doi:
UDK: 534.26

SOUND SCATTERING BY IDEAL AND ELASTIC BODIES IN THE FORM OF AN ELLIPTICAL CYLINDER

Клещев А. А., Колыхалин В. М., Попков С. В., Рытов Е. Ю.
Article language: русский

Annotation

The article investigates analytical solutions and computer calculations of sound scattering problems by ideal and elastic bodies in the form of an elliptical cylinder. In relation to the ideal elliptical cylinders, their interaction under irradiation by a plane sound wave is studied. The paper provides a solution to the three-dimensional problem of diffraction of a harmonic sound wave on an elastic isotropic shell in the form of an infinite elliptical cylinder. At the same time, in the Helmholtz vector equation for a vec-tor potential, the separation of variables is carried out using «Debye type» potentials. The advantage of this approach is that the potentials of the «Debye type» obey the scalar Helmholtz equation, in which the variables are separated in the selected system of elliptic cylindrical coordinates. As in the case of sound diffraction on a spheroidal elastic diffuser, the problem of finding the potential of a scattered sound wave is reduced to solving an infinite system of equations by the truncation method. This is due to the fact that even and odd Mathieu angular functions are orthogonal to each other only with the same wave size q, which is not observed in this case. In the Fraunhofer zone, the angular characteristic of scattering is of interest, the unknown decomposition coefficients of which are found using physical boundary conditions at both shell boundaries. From solving the problem of sound diffraction on an elastic elliptical shell, as a special case, it is possible to obtain a solution for a continuous elastic ellipti-cal cylinder. The solution presented in this paper expands the circle of elastic bodies with an analytical surface (circular cylinder, sphere, elongated and compressed spheroids), for which the problems of sound diffraction and scattering are strictly solved. Keywords: diffuser, elliptical cylinder, «Debye type» potentials, angular scattering characteristics, diffraction, elas-tic isotropic body, boundary conditions

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