Diffraction of a convergent sound wave by an elastic cylindrical shell with a longitudinal fixation

The problem of the diffraction of a zero-order convergent cylindrical wave by a cylindrical shell with a longitudinal fixation along one of its generatrices is considered. The problem is solved on the basis of using the so-called helical waves, which are aperiodic eigensolutions to the equations of the shell motion. The diffraction field is represented in the form of a convergent series in cylindrical harmonics. The method of the solution allows for a generalization to several cases of longitudinal fixation with conditions of different forms. The calculation of the scattering amplitude of the diffraction field is carried out for various frequencies and shell parameters.     

Diffraction of point-source-generated sound by an elastic cylindrical shell

The three-dimensional problem of the scattering of a harmonic sound wave by an elastic cylindrical shell is solved using Debye potentials. All potentials are represented in the form of integrals depending on the axial component of the wave vector.     

Diffraction radiation from a finite-conductivity screen

An exact solution has been found for the problem of diffraction radiation appearing when a charged particle moves perpendicularly to a thin finite screen having arbitrary conductivity and frequency dispersion. Expressions describing the diffraction and Cherenkov emission mechanisms have been obtained for the spectralangular forward and backward radiation densities.     

Suppression of the sound field produced behind an aperture in a screen by an extraneous source

The three-dimensional problem of the active suppression of sound behind an aperture in a perfectly rigid screen is formulated and solved.     

The dissipation of sound at an edge

A general formula is established for the rate at which acoustic energy is dissipated at the sharp edges of a rigid boundary by the generation of vorticity in the presence of a low, subsonic mean flow of uniform mean density. Experimental results relating to the radiation of sound from a jet pipe are used to show how the formula can be used to make quantitative predictions in the absence of a detailed knowledge of the unsteady flow field.     

Waves trapped by a thin curved screen in a waveguide with rigid walls

The conditions are derived for the existence of waves trapped by a symmetrical thin rigid screen in a two-dimensional waveguide with rigid walls. Asymptomatic formulas are found for the corresponding eigenvalues, while the asymptomatic structures differ from those pertaining to the eigenvalues of problems in bounded domains. Various generalizations of the results are discussed, and open questions are formulated.     

Diffraction of sound by an elastic cylinder near the surface of an elastic halfspace

Diffraction of an acoustic wave by an elastic cylinder near the surface of an elastic halfspace is considered. The solution relies on a Helmholtz-type integral equation and uses the Green function of an elastic halfspace. The latter function is represented in the form of an integral over the Sommerfeld contour on the plane of a complex variable that has the meaning of the angle of the wave incidence on the halfspace boundary. An integral equation for the sound pressure distribution over the cylinder surface is derived. This equation is reduced to an infinite system of equations for the Fourier-series expansion coefficients of this distribution. The results obtained are valid for the diffraction of a cylindrical wave and a plane wave. They also describe the diffraction of a spherical wave when the transmitter and receiver are far from the cylinder and lie in one plane that is orthogonal to the cylinder axis.     

Diffraction of sound by an elastic or impedance sphere located near an impedance or elastic boundary of a halfspace

An exact solution is obtained to the problem of sound diffraction by an elastic or impedance sphere located near an impedance or elastic boundary of a halfspace. The problem is solved using the Helmholtz integral equation in which the field of a point source in the halfspace with an elastic boundary is used as the Green function. The diffracted field is represented as a series expansion in spherical harmonics. The expansion coefficients are determined from a set of independent algebraic systems of equations. The matrix coefficients of these systems are determined as integrals of the products of the associated Legendre polynomials on the complex plane with respect to the real and complex angles of the sound incidence on the halfspace boundary. To decrease the number of such integrals, expansions using the Klebsh-Gordon coefficients are applied. As a result, algorithms for calculating the scattered field in the halfspace are obtained.     

