Diffraction by a metallic wedge covered with a dielectric material

In the literature, the usual formulation which assumes a constant impedance boundary condition does not permit one to express both the value of the geometrical optics field and the actual excited surface wave, since the impedance associated with the material for the reflection and for the surface wave are generally different. To obtain these elements in the field expression, we replace the notion of constant impedance by a differential operator. The general solution presented here preserves enough degrees of freedom to satisfy the continuity of fields at the internal junction of the two materials which cover each face of the wedge. The numerical calculations are based upon a function, related to the Maliuzhinets function, in a form which is easily computable.     

Sphere scattering of nonlinearly interacting acoustic waves

Sphere scattering of the field of nonlinearly interacting plane acoustic waves when the sphere is located in the region of nonlinear interaction between the primary pumping waves of a parametric antenna is considered. An analytic expression for the secondary field pressure at the difference frequency is obtained. This expression describes the process of nonlinear interaction of the incident and scattered waves. The secondary-field total pressure components, which characterize the interaction between the incident plane waves and scattered spherical waves are analyzed. The numerical results and experimental data are given.Taganrog. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 4–12, March–April, 1995.     

具有孔洞的双周期热弹性平面问题的复势

首先论述了针对调和变温场的热弹性平面问题的复变函数方法，给出了受调和变温时有限 多连通域中复势的一般表达式. 然后基于已知实部的双周期解析函数及其原函数的表示和多 值性分析，导出了双周期调和变温下具有双周期分布孔洞物体平面弹性问题的两个复势函数 的一般公式，由此论证了两种特殊情形下物体的温度应力为零.     

Reciprocity and power-flow theorems for the scattering of plane elastic waves in a half space

In this paper we present six field-reciprocity relations, and an additional six power-reciprocity relations for the far-zone scattered field if time-harmonic plane elastic waves are incident upon an obstacle in a half space. The incident waves are successively selected as to be either a P-wave, a SV-wave or a Rayleigh surface wave, each propagating in a prescribed direction. In the derivations we employ an explicit integral representation for the far-zone scattered field amplitude. The latter is obtained by expanding the half-space Green's displacement tensor in the far-zone region. Then, starting with the general Betti-Rayleigh theorem, the reciprocity identities are systematically inferred by inspection. We also present energy-conservation relations due to a single incident P-, SV- or Rayleigh wave.     

An inversion integral for crack-scattering data

The inverse problem of determining the size, shape and orientation of a flat crack from high-frequency far-field elastic waves scattered by the crack is investigated. The results show that desired information on a crack can be obtained from the first arriving scattered longitudinal waves only. It is shown that an approximate high-frequency solution to the direct problem, based on physical elastodynamics, yields an expression for the scattered far-field of longitudinal motion which suggests a solution to the inverse problem by application of Fourier-type inversion integrals to scattering data. Two kinds of inversion integrals are examined. The inversion problem becomes relatively simple if some a-priori information is available, either on the orientation of the plane of the crack or on a plane of symmetry. The method of inversion is verified for a flat crack of elliptical shape. Some computational technicalities are discussed, and the method is also applied to experimental scattering data.     

Scattering of sound waves by smooth convex elastic cylindrical shells

A plane acoustic wave travelling through an infinite inviscid fluid is scattered by an empty thin shell. A simple approximate but explicit formula is proposed to describe the behaviour of the acoustic pressure scattered by the shell, at an observation point situated in the far field, for backscattering. Only the contributions to the scattered field of specularly reflected, refracted and re-radiated wave are taken into account. The domain of validity of the proposed approximation is given. An example of the frequency dependent calculation is presented for the case of an Armco iron shell with elliptical cross shape immersed in water.     

Scattering of elastic waves by a small inclined surface-breaking crack

I we examine the scattering of Rayleigh waves by an inclined two-dimensional plane surface-breaking crack in an isotropic elastic half-plane. We follow the method already introduced by the authors (A and W , 1992a, J. Mech. Phys. Solids 40, 1683) to obtain an analytical solution when the parameter , which is the ratio of a typical length scale of the imperfection to the incident radiation's wavelength, is small. The procedure employed is the method of matched asymptotic expansions, which involves determining the scattered wave field both away from and near the crack. The outer solution is specialized from the general expansion in the first part of this work (A and W , 1992a, J. Mech. Phys. Solids 40, 1683), and the inner problem is exactly solved by the Wiener-Hopf technique. The displacement field and scattered Rayleigh waves are found uniformly to third order in , and concluding remarks are made about the general method as well as the results presented here.     

