Interaction of ultrasonic wave with void-containing layer in solid

Using a general mode for sound reflection from multilayered media,we present in this paper the expressions for sound reflection and transmissioncoefficients on void-containing interface layer in solid and derive the character-istic equation for symmetric and antisymmetric modes of the interface wavesalong the layer.The method for evaluating the effective elastic moduli ofvoid-containing solid is also introduced.The numerical calculation given in thispaper shows the influences of the void volume concentration and layer thick-ness on the sound reflection coefficients and interface wave velocity,providing atheoretical basis for inverse of the mechanical properties of void-containinglayer based on the ultrasonic measurement.     

正交各向异性板液/固界面的声反射与声透射

采用Legendre正交多项式法,对液/固界面声波反射和透射系数进行求解。利用Legendre正交多项式对正交各向异性板中的位移解进行展开,推导出板中的应力和波动控制方程。联立液/固界面的边界条件和波动控制方程,建立线性无关方程组,用以计算液/固界面的反射和透射系数及Legendre多项式的展开系数,计算所得铝板液/固界面的反射和透射系数与传递矩阵法的计算结果吻合良好。以单向纤维增强复合材料板为例,在不同的方位角下,分析了反射和透射系数随斜入射角度、入射波频率的变化关系,以及板中声场的位移分布。所取Legendre正交多项式截止阶数越大,可用来计算的频厚积范围越大。研究拓展了Legendre正交多项式法的适用范围,为材料力学性能的声学测量提供了理论基础。      

Coherent Transmission and Reflection by a monolayer of discrete scatterers

Coherent transmission and reflection of a plane wave through a monolayer of discrete particles are considered on the basis of simple and physically transparent formulae for the single scattering approximation (SSA) corrected by introducing a multiple scattering permittivity factor. This factor allows for multiple scattering of Waves between monolayer particles, opposite to the SSA. The multiple scattering permittivity factor is considered on the basis of the quasi-crystalline approximation (QCA) via ? matrix formalism. The multiple scattering permittivity factor and parameters for obtaining coherent transmission and reflection coefficients (the effective extinction coefficient and the transmission and reflection coefficients due to rescattering) are calculated within the scope of QCA and plotted for comparison with SSA results. The expressions for these values are simplified for small Rayleigh particles to simple analytical formulae.     

Normal modes of a poroelastic plate and their relation to the reflection and transmission coefficients

A poroelastic plate that obeys the Biot theory is considered. Compact new forms of its reflection and transmission coefficients, similar to those of the resonance scattering theory for an elastic plate, are derived. A numerical comparison of the reflection coefficient modulus with the plate normal modes, at low frequency, shows that a study of the reflection or transmission coefficient does not provide the same kind of information on the poroelastic plate than an investigation of guided leaky waves propagation.     

A generic approach to boundary reflection in periodic media

Waves in periodic media, whose propagation is governed by nearest neighbour interaction, are investigated. The reflection and transmission coefficients are derived for a plane wave incident from medium 1 upon medium 2, without invoking common approximations. The derivation is valid for a class of waves including magneto- and electro-inductive waves, waves on short loaded dipoles, nanoparticles, coupled waveguides and acoustic waves in monatomic media. For this last case hitherto unknown microscopic reflection and transmission coefficients are derived and shown to reduce in the continuous limit to the well-known expressions in terms of acoustic impedances.     

Elastic resonances of a periodic array of fluid-filled cylindrical cavities embedded in an elastic matrix

The resonant scattering by a periodic infinite array of fluid-filled cylindrical cavities in an elastic matrix is studied. The exact reflection and transmission coefficients of the array are calculated by means of a multiple scattering formalism taking into account all the interactions between the cavities. Numerical results are next given for low frequencies for which only the longitudinal and transverse zero modes propagate. A first study based on the analysis of the transmission coefficients clearly shows that the resonances of the array can be classified into two sets: those close to the resonances of a single cavity and those due to a resonant coupling between a cavity and its nearer neighbors. The resonant coupling is due to the interaction between the whispering-gallery surface waves propagating around each cavity. In the case of cavities with very close spacing, it is observed that the dispersion curves of the waves propagating along the array can also be classified into two sets: those with a positive group velocity have cut-off frequencies that correspond to the resonances of a single cavity, those with a negative group velocity have cut-off frequencies that correspond to the resonances resulting from the strong coupling. A new method for the analysis of the resonances is presented. It is based on the properties of the scattering matrix and consists in studying the resonant eigenvalues of the scattering matrix of the array once the background is removed. For the detection of very fine resonances, as well as in the separation of several resonances very close to each other, this method proves to be more efficient than one based on the analysis of the reflection and transmission coefficients.     

