Reflection and transmission of waves from a plane interface between two microstretch solid half-spaces

In this paper, we have investigated the wave propagation and their reflection and transmission from a plane interface between two different microstretch elastic solid half-spaces in perfect contact. It is shown that there exist five waves in a linear homogeneous isotropic microstretch elastic solid, one of them travel independently, while other waves are two sets of two coupled waves. It is also shown that these waves travel with different velocities, three of which disappear below a critical frequency. Amplitude ratios and energy ratios of various reflected and transmitted waves are presented when a set of coupled longitudinal waves and a set of coupled transverse waves is made incident. It is found that the amplitude ratios of reflected and transmitted waves are functions of angle of incidence, frequency and are affected by the elastic properties of the media. Some special cases have been reduced from the present formulation.     

Reflection and transmission of nonlinear waves from arterial branching

In this work, treating the arteries as a prestressed thin walled elastic tube and the blood as an inviscid fluid, we have studied the reflection and transmission of nonlinear waves from arterial branching, through the use of reductive perturbation method. The reflected and the transmitted waves at the bifurcation point are calculated in terms of the incident wave. The numerical results indicate that the reflected wave is comparatively small whereas the transmitted waves in branches are comparable with the incident wave. This result is quite consistent with the experimental measurements [N. Sergiopulos, M. Spiridon, F. Pythoud, J.J. Meister, On wave transmission and reflection properties of stenosis, J. Biomech. 26 (1996) 31-38].     

Effect of Columnar Grain Orientation on Ultrasonic Plane Wave Energy Reflection and Transmission Behaviour in Anisotropic Austenitic Weld Materials

This article describes a comprehensive quantitative analysis on effect of columnar grain orientation on ultrasonic plane wave energy reflection and transmission behaviour in acoustically anisotropic austenitic weld materials. The quantitative results are presented for following general interfaces (a) Isotropic-Anisotropic, (b) Anisotropic-Isotropic, (c) Fluid-Anisotropic, (d) Anisotropic-Fluid, (e) Anisotropic-Anisotropic, (f) Anisotropic-Free surface occur during the ultrasonic non destructive evaluation of austenitic weld materials. Explicit analytical expressions are presented for energy reflection and transmission coefficients at an interface between two arbitrarily oriented transversely isotropic materials. By applying explicit analytical expressions for energy reflection and transmission coefficients, numerical results are presented for several columnar grain orientations of the transverse isotropic austenitic weld material including both real and complex domain of the reflected and transmitted normal component of slowness vectors. Valid domains of incident wave vector angles, angular dependency of energy reflection and transmission coefficients and critical angles for reflected and transmitted waves are discussed. The existence of a reflected (or) transmitted second branch of quasi shear vertical waves and its consequence to the ultrasonic non destructive testing of austenitic weld materials are investigated. The presented comprehensive quantitative evaluation provides an overview on the effect of anisotropic properties on energy reflection and transmission coefficients in columnar grained austenitic weld materials.     

Nondiffracting X waves-exact solutions to free-space scalar wave equation and their finite aperture realizations

The authors report families of generalized nondiffracting solutions of the free-space scalar wave equation, and specifically, a subset of these nondiffracting solutions, which are called X waves. These nondiffracting X waves can be almost exactly realized over a finite depth of field with finite apertures and by either broadband or bandlimited radiators. With a 25-mm diameter planar radiator, a zeroth-order broadband X wave will have about 2.5-mm lateral and 0.17-mm axial -6-dB beam widths with a -6-dB depth of field of about 171 mm. A zeroth-order bandlimited X wave was produced and measured in water by a 10 element, 50-mm diameter, 2.5-MHz PZT ceramic/polymer composite J (0) Bessel nondiffracting annular array transducer with -6-dB lateral and axial beam widths of about 4.7 mm and 0.65 mm, respectively, over a -6-dB depth of field of about 358 mm. Possible applications of X waves in acoustic imaging and electromagnetic energy transmission are discussed.     

Elastic wave and energy propagation in angled beams

This investigation comprises an experimental and numerical study of elastic wave propagation in angled beams. Axial impact by two strikers of different lengths was applied to three steel beams, each bent to incorporate a “V” section of different angle in the middle. Finite element simulation using ABAQUS was employed to examine details of the elastic waves generated in the impact tests. The numerical results correlated well with experimental data, and computational simulation was utilized to analyse the propagation of energy associated with the elastic waves. This demonstrated that after several reflections from and transmission across the bends energy is progressively smeared throughout the entire beam and does not concentrate at any particular segment; the bulk of the energy is conveyed via flexural waves. Numerical simulation of wave propagation in a beam with a single angle was also undertaken to study the energy associated with waves reflected from and transmitted across the bend, and how these are affected by the bend angle. The effects of input pulse duration, beam thickness and beam material properties on energy reflection and transmission at a bend are also discussed; this leads to the conclusion that when a longitudinal pulse of a particular frequency impinges on a bend, the ratio between its wavelength and the beam thickness governs the energy reflected from and transmitted across the bend. Moreover, the bend junction geometry (curvature) is found to have a significant influence on the energy reflected and transmitted, especially for obtuse bend angles.     