Diffraction of a sound wave by the open end of a flanged waveguide with impedance walls

Diffraction of a plane sound wave by the open end of an impedance-wall waveguide connected to an opening in an impedance screen is considered. The plane wave is incident on the waveguide from a free half-space. Two versions of the problem are considered: for a semi-infinite waveguide and for a finite-length waveguide with a specified bottom impedance; the impedances of the walls, screen, and waveguide bottom can be different. The finite-length waveguide can be treated as an open cavity in the impedance screen. For the cavity of zero length, the problem is reduced to the diffraction by an impedance insert in the impedance screen. The solution in the external region determines the scattered field; the solution in the internal region allows one to determine the directional pattern of an array of receivers located in the cavity. The problem is solved using the integral Helmholtz equation with a specially selected Green’s function that provides the fulfillment of the boundary conditions. Formally, the problem is reduced to an infinite system of algebraic equations. The computational results obtained for bistatic and monostatic scattering patterns are presented.     

Diffraction by a half-plane with an irregular edge in the problem of radiowave propagation over a surface at small grazing angles

Assuming that in grazing propagation the field above an irregular surface results from diffraction by a screen with an irregular edge, we estimate the average values of dispersion, space correlation, and the angular power spectrum in the region of the penumbra and transition to the illuminated region of space. The statistical properties of the field calculated using this method are shown to be in qualitative agreement with experimental results. Institute of Radiophysics and Electronics of the Ukrainian National Academy of Sciences, Khar'kov, Ukraine. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 8, pp. 965–979, August, 1997.     

Diffraction of X-radiation on a coherent sound wave

The scattering of X-rays on lattice vibrations is examined for two cases: (a) the sound is coherent and described by the Glauber state; and (b) the sound is incoherent and described by the occupation numbers of phonon state. The calculation of the scattering probability shows that in case (a) the intensity of scattering radiation can be modulated by the sound, whereas in case (b) this is impossible. In order to have this modulation effect, the conditions τΩ «1, Δ ⩽ δ where Ω is the sound frequency, τ the duration of interaction of the X-quantum with the atom, Δ the angular width of the Bragg maximum, and δ the angle between the directions of elastic- and one-phonon scattering, must be satisfied.     

Diffraction of a plane electromagnetic wave by a slot in a conducting screen with a transverse dielectric layer

The problem of diffraction of a plane electromagnetic wave by a slot in a planar perfectly conducting arbitrary thick screen with an infinite planar dielectric layer passing through the slot transversely to the screen is solved rigorously. In each of the field existence domains (two domains on either side of the screen and the interior of the slot), the solution is represented as an expansion in piecewise harmonic or exponential modes that allow for reflection and refraction at the boundaries of the dielectric layer. It is found that a set of functions describing such modes is complete enough to construct a solution satisfying all boundary conditions of the diffraction problem. The procedures of solution construction for the case at hand and for the same diffraction structure without the dielectric layer are compared.     

部份相干光照明的随机孔屏衍射特性

本文从部份相干理论出发，导出了随机孔屏的衍射强度期望分布及涨落方差表达式；对随机孔屏的衍射特性作了较深入的分析；讨论了光源的空间特性对衍射图形的影响；研究表明：衍射强度的光场分布不仅与孔和屏的几何特性有关，还与光源的形状和大小密切相关，文中还指出：在特定明情况下，形状一定的小孔无论在数目还是尺寸上发生随机变化，都不会改变衍射场的强度期望分布和涨落方差分布。     

Diffraction of sound from a dipole source near to a barrier or an impedance discontinuity

Pierce's formulation for the diffraction of spherical waves by a hard wedge has been extended to the case of the sound field due to a dipole source. The same approach is also used to extend a semiempirical model for sound propagation above an impedance discontinuity due to a dipole source. The resulting formulas have been validated by comparing their numerical solutions with that computed by summing the sound fields due to two closely spaced monopole sources of equal magnitude but opposite in phase. These new formulations are then used to develop a simple model for calculating the dipole sound field diffracted by a barrier above an impedance ground. Applications of these models relate to transportation noise prediction, particularly railway noise abatement, for which dipole sources are commonly used. The numerical predictions have been found to compare reasonably well with indoor measurements using piezoceramic transducers as dipole sources.