High-frequency asymptotics of acoustic pressure for bounded wave beam scattering by an elastic sphere

Asymptotic high-freqeuncy estimates are obtained for the amplitudes of specular and non-specular reflections with extraction of the contribution of sound reradiation into the surrounding medium by Rayleigh type surface elastic waves. The conditions are found that govern the magnification of scattering in the opposite direction. The theoretical explanation of the book reflection effect /1/ for bounded sound beam incidence on the plane interface of a fluid-elastic solid is given by many authors in different situations (/12/, say). As for non-specular reflection of a plane sound wave by bounded elastic bodies (plates, cylinders, rods, and shells enclosed in a screen), studied most thoroughly in /3–9/, this effect is a consequence of satisfying the space-time resonance conditions between the incident acoustic wave and the normal surface waves excited in an elastic solid under total internal reflection.     

The sommerfeld half-plane problem revisited III: Parallel plate media with mixed boundary conditions

A plane wave is normally incident upon an infinite stack of equally spaced parallel plates which are semi-infinite and not staggered. The plates satisfy the so-called “Rawlins” boundary conditions. This problem is formulated as a pair of simultaneous integral equations of the Wiener-Hopf type and solved by a method proposed by A. E. Heins in 1950.     

多级透水板消波的一个特解

本文对无限长常水深平底渠道中一小振幅入射波经由多个间隔相等、透水性能一致的细孔透水板的反射和透射进行了研究,得到了相邻两板间距l为入射波半波长的倍数时的一个特解.结果表明,当无量纲的孔隙影响参数G₀等于透水板个数的一半时消波效果最佳,入射波能量的50%能被消掉.此时反射波与透射波的振幅相等.     

The Effect of a Fixed Vertical Barrier on Obliquely Incident Surface Waves in Deep Water

A plane wave in deep water is obliquely incident on an infinitelylong fixed vertical barrier immersed to a given depth. Partof the wave energy is reflected by the barrier and part is transmittedunder the barrier. Expressions for the reflection and transmissioncoefficients are derived in terms of an integral equation foreither the potential across the barrier or the horizontal velocityunder the barrier. The known exact solution for normally incidentwaves is then used as a one term Galerkin approximation to givevery accurate upper and lower bounds for the reflection andtransmission coefficients for all wavelengths and angles ofincidence.     

Reflection from a Wavy Boundary between Two Transparent Media

A mathematical model is proposed for the reflection of a plane electromagnetic wave from a transparent medium with a periodic wavy boundary. Numerical results are reported for the reflection characteristics. Translated from Prikladnaya Matematika i Informatika, No. 3, pp. 33–42, 1999.     

The diffraction of plane gravitational waves by the edge of an ice cover

The diffraction of plane surface gravitational waves by the edge of an ice cover lying on the surface of an incompressible fluid of infinitely great depth is considered. The ice cover is simulated by a thin elastic plate. The wave reflection and transmission coefficients are determined when it interacts with the ice cover. A wave field is constructed in the fluid under the conditions that a periodic lumped force and a lumped moment act on the edge of the ice cover. It is shown that as the incident wavelength increases the reflection coefficient tends to zero and the transmission coefficient tends to unity.     

The transmission of a plane acoustic wave through a non-uniform thermoelastic layer

The reflection and refraction of a plane acoustic wave by a thermoelastic plane layer, non-uniform in thickness, bounded by non-viscous heat-conducting liquids, generally different, is considered. The system of equations for small perturbations of the thermoelastic medium is reduced to a system of ordinary differential equations, the boundary-value problem for which is solved by two methods: the spline-collocation method and the power-series method. Analytic expressions are obtained which describe the wave fields outside the layer. The results of calculations of the intensity transmission coefficient of the acoustic wave are presented.     

Artificial boundary conditions for two-dimensional equations of fluid dynamics. 1. Convective wave equation

The article models external flow problems on artificially bounded regions. In the linear approximation we examine the reflection of acoustic waves in a moving medium, incident at various angles on a fixed boundary. We consider the construction of various boundary conditions and estimate their reflecting properties for plane waves and waves from point sources. The plane wave approximation is justified theoretically. A method is proposed for estimating the integral reflection coefficient for waves with a whole range of incidence angles. __________ Translated from Prikladnaya Matematika i Informatika, No. 24, pp. 76–110, 2006.     