Effect of a submerged vertical barrier on flexural gravity waves

An explicit solution is provided for the scattering of flexural gravity waves by a rigid vertical barrier submerged in an infinite depth of water. By applying recently developed mode-coupling relation for eigenfunctions, the mixed boundary value problem has been converted to solve dual integral equations with kernel consisting of trigonometric functions. And then complete analytical solutions are derived with an aid of singular integral equations whose solutions are bounded at the end points. The important hydrodynamical scattering quantities such as reflection and transmission coefficients associated with the flexural gravity wave scattering have been obtained analytically in terms of modified Bessel functions and Struve functions. It is observed that these quantities are sensitive to both combined as well as individual effect of plate thickness and barrier depth of submergence. Numerical results are computed and explained graphically for different parameters such as time period and non-dimensional wave length. Further, the effect of compressive force and plate thickness on the flexural gravity waves against a submerged vertical barrier is studied.     

The laws of plane defect wave propagation across the interface between two viscoplastic media

Relations determining the laws of reflection and refraction of a plane wave in the defect field at an interface between two viscoplastic media are obtained based on the dynamic equations of the continuum theory of defects. The reflection and transmission coefficients relating the amplitudes of reflected and transmitted waves to the incident wave amplitude are determined. The obtained relations are applied to a particular case of media with weakly decaying waves.     

Reflection and transmission of ultrasound by a region of damaged material

Reflection and transmission of ultrasonic waves by a layer-like region of distributed microcracks in a bulk material has been investigated. It has been assumed that for sufficiently low frequencies and far away from the damaged layer, the reflected and transmitted waves are plane waves. By applying the Betti reciprocal theorem to a cell containingN cracks, and by choosing one elastodynamic state as the actual wave state and the other as a suitably chosen auxiliary wave state, the reflection and transmission coefficients have been expressed in terms of integrals over theN cracks. Simple expressions have been obtained for the case that all cracks are identical and parallel to each other. For the case that the cracks do not interact with each other, numerical results for the reflection and transmission coefficients are presented for a distribution of penny-shaped cracks. The variation of these coefficients with frequency, relative layer thickness and angle of incidence has been displayed in graphs.     

Acoustic scattering in a waveguide with a height discontinuity bridged by a membrane: a tailored Galerkin approach

This article is concerned with the reflection and the transmission of fluid–structure-coupled waves at the junction between two flexible waveguides of different heights. Unlike previous studies, in which the waveguides are joined at the height discontinuity by a rigid or soft strip, in this study, the height discontinuity is bridged by a membrane. The aims are first to develop a solution method that enables a wide range of conditions to be applied at the edges of the bridging membrane and then to ascertain the effects that these have on the reflected and the transmitted fields. Numerical results are presented which confirm that that the conditions applied at the edges of the bridging membrane do have significant effects on the reflected and the transmitted components of power.     

Generating Bessel beams by use of localized modes

We propose a novel method for generating both propagating and evanescent Bessel beams. To generate propagating Bessel beams we propose using a pair of distributed Bragg reflectors (DBRs) with a resonant point source on one side of the system. Those modes that couple with the localized modes supported by the DBR system will be selectively transmitted. This is used to produce a single narrow band of transmission in kappa space that, combined with the circular symmetry of the system, yields a propagating Bessel beam. We present numerical simulations showing that a propagating Bessel beam with central spot size of approximately 0.5lambda0 can be maintained for a distance in excess of 3000lambda0. To generate evanescent Bessel beams we propose using transmission of a resonant point source through a thin film. A transmission resonance is produced as a result of the multiple scattering occurring between the interfaces. This narrow resonance combined with the circular symmetry of the system corresponds to an evanescent Bessel beam. Because propagating modes are also transmitted, although the evanescent transmission resonance is many orders of magnitude greater than the transmission for the propagating modes, within a certain distance the propagating modes swamp the exponentially decaying evanescent ones. Thus there is only a certain regime in which evanescent Bessel beams dominate. However, within this regime the central spot size of the beam can be made significantly smaller than the wavelength of light used. Thus evanescent Bessel beams may have technical application, in high-density recording for example. We present numerical simulations showing that with a simple glass thin film an evanescent Bessel beam with central spot size of approximately 0.34lambda0 can be maintained for a distance of 0.14lambda0. By choice of different material parameters, the central spot size can be made smaller still.     