各向异性表面光学的格林函数公式及其应用

本文通过对麦克思韦方程组的变换和反演得到各向异性介质的表面光学格林函数.用它计算辐射场可以直接得到s和p偏振波的表示式,因而在计算界面效应时可以自然地引入菲涅耳系数.作为应用,本文计算了当存在界面和薄膜时极化所产生的辐射场.     

Deformation Features on the Free Surface and Rigid Interface during Elastic Wave Reflection

Analytical expressions defining the reflection coefficients have been derived in the framework of the known problem of elastic wave reflection from the free surface and rigid interface. The found reflection coefficients are used to analyze the dependences of different strain and rotation components during elastic wave reflection from the free surface and rigid interface in the case of ideal contact and possible slip on the wave incidence angle and elastic parameters of the medium. Deformation features of elastic media at the studied interfaces are considered for incident longitudinal and transverse waves.     

超声与固体中含气泡层的相互作用

本文利用固体层状媒质声反射模型,给出了固体中含气泡层声反射和透射系数的表达式,并由此导出沿固体中含气泡薄层对称和反对称模式界面波的特征方程式。本文还介绍了含气泡固体有效弹性模量的估算方法,文中给出的数值计算具体说明了气泡体积浓度和气泡层厚度对声反射系数、声透射系数以及反对称模式界面波传播速度的影响,本文的研究为根据声反射系数和界面波的传播速度的测量反演固体间气泡层的力学性能提供了理论依据。 关键词：     

Calculations of the reflection and transmission of ultrasound by cracks in steel filled with solid sodium

The reflection and transmission coefficients are calculated for 2.25 MHz compression and shear waves incident on idealized cracks (ie, a slot with smooth, flat, parallel faces) in steel filled with solid sodium. The coefficients are calculated as a function of crack width and angle of incidence. Both polarizations (SV and SH) of shear wave are considered, as well as compression wave incidence. It is concluded that a crack of width 0.01 mm or greater, full of solid sodium, will return at least 10% of the incident compression wave amplitude. With a suitable choice of inspection angle, 40% reflection of the incident amplitude can be achieved for either compression or shear (SV) waves. The use of shear waves with the uncommon SH polarization also looks promising.     

广义传播矩阵法分析分层各向异性材料对电磁波的反射与透射

在实验室坐标系下由Maxwell旋度方程出发构造了横向场的状态矢量和耦合矩阵,讨论了各 向异性介质中的特征波.通过引入横向场的传播矩阵,进而得到分层各向异性介质的反射系数和透射系数的解析表达式.该式可以适用于一般情况,包括分层单轴各向异性材料和回旋介质,以及半空间各向异性介质的反射和透射问题. 关键词： 广义传播矩阵 各向异性介质 反射与透射     

Attenuation coefficient estimation using experimental diffraction corrections with multiple interface reflections

The ultrasonic attenuation coefficient of a fluid or solid is an acoustic parameter routinely estimated for the purpose of materials characterization and defect/disease detection. This paper describes a broadband attenuation coefficient estimation technique that combines two established estimation approaches. The key elements of these two approaches are: (1) the use of magnitude spectrum ratios of front surface, first back surface, and second back surface reflections from interfaces of materials with plate-like geometries, and (2) the use of an experimental diffraction correction approach to avoid diffraction losses. The combined estimation approach simplifies the attenuation coefficient estimation process by eliminating the need to explicitly make diffraction corrections or calculate reflection/transmission coefficients. The approach yields estimates of the attenuation coefficient, reflection coefficient, and material density. Models, experimental procedures, and signal analysis procedures, which support implementation of the approach, are presented. Attenuation coefficient and reflection coefficient estimates are presented for water and solid samples with estimates based on measurements made with multiple transducers.     

Reflection and transmission of phonons at a planar interface between two dissimilar solids

Two semi-infinite dissimilar crystals with, however, the same crystal structure and lattice parameter are in contact at a planar interface. Using a simple force constant model, restricted to near-neighbour interaction reflection and transmission coefficients for sound waves propagating along one solid are calculated. At low frequencies the reflection and transmission coefficients are determined solely by the force constants and the atomic masses in the two media. At high frequencies the transmission coefficient becomes small if the force constant at the interface between the two media is weak. Information of the local force constant in the interface region can be gained at least in principle, by measuring the reflection and transmission coefficients at high frequencies.     

Calculation of amplitudes of acoustic normal modes from the reciprocity principle

Recently, J. D. Achenbach [J. Acoust. Soc. Am. 116, 1481-1487 (2004)] put forward, on heuristic grounds, an elegant technique to calculate amplitudes of guided waves in an elastic solid. The technique is based on application of the reciprocity principle. In this article, the technique is applied to acoustic waveguides. A mathematical justification of the technique is obtained. The technique is extended to enable calculation of excitation coefficients of modes of both discrete and continuous spectra by a given sound source. The results are shown to be identical to those derived with the traditional methods that rely on integral transforms.     

