Point source scattering in a porous barrier

Diffraction of a spherical acoustic wave due to the coupling of pressure release and absorbing half planes in a moving fluid

An exact analytic solution of the problem of diffraction of a plane acoustic wave on a cone of arbitrary aperture angle was obtained and studied in [1]. For the case of spherical wave diffraction on a cone a formula is known [2] which relates the solutions of the spherical and plane wave diffraction problems. This study will employ the results of [1, 2] to derive and investigate an exact analytical solution of the problem of diffraction of a spherical acoustic wave on a cone of arbitrary aperture angle. Results of numerical calculations will be presented and compared with analogous results for a plane wave.

A new method termed Directive Line Source Model (DLSM) is presented for predicting the diffracted field produced by a sound wave incident on a rigid or pressure release half plane. In the new method the edge of the half plane is modeled as an infinite set of directive point sources continuously distributed along the edge. Because DLSM is fast, simple and intuitive, it is a promising tool for the study of diffraction. It can be applied for several types of incident radiation: omnidirectional cylindrical and spherical waves, plane waves, as well as waves from directional sources. Wedges may also be treated. Finally, DLSM can handle diffraction by an arbitrarily shaped edge profile, for example, a half plane having an edge that is jagged instead of straight. Results for plane, cylindrical and spherical incident waves, as well as for arrays of line and point sources, are presented and their agreement with known analytical solutions is demonstrated. Predictions based on DLSM compare favorably with experimental data.

Scattering of acoustic waves from a point source over an impedance wedge

We have studied the problem of diffraction of an electromagnetic spherical wave by a perfectly conducting finite strip in a homogeneous bi-isotropic medium and obtained some improved results. The problem was solved by using the Wiener-Hopf technique and Fourier transform. The scattered field in the far zone was determined by the method of steepest descent. The significance of the present analysis was that it recovered the results when a strip was widened into a half plane.

The plane wave diffraction by a thin material strip is analyzed using the Wiener-Hopf technique and approximate boundary conditions. An asymptotic solution is obtained under the condition that the strip width is large compared with the wavelength. Applying the saddle point method, the scattered far field is evaluated asymptotically. Numerical results on the radar cross section are presented.

The diffraction by a thin material strip is analyzed for the E-polarized plane wave incidence using the Wiener-Hopf technique together with approximate boundary conditions. An asymptotic solution is obtained for the case where the thickness and the width of the strip are small and large compared with the wavelength, respectively. The scattered field is evaluated asymptotically based on the saddle point method and a far field expression is derived. Scattering characteristics are discussed in detail via numerical results of the radar cross section.

In the field of diffraction of acoustic, electro-magnetic and elastic waves the ray method has proven to be a powerful tool to obtain reliable results for the behaviour of short waves. In ship hydrodynamics where the generation of short waves by a slowly sailing vessel and the diffraction of short surface waves by these vessels is of importance recently the ray method is applied successfully. In this presentation we present two cases, each with its own free surface condition, treated with this method.

Artificial boundary conditions and finite difference approximations for a time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain

Two basic refinements of the finite-difference method for 3-D dc resistivity modeling are presented. The first is a more accurate formula for the source singularity removal. The second is the analytic computation of the source terms that arise from the decomposition of the potential into the primary potential because of the source current and the secondary potential caused by changes in the electrical conductivity. Three examples are presented: a simple two-layered model, a vertical contact, and a buried sphere. Both accurate and approximate Dirichlet boundary conditions are used to compute the secondary potential. Numerical results show that for all three models, the average percentage error of the apparent resistivity obtained by the modified finite-difference method with accurate boundary conditions is less than 0.5%. For the vertical contact and the buried sphere models, the error caused by the approximate boundary condition is less than 0.01%.

The solution of exterior interface problems using a variational method with Lagrange multipliers

С помощью непрерывно-неоднородных упругих покрытий можно эффективно изменять характеристики рассеяния тел в определенных направлениях, если подобрать соответствующие законы неоднородности для механических параметров покрытия. В статье рассматривается задача дифракции сферической звуковой волны на однородном изотропном упругом цилиндре с радиально-неоднородным упругим покрытием. Полагается, что бесконечный круговой цилиндр с покрытием помещен в идеальную безграничную жидкость, законы неоднородности материала покрытия описываются дифференцируемыми функциями, на тело падает гармоническая сферическая звуковая волна, излучаемая точечным источником. В случае установившихся колебаний распространение малых возмущений в идеальной жидкости описывается скалярным уравнением Гельмгольца, а в упругом однородном изотропном цилиндре — скалярным и векторным уравнениями Гельмгольца. Колебания неоднородного изотропного упругого цилиндрического слоя описываются общими уравнениями движения сплошной среды. Аналитическое решение рассматриваемой задачи получено на основе известного решения аналогичной задачи дифракции плоской волны. Потенциал скорости сферической волны представляется в интегральной форме в виде разложения по цилиндрическим волновым функциям. При этом подынтегральное выражение оказывается аналогичным по форме выражению потенциала скорости плоской волны. Поэтому потенциал скорости рассеянной волны в случае падения сферической волны на цилиндр с покрытием записывается в виде интеграла, подынтегральное выражение которого аналогично по форме выражению потенциала скорости рассеянной волны при падении плоской волны на тело. Для вычисления подынтегральной функции необходимо определить поле смещения в неоднородном покрытии, решая построенную краевую задачу для системы обыкновенных дифференциальных уравнений второго порядка. Рассматриваются вычислительные аспекты оценки интеграла.

Existing Green functions for a conducting wedge in the form of infinite series of orthogonal eigenfunctions are known to suffer from slow and conditional convergence 1) near the source point, due to the singularity of the Green functions at source points, and 2) when the source point is near the surface of the wedge, due to the presence of a nearby image source. As a result, such expansions are unsuited for the exact solution of singular integral equations wherein values of the Green functions at the source point do appear inside the integral. In this paper, alternative expansions are proposed which converge rapidly for any combination of the source and observation points. The main idea is to extract in closed form both the singular term and the nearby image term together with certain simple asymptotic terms. This helps isolate the inherent singularities and, thus, transform the remaining part of the Green function into a rapidly converging series of elementary terms. Numerical examples and case studies illustrate the stability and high accuracy of the new expansions. Application to the solution of an integral equation associated with wave diffraction by perfectly conducting curved strips in the vicinity of a wedge is exemplified.

This chapter considers the diffraction of a plane acoustic wave illuminating completely the surface of a right-circular impedance cone. Formulation of the problem is also given for an arbitrary convex cone and uniqueness of the solution is discussed. By separating the radial variable the problem at hand is then reduced to that for a spectral function. Further separation of the angular variables for the circular cone leads to integral equations for the Fourier coefficients. The use of the Sommerfeld integral enables one to describe the far-field asymptotics for, in particular, the reflected wave, the spherical wave from the vertex of the cone, and the surface waves.

Fresnel diffraction is a fundamental wave phenomenon. This article explains its physical nature using the examples of the diffraction of acoustic waves at soft and hard half-planes and at large apertures on a black screen. It is shown that the shadow radiation by opaque screens plays a central role in these diffraction phenomena. Fresnel-Kirchhoff diffraction at large apertures is presented as an asymptotic form of the shadow radiation. Fresnel and Grimaldi-type diffraction at the soft and hard half-planes is revealed as interference of the shadow radiation and the incident wave.