Wave propagation in joined thin dissimilar elastic tubes containing viscous fluid

The aim of the present paper is to investigate theoretically the reflection and transmission of the deformations and stress waves in thin dissimilar eleastic tubes joined longitudinally and containing pulsatile fluid flow. With the long wavelength approximation, there exist two waves (with different velocities) corresponding to a single frequency. Superimposition of the two waves for each tube produces two reflected and two transmitted waves each with constant amplitudes which are determined from four dominant conditions of the six conditions at the joint cross-section. Rate of energy transfer in the system is also formulated. Although the application of the theory is two-fold: to engineering structures where a segment of high strength pipe may be inserted in a weaker tube for reasons of corrosion resistance for example, and the arterial system when an artificial implant is interposed or a contraction or stenose forms, the numerical examples are given for the latter. Effects of frequency on the reflection and transmission are illustrated for blood pulse in a natural artery joined with an artificial graft. Our numerical results correspond here to zero initial stresses. It is found that there is no discontinuity in the circumferential tension at a joint. The theoretical approach is justified since it would be extremely difficult to find the stresses at the joint experimentally.     

Lamb wave scattering analysis for reflector characterization

The potential use of guided waves for defect characterization is studied. The influence of defect shape and size on transmitted and reflected fields is considered. Using the hybrid boundary element technique, the reflection and transmission coefficients for selected guided wave modes are numerically calculated and compared to experimental data. Selecting the aspect ratio as a shape parameter for various defects, the transmission and reflection coefficients are measured for certain guided wave modes input to the defect. The influence of defect size is then studied by monitoring the transmission and reflection coefficients for defects of various shapes and depths. The studies presented indicate that defect characterization is possible if a proper mode selection criteria can be established. The suitable features related to transmission and reflection coefficient data can also be used for algorithm development and implementation purposes of defect characterization.     

Diffraction of water waves by slender barriers

Linear water-wave theory is used to tackle the problem of diffraction of surface waves by a fixed slender barrier in deep water for two basic situations: (i) when the barrier is partially immersed, and (ii) when the barrier is completely submerged. Analytical expressions for the first-order corrections to the reflection and transmission coefficients are derived in terms of integrals involving the shape functions describing the two sides of the slender barrier. A relatively straightforward perturbation technique is used along with the application of Green's theorem in the fluid region. Corresponding analytical expressions representing the reflection and transmission coefficients are also deduced, (i) for a nearly vertical barrier and (ii) for a vertically symmetric slender barrier, as special cases for both the problems. For a nearly vertical barrier it is observed, analytically, that there is no first-order correction to the transmitted wave at any frequency. Computations for the reflection and transmission coefficients up to O(), where ; is a small nondimensional number, are also performed and presented here.     

板状粘接结构中对称和反对称纵波与界面的相互作用

为了激发粘接结构中的导波或界面波,通常需要将声波从两半无限介质同相位或反相位地同时入射多层系统。针对此问题,基于矩阵方法,推导了界面处于理想连接的情况下,对称或反对称纵波从上下半无限空间入射时,三层板状粘接结构中纵、横波的反射与透射系数表达式。分析了入射角度、粘接层厚度以及基体材料等对声波反射(或透射)特性的影响。结果表明,对称或反对称纵波垂直入射时不发生波型转换。粘接结构中声波的反射(或透射)特性与入射角度、频率以及粘接层厚度等参数密切相关。在相同的粘接层厚度(或频率)范围内,随着声波频率(或粘接层厚度)的增加,谐振频率曲线向低频漂移。该方法可作为粘接结构中体波或导波传播特性研究的重要理论基础。     

Bessel pulse beams and focus wave modes

Free-space propagation of ultrashort pulses is investigated. Space-time couplings are reduced for a particular form of beams that is termed a pulse beam, or a type 3 pulsed beam. General conditions for the formation of pulse beams in the paraxial approximation are presented. The free-space propagation of spatially localized ultrashort laser pulses is investigated. This treatment is based on a particular pulsed form of the well-known Bessel beam, which is termed a Bessel pulse beam. The connections with focus wave modes and X waves are discussed.     

Shear wave passage through a vacuum gap between piezoelectric crystals with relative longitudinal displacement

The influence of relative longitudinal displacements of two piezoelectric crystals separated by a vacuum gap on the reflection and transmission of shear waves through the gap between these crystals is considered. We predict the possibility of enhancing the reflected wave under conditions of wave front reversal for the wave transmitted through the gap.     

