Diffraction of a plane electromagnetic wave obliquely incident upon the edge of a wedge with a dielectric coating

The diffraction of a plane electromagnetic wave obliquely incident upon the edge of a coated wedge is considered. The generalized impedance boundary conditions (GIBC's) on the wedge's faces are used to simulate the effect of the coatings. To insure the well-posedness of the problem, special contact conditions (CC's) on the edge are additionally imposed. By using Sommerfeld integrals, the problem is reduced to a system of coupled functional equations, which is solved by the perturbation method. It is shown that, for a certain range of the angles of oblique incidence, the solution can be represented in the form of convergent series that are Neumann series for linear equations with contracting operators. Nonuniform asymptotics of the wave field for regions outside a neighborhood of the edge of the wedge are constructed. Bibliography: 9 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 218, 1994, pp. 72–95. Translated by L. G. Vardapetyan and M. A. Lyalinov.     

Diffraction of a plane wave by a step discontinuity in an impedance plane

In the present paper, the high-frequency diffraction of a plane wave by a right-angle step discontinuity in an impedance plane is analyzed with the help of the uniform geometric theory of diffraction, beginning with the Maluzhenets solution. The principal term of an asymptotic solution of the problem, which is uniform with respect to the angle of incidence of the plane wave and the angle of observation, is derived. The excitation of primary and multiply diffracted fields radiated from the upper edge, as well as surface waves, is considered (the lower edge does not radiate cylindrical or surface waves owing to a right-angle step). For simplicity, the details of computation are given here for a right-angle step discontinuity. A similar procedure is applied to other examples with more complicated geometry. Bibliography: 7 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 97–108. Translated by V. V. Zalipaev.     

Diffraction of a plane wave by a circular disk

In this paper we solve the problem of diffraction of a normally incident plane wave by a circular disk. We treat both the hard and soft disk. In each case we obtain the solution as a series which converges when the product of the wave number and the radius of the disk is large. Our construction leads directly to asymptotic approximations to the solution for large wave number.     

Diffraction of a plane wave by a narrow cone

The problem of diffraction of a plane scalar wave by a narrow cone is considered. The shape of the cone is arbitrary. The boundary condition is the Dirichlet or Neumann one. The wave scattered by the cone vertex arises as a result of the diffraction process. The subject of this paper is to calculate the wave amplitude. If the cone is narrow, it is possible to obtain simpler approximate formulas in comparison with Smyshlayev's one. The exactness of the approximate formulas is checked numerically. The etalon is a solution in explicit form in the axially symmetric case. The calculation shows that our formula is more exact in the case of the Dirichlet boundary condition than Felsen's formula. The approximate formula is a generalization of Felsen's one for circular cone to an arbitrary narrow cone in the case of the Neumann boundary condition. Bibliography: 6 titles. Dedicated to N. N. Uraltseva on her jubilee Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 221, 1995, pp. 67–74. Translated by D. B. Dement'ev.     

Diffraction of the plane wave by a transparent wedge: The Sommerfeld-Malyuzhinets approach

The time-harmonic diffraction of the plane wave by a transparent wedge of an arbitrary opening is examined by the Sommerfeld-Malyuzhinets approach. The velocities of wave propagation inside and outside the wedge are equal. An explicit solution is presented, which is studied asymptotically as kr → ∞ and kr → 0. Bibliography: 2 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 354, 2008, pp. 157–172.     

Diffraction of a plane acoustic wave on an impedance cone. Surface waves

Diffraction of a plane wave by a circular impedance cone is studied. Surface waves propagating from the vertex of the cone are discussed. The excitation coefficient is computed with the help of the incomplete separation of variables in the problem. Bibliography: 14 titles.     

Diffraction of a plane electromagnetic wave on a wedge-shaped inclusion

A technique is developed for reducing the problem of diffraction by a wedge-shaped inclusion to functional equations in the complex plane. An original formulation of the radiation conditions is proposed that enables one to formulate the diffraction problem in this case. An existence and uniqueness theorem is proven. For the case of a sufficiently small opening span of the angle a formula is derived which is a good approximation to the solution to the problem.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Stekova AN SSSR, Vol. 195, pp. 29–39, 1991.     

