度耦合控制下,射流温度对扰动模态的不稳定区域大小及扰动增长率影响显著,射流温度与来流温度不同时,温度的脉动使得流动转捩为湍流的速度加快,边界层速度型更加饱满,抗干扰能力增强,流动稳定性提高;高频的吹吸扰动对流场的控制效果优于低频扰动,扰动频率超过400 Hz时,第二模态扰动波时间增长率降低,扰动分量对边界层速度剖面和温度剖面的修正加快,第二模态更加稳定;扰动振幅减小为主流速度的1%时,仅出现时间增长率较小的第二模态,控制效果较好,进一步减小时,第一模态重新出现,并且波数范围与第二模态先重合后分离,对应的时间增长率先增加后减小.研究结果为边界层转捩控制技术提供了新的思路.     

A Model for Periodic Nonlinear Electric Field Structures in Space Plasmas

In this study, we present a physical model to explain the generation mechanism of nonlinear periodic waves with a large amplitude electric field structures propagating obliquely and exactly parallel to the magnetic field. The ``Sagdeev potential' fromthe MHD equations is derived and the nonlinear electric field waveforms are obtained when the Mach number, direction of propagation, and the initial electric field satisfy certain plasma conditions. For the parallel propagation, the amplitude of theelectric field waves with ion-acoustic mode increases with the increase of initial electric field and Mach number but its frequency decreases with the increase of Mach number. The amplitude and frequency of the electric field waves with ion-cyclotron mode decrease with the increase of Mach number and become less spiky, andits amplitude increases with the increase of initial electric field. For the oblique propagation, only periodic electric field wave with an ion-cyclotron mode obtained, its amplitude and frequency increase with the increase of Mach number and become spiky. From our model the electric field structures show periodic, spiky, and saw-tooth behaviours corresponding to different plasma conditions.     

Exact wave-based Bloch analysis procedure for investigating wave propagation in two-dimensional periodic lattices

This paper presents an exact, wave-based approach for determining Bloch waves in two-dimensional periodic lattices. This is in contrast to existing methods which employ approximate approaches (e.g., finite difference, Ritz, finite element, or plane wave expansion methods) to compute Bloch waves in general two-dimensional lattices. The analysis combines the recently introduced wave-based vibration analysis technique with specialized Bloch boundary conditions developed herein. Timoshenko beams with axial extension are used in modeling the lattice members. The Bloch boundary conditions incorporate a propagation constant capturing Bloch wave propagation in a single direction, but applied to all wave directions propagating in the lattice members. This results in a unique and properly posed Bloch analysis. Results are generated for the simple problem of a periodic bi-material beam, and then for the more complex examples of square, diamond, and hexagonal honeycomb lattices. The bi-material beam clearly introduces the concepts, but also allows the Bloch wave mode to be explored using insight from the technique. The square, diamond, and hexagonal honeycomb lattices illustrate application of the developed technique to two-dimensional periodic lattices, and allow comparison to a finite element approach. Differences are noted in the predicted dispersion curves, and therefore band gaps, which are attributed to the exact procedure more-faithfully modeling the finite nature of lattice connection points. The exact method also differs from approximate methods in that the same number of solution degrees of freedom is needed to resolve low frequency, and arbitrarily high frequency, dispersion branches. These advantageous features may make the method attractive to researchers studying dispersion characteristics, band gap behavior, and energy propagation in two-dimensional periodic lattices.     

SH-wave propagation and scattering in periodically layered composites with a damaged layer

Plane SH-wave propagation in periodically layered elastic composites with a damaged layer is investigated. Two different models are developed to approximate the damaged layer, namely, a periodic array of cracks and continuously distributed springs in the layer. In the first model, the total wave field in the elastic stack of layers with cracks is described as a sum of incident wave field modeled by the transfer matrix method and the scattered wave field governed by an integral representation in terms of the crack-opening-displacements on the crack-faces. The integral equation derived from the boundary conditions on the crack-faces is solved numerically by a Galerkin method. By using Bloch–Floquet theorem the crack-opening-displacements for a periodic array of cracks are expressed by the crack-opening-displacement on a reference crack. In the spring model, the spring constant is estimated by the material properties and the crack density and the modified transfer matrix method is used to compute the wave reflection and transmission coefficients. Numerical results obtained by both models are presented and discussed. Special attention of the analysis is devoted to wave transmissions and reflections, band gaps, wave localization and resonance phenomena due to damages. The influences of the damage types (periodic cracks and stochastic cracks approximated by distributed springs) on the wave field pattern and the band gaps are analyzed.     