Acoustic scattering from baffled membranes that are backed by elastic cavities

An elastic membrane backed by a fluid-filled cavity in an elastic body is set into an infinite plane baffle. A time harmonic wave propagating in the acoustic fluid in the upper half-space is incident on the plane. It is assumed that the densities of this fluid and the fluid inside the cavity are small compared with the densities of the membrane and of the elastic walls of the cavity, thus defining a small parameter . Asymptotic expansions of the solution of this scattering problem as →0, that are uniform in the wave number k of the incident wave, are obtained using the method of matched asymptotic expansions. When the frequency of the incident wave is bounded away from the resonant frequencies of the membrane, the cavity fluid, and the elastic body, the resultant wave is a small perturbation (the “outer expansion”) of the specularly reflected wave from a completely rigid plane. However, when the incident wave frequency is near a resonant frequency (the “inner expansion”) then the scattered wave results from the interaction of the acoustic fluid with the membrane, the membrane with the cavity fluid, and finally the cavity fluid with the elastic body, and the resulting scattered field may be “large”. The cavity backed membrane (CBM) was previously analyzed for a rigid cavity wall. In this paper, we study the effects of the elastic cavity walls on modifying the response of the CBM. For incident frequencies near the membrane resonant frequencies, the elasticity of the cavity gives only a higher order (in ) correction to the scattered field. However, near a cavity fluid resonant frequency, and, of course, near an elastic body resonant frequency the elasticity contributes to the scattered field. The method is applied to the two dimensional problem of an infinite strip membrane backed by an infinitely long rectangular cavity. The cavity is formed by two infinitely long rectangular elastic solids. We speculate on the possible significance of the results with respect to viscoelastic membranes and viscoelastic instead of elastic cavity walls for surface sound absorbers.     

一种求解瑞利波散射问题的修正边界元方法

边界元法的一大优势是用于求解半空间等无限域问题,然而对于弹性波的传播问题,传统边界元法在采用全平面或全空间格林函数时,在截断边界处仍会产生虚假的反射回波,直接影响到散射场的求解准确性。因此,本文在传统边界元法基础上提出一种修正边界元法,用于计算无限大半平面中的弹性波场问题。该方法以瑞利波形式的远端散射场代替原本因截断而舍去的部分,通过互易定理建立单位瑞利波和全平面格林函数的积分方程,求得修正系数,并代入修正边界元矩阵,计算出瑞利波的散射场。为验证本文所提方法,文中将多个算例的结果与解析解对比,并用该方法计算了不同缺陷的散射场。这些对比结果表明,本文所提修正边界元法可准确求解瑞利波散射场,为基于表面波的缺陷反演问题研究提供了有效的正演途径。     

Acoustic radiation force on an elastic cylinder in a Gaussian beam near an impedance boundary

Acoustic radiation force (ARF) is studied by considering an infinite elastic cylinder near an impedance boundary when the cylinder is illuminated by a Gaussian beam. The surrounding fluid is an ideal fluid. Using the method of images and the translation-addition theorem for the cylindrical Bessel function, the resulting sound field including the incident wave, its reflection from the boundary, the scattered wave from the elastic cylinder, and its image are expressed in terms of the cylindrical wave function. Then, we deduce the exact equations of the axial and transverse ARFs. The solutions depend on the cylinder position, cylinder material, beam waist, reflection coefficient, distance from the impedance boundary, and absorption in the cylinder. To analyze the effects of the various factors intuitively, we simulate the radiation force for non-absorbing elastic cylinders made of stainless steel, gold, and beryllium as well as for an absorbing elastic cylinder made of polyethylene, which is a well-known biomedical polymer. The results show that the impedance boundary, cylinder material, absorption in the cylinder, and cylinder position in the Gaussian beam significantly affect the magnitude and direction of the force. Both stable and unstable equilibrium regions are found. Moreover, a larger beam waist broadens the beam domain, corresponding to non-zero axial and transverse ARFs. More importantly, negative ARFs are produced depending on the choice of the various factors. These results are particularly important for designing acoustic manipulation devices operating with Gaussian beams.     

On the Solution of an Elliptical Inhomogeneity in Plane Elasticity by the Equivalent Inclusion Method

Stress analysis of an elliptical inhomogeneity in an infinite isotropic elastic plane is a classical elasticity problem, which is usually solved by means of the complex variable formulation. In this work, we demonstrate that an alternative method of solution for such a problem, via the equivalent inclusion method, may be more convenient and straightforward without recourse to complex potentials or curvilinear coordinates. The explicit analytical solution can be derived through simple algebraic manipulation, although the longitudinal eigenstrain component should be handled with care in the case of plane strain. Since the exterior Eshelby tensor for an elliptical inclusion is available in closed-form, the present study provides a full field stress solution expressed in Cartesian coordinates. Furthermore, the in-plane stress components are represented in terms of Dundurs’ parameters. The solution methodology and the convenient formulae of the stress concentration may be of practical use to the engineers in developing benchmarks for design evaluation.     