Diffraction of a plane wave on a slippery elastic wedge

Diffraction of a plane elastic wave on a slippery wedge is considered; by a slippery wedge we mean a wedge in which the tangent tension and the normal component of the displacement vector are equal to zero on its surface. It is known that one can construct an explicit solution of this problem. The Sommerfeld representation of this solution is found in construct the paper. Bibliography: 6 titles.     

Diffraction of a plane wave by an infinite elastic plate stiffened by a doubly periodic set of rigid ribs

The diffraction of a plane wave by an infinite elastic plate stiffened by a doubly periodic set of rigid ribs of moderate wave dimensions is studied. The problem is reduced to an infinite quasiregular system of linear algebraic equations, and their solution describes the amplitudes of the waves propagating from the plate into the fluid.     

Diffraction of a plane acoustic wave on an elastic sphere located near the bottom

On the basis of numerical computations we analyze the echo-signals from a steel spherical shell located near the bottom of water under the action of a quasimonochromatic pulse. We study the effect of the distance between the sphere and the bottom on the echo-pulse. Translated fromMatematichni Metodi i Fiziko-mekhanichni Polya, Vol. 40, No. 1, pp. 79–84.     

Diffraction of a monochromatic plane shear wave on a reinforced cylindrical cavity in an elastic half-space

This article examines a boundary-value problem concerning the diffraction of a monochromatic plane shear wave on a reinforced cylindrical cavity in an elastic half-space. It is assumed that longitudinal shear stresses are absent and that the normal displacements over the entire boundary are specified. Through the use of a special form of the Lamé representation in cylindrical coordinates, the problem is reduced to the determination of scalar functions which satisfy the Helmholtz equation. The coefficients of the Fourier expansions of these functions in the angular coordinate are written as the sum of Fourier and Weber integrals. The densities of these integrals are determined exactly. A specific example is examined.Translated from Dinamicheskie Sistemy, No. 5 pp. 42–49, 1986.     

Diffraction echo signal generated by the incidence of a plane wave on a prolate spheroid

The problem of the diffraction of a plane wave by a prolate spheroid placed in a fluid is considered in the high-frequency approximation. The spheroid is hereby either a solid body or a shell. The contribution to the echo signal, i.e., the back-reflected field, of diffraction waves of creep and break-off type is investigated. Computational formulas for the geometric divergences of surface rays and also of creep and break-off waves are obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituts im. V. A. Steklova AN SSSR, Vol. 140, pp. 18–35, 1984.     

Short-wavelength grazing scattering of a plane wave by a smooth periodic boundary. II. Diffraction by an infinite periodic boundary

The short-wavelength asymptotic behavior of the field near a reflecting boundary (the Fock zone and the neighborhood of the limit ray) is constructed for the problem of the diffraction of a plane wave by a smooth periodic boundary.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Seklova AN SSSR, Vol. 173, pp. 60–86, 1990.     

Diffraction of a plane elastic wave by a wedge with a special form of boundary conditions

An exact solution of the antiplane problem of the diffraction of a plane elastic SH-wave with a step profile by a wedge is obtained. The stresses on the wedge sides are assumed to be proportional to a linear combination of the displacements, velocities and higher derivatives with respect to time of the displacements along the wedge axis. A solution of the problem is obtained using integral transformations with subsequent transformation using Cagniard's method. Solutions of the corresponding problems with boundary conditions of the Winkler and inertial types are considered. When a wave with a linear profile is incident on the wedge the stresses suffer a discontinuity of the second kind on the diffraction wave front; the same type of feature is observed in the problem with the inertial condition.     

Diffraction of a plane acoustic wave by a non-uniform thermoelastic cylindrical layer bounded by inviscid heat-conducting fluids

The diffraction of sound by a radially laminated isotropic thermoelastic cylindrical shell is considered. The system of equations for small perturbations of a hollow thermoelastic cylinder is reduced to a system of ordinary differential equations, the boundary-value problem for which is solved by the spline-collocation method. Expressions are obtained describing the wave field outside the cylindrical layer. Results of calculations of polar radiation patterns of the amplitude of the scattered acoustic wave in the far zone are presented.