A roller device to scan for surface-breaking cracks and to determine crack depth by a self-calibrating ultrasonic technique

A roller device using a square or a rectangular configuration of four roller transducers is used to scan a surface for surface-breaking cracks, by monitoring the reflection and transmission of surface waves. A self-calibrating ultrasonic technique is presented to determine the reflection and transmission coefficients or their ratio. For two configurations, namely, when one or both front rollers have crossed the surface trace of the crack, expressions have been obtained for the reflection and transmission coefficients in terms of measured voltages only, independent of parameters defining the coupling of the transducers to the specimen and the attenuation of surface waves propagating over the specimen. For a two dimensional configuration of a crack normal to the surface, the experimental results for the magnitude of the transmission coefficient show good agreement with theoretical results. For that case, the crack depth can be determined from the measured data.     

利用波动法研究曲梁结构中的波形转换和能量传递

基于Flugge理论,建立了薄壁均质常曲率曲梁面内运动的6阶微分控制方程,得到了曲梁的频散特性曲线和6种波的轴向位移和径向位移的比值,推导了位移和内力响应的表达式以及物理域和波数域的变换矩阵。利用波的传递和反射矩阵对曲梁和半无限长直梁耦合时的能量传递系数和反射系数进行了求解分析。对于半无限长直梁中给定的拉伸波或弯曲波入射,得到了和频率,曲率半径和伸展角度相关的各种波传递和反射的能量系数表达式。数值结果表明,纵波和弯曲波在经过曲梁结构之后发生了波形转换,并研究了能量传递和反射系数随频率,伸展角度,曲梁曲率半径和截面尺寸比的变化。结果表明,无限长直梁和曲梁耦合系统中,低频时,经过曲梁反射和传递后的弯曲波和纵波会相互转化;高频时弯曲波和纵波都能够没有散射地通过曲梁而进行传播。为改善高频时曲梁中的能量衰减效果,研究了在曲梁结构中插入单个、多个中间支撑或阻振质量块时的能量传递和反射系数。结果表明,阻振质量块能够很好地阻止高频时曲梁中能量的传递,对于周期分布的多个阻振质量块,能量传递系数随频率的变化存在周期结构的阻带特征。这些研究结果为曲梁结构的设计提供定性的理论基础。     

Reflection and refraction of plane waves at the interface between piezoelectric and piezomagnetic media

The paper analyzes the reflection and refraction of a plane wave incidence obliquely at the interface between piezoelectric and piezomagnetic media. The materials are assumed to be transversely isotropic. Numerical calculations are performed for BaTiO₃/CoFe₂O₄ material combination. Four cases, incidence of the coupled quasi-pressure (QP) and quasi-shear vertical (QSV) wave from BaTiO₃ or CoFe₂O₄ media, are discussed. The reflection and transmission coefficients and energy coefficients varying with the incident angle are examined. Calculated results are verified by considering the energy conservation. Results show that the reflected and transmitted wave fields in the sagittal plane consist of six kinds of waves, i.e. the coupled QP and QSV waves, evanescent electroacoustic (EA) and magnetic potential (MP) waves in the piezoelectric medium (BaTiO₃), evanescent magnetoacoustic (MA) and electric potential (EP) waves in the piezomagnetic medium (CoFe₂O₄), among which the EA, MA, MP and EP waves propagate along the interface. The most amount of the incident energy goes with the waves that are the same type as the incident wave, while the energy arising from wave mode conversion occupies a less part of the incident energy. The electric energy in BaTiO₃ is higher than the magnetic energy in CoFe₂O₄; they both attain their maximum values at/before the critical angle. Critical angles have little effect on evanescent waves except when the total reflection takes place. These results would provide useful complementary information for magnetoelectric composite materials.     

Bowtie limited diffraction beams for low-sidelobe and large depthof field imaging

Limited diffraction beams such as Bessel beams and X waves have a large depth of field and thus could have many applications. However, these beams have higher sidelobes as compared to conventional focused beams in their focal planes. In this paper, a new class of limited diffraction beams is developed. These beams are termed bowtie limited diffraction beams because they have bowtie shapes in a plane perpendicular to the beam axis. To obtain pulse-echo images of low sidelobes and a large depth of field, a bowtie limited diffraction beam is used in transmission and its 90° rotated response (around the beam axis) is used in reception. Unlike the summation-subtraction method developed previously, this method does not reduce image frame rate or dynamic range of signals and is not motion sensitive. The theory of the bowtie limited diffraction beams is developed. Computer simulation of the theoretical beams under practical conditions, such as finite aperture, finite bandwidth, and causal excitation, is performed with the Rayleigh-Sommerfeld diffraction formula. The simulated beams are very close to those predicted analytically over a large depth of field