Application of number-theoretic grids in problems of sound diffraction by elastic bodies
https://doi.org/10.22405/2226-8383-2022-23-5-206-226
Abstract
The article considers the problem of a plane harmonic sound wave diffraction by an elastic ellipsoid. To represent the scattered field, a representation in the form of a Kirchhoff integral is used. This leads to the need to solve the Fredholm integral equation of the second kind to determine the displacement potential in the scattered wave on the surface of the scatterer. It
is shown that the use of quadrature formulas based on number-theoretic grids allows you to reduce the number of calculations for the approximate calculation of integrals, when solving the integral equation and when calculating the scattered acoustic pressure in near field. This method is compared with the calculation of integrals by the simple cell method, which has the
same order of accuracy. The time of solving the problem is compared with the calculation of pressure in the vicinity of the ellipsoid based on the solution of an integral equation by two methods for calculating integrals.
About the Authors
Nikolai Nikolaevich Dobrovol’skii
Tula State Lev Tolstoy Pedagogical University, Tula State University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
Sergey Alekseevich Skobel’tsyn
Tula State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
Lev Alekseevich Tolokonnikov
Tula State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
Nikolai Vladimirovich Larin
Tula State University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
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Review
For citations:
Dobrovol’skii N.N., Skobel’tsyn S.A., Tolokonnikov L.A., Larin N.V. Application of number-theoretic grids in problems of sound diffraction by elastic bodies. Chebyshevskii Sbornik. 2022;23(5):206-226. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-5-206-226
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