The integral equation method in problems of diffraction by a finite impedance section of a medium interface

A 3D problem of reflection of a plane electromagnetic wave by a local impedance section of a wavy surface is considered. The boundary value problem for the system of Maxwell’s equations in a region with an irregular boundary is reduced to solution of systems of hypersingular integral equations. A numerical algorithm is proposed for solution of these systems. Results of numerical computations are presented.     

Reflection of plane waves from a rigid wall and a free surface in a transverse isotropic medium

For the general solution of two-dimensional equations of dynamics of a transverse isotropic medium with the Carrier–Gassmann condition, we give a representation in terms of two resolvent functions satisfying two separate wave equations. The problem of reflection of plane waves from a rigid wall and a free surface is solved. The coefficients of reflection and transformation of the plane waves are found. These formulas yield a solution for isotropic media too. Some special cases are consideredwhere the shapes (amplitudes) of the reflectedwaves are not uniquely determined, but linearly related with the shape of the incident wave.     

基于厚板拉伸振动精确化方程求解动应力集中问题

过去,对拉伸平板考虑应力集中的工程设计多借鉴弹性力学平面问题分析求解结果,例如弹性力学Kirsch问题的解或弹性动力学平面问题的解．基于厚板拉伸振动精确化方程,对含圆孔平板中弹性波散射与动应力集中问题进行了研究．研究结果表明:1) 两种模型得到的开孔附近的应力是不同的;2) 当入射波波数变大或者说入射波频率变高时,动应力集中系数最大值趋于单位1．含孔平板拉伸振动的动应力集中系数最大值达到3.30,以及基于弹性动力学平面问题模型得到的结果为2.77．对数值计算结果做了分析讨论, 可以看到,当孔径厚度比是a/h=0.10,基于平板拉伸振动精确化方程得到的动应力集中系数可以达到最大值,超出基于弹性动力学平面问题所得到结果的19%．分析方法和数值计算结果可望能在工程平板结构的动力学分析和强度设计中得到应用．     

Reflection of plane waves from the boundary of a pre-stressed compressible elastic half-space

The effect of pre-stress on the propagation and reflection ofplane waves in an incompressible isotropic elastic half-spacehas been examined recently by the authors (Ogden & Sotiropoulos,1997). In the present paper the corresponding analysis for compressiblematerials is detailed. In the two-dimensional context consideredfor incompressible materials the (homogeneous) plane waves werenecessarily shear waves. By contrast, in the compressible contextpure shear waves can propagate only in specific directions inthe considered principal plane and, in a general direction,a quasi-shear wave may be accompanied by a quasi-longitudinalwave, as is the case in the anisotropic linear theory. The dependenceof the (in-plane) slowness section on the pre-stress (and finitedeformation) and on the choice of constitutive law is elucidated.This information is used to determine the reflection coefficientsfor reflection of either a (quasi-) shear wave or a (quasi-)longitudinal wave from the boundary of the half-space and tocharacterize the different cases which arise depending on thegeometry of the slowness section. The theoretical results are illustrated by numerical calculationsfor the range of possible types of behaviour with referenceforms of strain-energy function and different states of finitedeformation and to the question of stability of the half-space.     

Reflection and transmission of sound waves through the interfacial boundary of two joined elastic half-strips

A numerical solution of the problem of the incidence of plane harmonic waves on the interfacial boundary of two joined half-strips with different elastic properties is presented. A detailed analysis is given of the reflection and transmission of the incident wave energy through the inter-facial boundary, and the nature of the state of stress and strain is investigated in its neighbourhood. The wave fields in longitudinally inhomogeneous media were studied earlier in /1–3/ etc.     

Reflection and transmission of plasma waves at the interface of crystallites

A linearized problem of the reflection and transmission of a plasma wave at the boundary of a half-space (namely, the plane separating two crystallites) is formulated and analytically solved. The electron distribution function and the electric field inside the half-space of a degenerate plasma are found. The reflection and transmission coefficients are determined as functions of the input parameters of the problem. The longwave limit (i.e., the resonance case when the oscillation frequency of the self-consistent electric field is close to the natural (Langmuir) oscillation frequency) is analyzed.     