Trifurcation of band-gap structure and coexistence of lattice-like states and critical states in piezoelectric period-doubling superlattices

We study the propagation of electromagnetic wave in piezoelectric period-doubling superlattices with using the generalized 4 × 4 transfer matrix method, and the dynamics of electromagnetic wave and acoustic wave is treated on equal footing. The band-gap structure trifurcates, which is understood within the framework of perturbation theory under periodic boundary condition. The uncoupled phononic branch of field distributions is Bloch-wave-like. For the coupled polaritonic branch, the lattice-like field distributions, for which Thue-Morse sequence is famous, also manifest in this piezoelectric period-doubling system and coexist with critical states. They can be characterized as extended if the superlattice size considered is large enough. In fact, our study suggests that such lattice-like field distributions are common phenomena in piezoelectric superlattices irrespective of lattice types and depend only on the frequency and domain widths, they reflect the intrinsic symmetry of the transfer matrices for the particular domain setting and frequency.     

修正的频域有限差分法在二维金属光子晶体分析中的应用

与介质光子晶体相比,金属光子晶体的带隙特性在毫米波和亚毫米波波段有着重要的应用价值.基于Yee网格的频域有限差分法推导得出的本征模方程,求解后能方便而又可靠地得出介质光子晶体的带隙图和场分布.但由于金属与介质的本质差异,该方法不能直接应用于金属光子晶体.文中引入了金属表面边界条件,推导了二维金属周期结构的光子带隙本征模方程.通过数值计算,得出了不同晶格结构（正方/三角格子）下两种模式（TE/TM）的全禁带特性,并与介质周期结构的禁带特性进行对比,分析了金属周期结构在模式选择和器件集成方面的优点. 关键词： 金属光子晶体 频域有限差分法 全禁带     

修正的频域有限差分法在二维金属光子晶体分析中的应用

与介质光子晶体相比,金属光子晶体的带隙特性在毫米波和亚毫米波波段有着重要的应用价值.基于Yee网格的频域有限差分法推导得出的本征模方程,求解后能方便而又可靠地得出介质光子晶体的带隙图和场分布.但由于金属与介质的本质差异,该方法不能直接应用于金属光子晶体.文中引入了金属表面边界条件,推导了二维金属周期结构的光子带隙本征模方程.通过数值计算,得出了不同晶格结构（正方/三角格子）下两种模式（TE/TM）的全禁带特性,并与介质周期结构的禁带特性进行对比,分析了金属周期结构在模式选择和器件集成方面的优点.     

Spectrum and losses of surface magnetostatic waves in a 1D magnon crystal

The spectrum and propagation losses of a surface magnetostatic wave in a 1D ferrite magnon crystal are experimentally studied as a function of angle φ between the wavevectors of the surface magnetostatic wave and periodic crystal lattice. Variation in the positions of Bragg forbidden bands with angle φ is described. A wide transmission band is discovered near long-wave frequency boundary f ₀ of the surface magnetostatic wave in a narrow interval of angles around φ ≈ 57°. In the interval 70° < φ < 90° and at frequencies below f ₀, there exists a magnetostatic wave with a wavevector that is normal to the bias field.     

The field of radiative forces and the acoustic streaming in a liquid layer on a solid half-space

The acoustic field and the field of radiative forces that are formed in a liquid layer on a solid substrate are calculated for the case of wave propagation along the interface. The calculations take into account the effects produced by surface tension, viscous stresses at the boundary, and attenuation in the liquid volume on the field characteristics. The dispersion equations and the velocities of wave propagation are determined. The radiative forces acting on a liquid volume element in a standing wave are calculated. The structure of streaming is studied. The effect of streaming on small-size particles is considered, and the possibilities of ordered structure formation from them are discussed.     

一维周期结构散射近-远场外推的两种方法

 首先讨论了自由空间中一维周期结构近-远场外推的Floquet模方法,即对FDTD计算所得散射近场中输出边界上散射场进行级数展开,求出各阶Floquet模的复数幅值,再求得远区场。接着介绍了求解一维周期结构远区散射场的周期Green函数方法,即根据FDTD计算所得散射近场中输出边界上散射场,求得等效面电磁流后,再借助周期Green函数进行外推得到远区场。两种方法均仅用一个周期单元内的散射近场进行外推。计算结果验证了上述两种方法外推的有效性。     

Analysis of wave propagation in a thin composite cylinder with periodic axial and ring stiffeners using periodic structure theory

Wave propagation characteristics of a thin composite cylinder stiffened by periodically spaced ring frames and axial stringers are investigated by an analytical method using periodic structure theory. It is used for calculating propagation constants in axial and circumferential directions of the cylindrical shell subject to a given circumferential mode or axial half-wave number. The propagation constants corresponding to several different circumferential modes and/or half-wave numbers are combined to determine the vibrational energy ratios between adjacent basic structural elements of the two-dimensional periodic structure. Vibration analyses to validate the theoretical development have been carried out on sufficiently detailed finite element model of the same dimension and configuration as the stiffened cylinder and very good agreement is obtained between the analytical and the dense finite element results. The effects of shell material properties and the length of each periodic element on the wave propagation characteristics are also examined based on the current analytical approach.