On the plane-wave extinction cross-section of an obstacle

Summary A time-harmonic plane electromagnetic wave is incident upon an obstacle of finite dimensions. The properties of the obstacle are such that electromagnetic power is both absorbed and scattered. A close relation exists between the extinction cross-section of the obstacle and the amplitude and phase of the scattered wave in the direction of propagation of the incident wave. The exact form of this relation, the cross-section theorem, is proved by making use of an explicit representation of the scattered field. The result is valid for a plane wave with arbitrary elliptic polarization. Finally, a similar relation for the scattering of sound waves is given.     

Scattering of elastic waves by an inclusion with an interface crack

A method of perturbation is used to derive an integral representation of the displacement field for the scattering of a plane wave from an inclusion with an interface crack. In the long-wave approximation it is shown that the solution of only an associated static problem is required and formal expressions are derived for the scattered far field amplitudes and scattering cross section. In the case of a cylindrical inclusion the solution of the associated static problem is then used to find in a closed form the corresponding expressions for plane incident P- and S-waves.     

Spectral method for multiple edge diffraction by a flat strip

A spectral iteration scheme is employed to analyze time-harmonic and transient scattering of an E- or H-polarized incident plane wave by a perfectly conducting plane strip. The scattered field is synthesized by successive interactions between the edges, with each interaction modeled by half-plane diffraction. The plane wave spectrum generating a particular order of diffraction consists, in addition to the incident plane wave excitation, of a portion determined from the previous diffraction. The multiple integral spectral representations constructed in this manner satisfy the edge condition, and they are in a form suitable for inversion into the time domain by the modified Cagniard-deHoop method. Asymptotic reductions for special cases yield agreement with results from other methods, when available. Numerical calculations including up to triple diffraction have been performed for H- and E-polarized impulse and Gaussian pulse scattering. The results are clearly seen to repair the deficiencies of wavefront approximations at longer observation times, and from comparison with data generated independently by eigenfunction expansion, they describe accurately the total scattered response, owing to the high damping rate of higher-order diffractions.     

Scattering of an incident wave from an interface separating two fluids

We consider the scattering of an incident pulse from an interface separating two fluids. The interface can be either an elastic membrane or a two-fluid interface with surface tension. By considering the limit where the ratio of acoustic wavelength to the surface wavelength is small, we systematically derived a boundary condition relating the scattered wave and the surface deformation. This condition is local and can be used to derive a partial differential equation for the deformation of the interface. This equation includes the contribution of the acoustic waves induced by the motion of the interface and once it is solved it can be used to determine the scattered field. At leading order in our analysis we find the plane wave approximation. The addition of the next order terms results in an on surface condition equivalent to that of Kriegsmann and Scandrett. We present numerical calculations to show that our results are in good agreement with the exact numerical solution as well as that of Kriegsmann and Scandrett. Physical situations where the conditions of our analysis are valid are presented.     

含有限裂纹弹性体中二次反射波的影响

处理了无界体中一无限长、有限宽的平面应变裂纹,对任意入射膨胀波的散射问题．这里采用了Wiener－Hopf技术及标准迭代方法,得到了二次反射波到达后的应力强度因子的解析表达式,并给出了数值结果。     

Scattering of electromagnetic waves by an acoustic disturbance in the atmosphere

Summary The variations in density associated with an acoustic wave are shown to influence the propagation of an electromagnetic wave. The variation in electric permittivity of the atmosphere caused by an acoustic wave is expressed by the power density of the wave. Under the assumption that the acoustic waves are spherical, the scattered field at large distances is given in terms of definite integrals which are evaluated by means of the method of Stationary Phase. The limiting case of plane acoustic waves is discussed, and two numerical examples are given.     

The effect of initial stresses on harmonic stress fields within the stratified half plane

The effect of initial stresses on dynamic (harmonic) stress fields within an elastic stratified half plane is investigated. It is assumed that the point-located harmonic force acting on the free plane of the layer by which the half plane is stratified causes this stress field. By employing displacement potentials and the exponential Fourier transform the governing system of partial differential equations of motion is solved. The necessary inverse transformations including rigorous mathematical complexity is performed numerically. The analysis of the numerical results, which shows the influence of the homogeneous initial stresses on the distribution of the stresses on the inter-medium plane, is made. These analyses are examined for various problem parameters and it is assumed that the material of both the layer and the half plane is homogeneous, isotropic, compressible and linearly elastic. It has been observed that the initial stresses may change significantly the values of the superimposed harmonic stresses.