Reflection of structural waves at a solid/liquid interface

This paper investigates the reflection characteristics of structural or guided waves in rods at a solid/liquid interface. Structural waves, whose wavelengths are much larger than the diameter of the rod, are described in a first approximation by classical one-dimensional wave theory. The reflection characteristics of such waves at a solid/liquid (melting) interface has been reported by two different ultrasonic measurement techniques: first, measuring the fast regression rate of a melting interface during the burning of metal rod samples in an oxygen-enriched environment, and second, monitoring the propagation of the solid/liquid interface during the slow melting and solidification of a rod sample in a furnace. The second work clearly shows that the major reflection occurs from the solid/liquid interface and not the liquid/gas interface as predicted by plane longitudinal wave reflectivity theory. The present work confirms this observation by reporting on the results of some specially designed experiments to identify the main interface of reflection for structural waves in rods. Hence, it helps in explaining the fundamental discrepancy between the reflection characteristics at a solid/liquid interface between low frequency structural waves and high frequency bulk waves, and confirms that the detected echo within a burning metallic rod clearly represents a reflection from the solid/liquid interface.     

一维准周期结构声子晶体透射性质的研究

提出了一维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了数值计算，并与周期结构的透射系数进行了比较.计算结果表明，弹性波通过一维准周期结构声子晶体时，同样会有带隙的出现，且带隙所在频率范围与周期结构的情形完全一样，不同的是在准周期结构声子晶体中，带隙内有很强的局域共振模.对此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： 准周期结构 声子晶体 局域化     

One-sided omnidirectional constant transmission between two isotropic media

In this paper, the reflection and transmission at the planar interface between an isotropic achiral medium (IAM) and an isotropic chiral medium (ICM) are theoretically studied. For one of the circularly polarized (CP) waves fullfilling the wavenumber matching condition incident from IAM with incident angle from 0 to π/2, the amplitude reflection and transmission coefficients are constant. The phenomenon is called the omnidirectional constant transmission (OCT). In the situation of CP waves incident from ICM, OCT will not occur, but the absolute values of the amplitude reflection and transmission coefficients can be constants in a range of incident angle under certain conditions. It is suggested that for OCT to occur, both the wavenumber matching condition and the mode matching condition should be satisfied.     

On the theory of X-ray coherent reflection from a rough surface

A solution of the problem of X-ray specular reflection from a statistically rough surface is presented. It is based on using the Green function formalism. The Kirchhoff formula is used to describe the transmission of the wave field through a rough interface. Generally, microscopically exact expressions for the coefficients of transmission through a rough surface and reflection from it are obtained by taking multiple scattering effects into account. Averaging of the obtained expressions over possible realizations of random roughness of the interface between media allows to obtain rigorous expressions for specular reflection and transmission coefficients. The behavior of exact solutions in the limiting case of infinite correlation lengths is studied. It is shown that, in this case, the obtained solution corresponds to the Debye-Waller normalization. Expressions for the reflection and transmission coefficients making it possible to carry out numerical calculations are obtained in the Bourret approximation of multiple-scattering theory.     

A New Method for Calculation of Single Seismic Phase of Cylindrically Multilayered Media Including Liquid Interlayer

A new method based on generalized reflection and transmission （R/T） coefficients method is proposed to calculate the single seismic phase （SSP） of cylindrically multilayered media including liquid interlayer. The use of normalization factors and normalized Lamé coefficients makes the algorithm stable numerically. Using the modified R/T matrices, we derive the iterative expressions of generalized R/T matrices, and by using the iterative relation we determine the SSP of each interface and the full waveforms. To show the superiority of this new approach for investigating of reflection and transmission properties of cylindrically multilayered media, we simulate the full waveforms and SSPs of cased hole model with annulus I （casing-cement interface） channelling （or, cross-flow）. The generalized reflection coefficient spectra and SSPs of interfaces obtained show the propagation mechanism of each component of full waveform clearly.     

A concise and efficient scattering matrix formalism for stable analysis of elastic wave propagation in multilayered anisotropic solids

This paper presents a concise and efficient scattering matrix formalism for stable analysis of elastic wave propagation in multilayered anisotropic solids. The formalism is capable of resolving completely the numerical instability problems associated with transfer matrix method, thereby obviating the extensive reformulation in its modified versions based on delta operator technique. In contrast to the earlier reflection matrix formalisms, all scattering matrices are obtained in a direct manner without invoking wave-propagator or scatterer operator concepts. Both local and global reflection and transmission matrices corresponding to scatterings in two and more layers are derived. The derivation of global scattering matrices in terms of the local ones is carried out concisely based on physical arguments to provide better insights into scattering mechanism. Another formulation which is even more succinct is also devised for obtaining the global scattering matrices directly from eigensolutions. The resultant expressions and algorithm are terse, efficient and convenient for implementation.