Propagation of longitudinal viscoelastic waves in a three-layer medium

The nonstationary problem of propagation of a longitudinal plane one-dimensional stress wave through a plane-parallel viscoelastic layer of finite thickness separating two linear elastic half-spaces with different properties is solved in the linear formulation. A plane wave traveling in one of the half-spaces is normally incident on the boundary of the layer (one-dimensional problem). The field in the other elastic half-space, excited as a result of the multiple reflection of the fronts from the boundaries of the layer, is investigated. Graphs of the small displacements at a given point of the elastic half-space are presented. The solution of the problem is based on the dynamic correspondence principle formulated by Bland [3].Central Scientific-Research Institute of Machine Building, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 151–156, January–February, 1971.     

Scattering of a plane acoustic wave on a periodic array of piston radiators embedded into a rigid screen

The stationary scattering of a plane acoustic wave on a periodic or a doubly periodic set of piston radiators elastically connected with a rigid screen is considered. The screen separates two half-spaces filled with media possessing different acoustic properties. The model considered takes into account energy losses in the elastic ties between the piston radiators and rigid screen. The problem solution in the case where only one half-space is filled with an acoustic medium is found as a special case. The results of numerically analyzing the reflection coefficients of a plane wave as functions either of the frequency of the incident wave or of the angle of incidence of the plane acoustic wave for different values of the parameters involved are presented. Bibliography: 4 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 125–137. Translated by G. L. Nikitin.     

The Wave Field near the Point of Incidence of the Limiting Ray

The plane scalar problem on the refraction of a high-frequency wave, given by its ray expansion, from a curvilinear interface of two media is considered. It is assumed that the velocity in the medium where the refracted wave propagates is larger than the velocity in the medium where the incident wave propagates. It is also assumed that, on the interface, there is a point on one side of which the ordinary refraction of the wave holds and on the other side of which the complete internal reflection of the wave occurs. An analytic expression of the wave field near this limiting point is found. Bibliography: 8 titles.     

Investigating the Reflection of an Electromagnetic Field from a Wavy Periodic Boundary between Transparent Media

The article investigates the mathematical model for the reflection of a plane H-polarized electromagnetic wave from a transparent medium with a periodic wavy boundary. Numerical results are presented for the reflection and distribution of the fields on the boundary.     

Numerical study of unsteady rarefied diatomic gas flows in a plane microchannel

The numerical solution of a kinetic equation for a diatomic gas (nitrogen) is used to study two-dimensional unsteady gas flows in a plane microchannel caused by discontinuous in the initial distributions of macroscopic gas parameters. The plane discontinuity fronts are perpendicular to the walls of the channel. The arising flows are model ones for gas flows in a shock tube and a microchannel. The reflection of an incident shock wave from a flat end face is studied. It is found that the gas piles up at the cold wall, which slows down the shock wave detachment. The numerical results are in qualitative agreement with experimental data.     

Scattering of fluid loaded elastic plate waves at the vertex of a wedge of arbitrary angle, I: analytic solution

This article is the first part of an investigation into thescattering of fluid coupled structural waves by an angular discontinuityat the junction of two plates of different material properties.These two thin elastic plates are semi-infinite in extent thereforeforming the faces of an infinite wedge, the interior of whichcontains a compressible fluid. A plane unattenuated structuralwave is incident along the lower face of the wedge and is scatteredat the apex. The edges of the elastic plates may be joined ina variety of different ways, for example, they may be pin-jointedto an external structure or welded to each other. In the formercase, the plates will experience only the usual flexural vibrationswhereas in the latter case longitudinal (in-plane) disturbanceswill be generated and will propagate away from the wedge apex. An exact explicit solution is sought in terms of a Sommerfeldintegral representation for the fluid velocity potential. Thispermits the boundary-value problem to be recast as a functionaldifference equation which is easily solved in terms of the Maliuzhinetsspecial function (Maliuzhinets, Soviet Phys. Dokl. 3 1958).The chosen ansatz for the solution is of a different form fromthat used previously by the authors for the less complicatedmembrane wedge problem. The new ansatz has several analyticand numerical advantages which enable the reflection and transmissioncoefficients to be expressed explicitly in a compact form thatis ideal for computation. In the second part of this study a full numerical investigationof the reflection and transmission coefficients will be presentedfor a variety of interesting parameter ranges and edge conditions.