Geodesic
Scattering by a cylinder with an inhomogeneous coating of sound waves emitted by a linear source in a plane waveguide
Matematičeskoe modelirovanie, Tome 33 (2021) no. 8, pp. 97-113.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article is dedicated to the mathematical modeling of the acoustic field, which is scattered by the absolutely rigid circular cylinder with the continuously inhomogeneous coating. The cylinder is placed in a flat waveguide, which is filled with an ideal fluid. Density and the elastic moduli of the coating material are described by continuous functions of the radial coordinate. One of the waveguide boundaries is ideal (absolutely hard or acoustically soft), while the other differs arbitrarily little from the ideal one. The primary perturbation field is a harmonic sound wave emitted by a long linear source. The acoustic field in the waveguide is investigated as the sum of the source and the scatterer contributions. The scatterer contribution is determined on the basis of the problem solution of the cylindrical sound wave diffraction by the rigid cylinder with the continuously inhomogeneous elastic coating located in free space. Using the integral form of the cylindrical wave recording and the integral representation of wave cylindrical functions by the Cartesian basis solutions of the Helmholtz equation, the contributions from the source and the scatterer are in the form of a superposition of plane waves in terms of the multiple reflections from the waveguide boundaries. The results of calculations of acoustic fields in a waveguide are presented, when one boundary of the waveguide is absolutely rigid and the other slightly differs from acoustically soft. We showed that with the help of the inhomogeneous coating it is possible to change the sound reflecting properties of a cylindrical body in a waveguide.
Keywords: scattering, sound waves, cylinder, inhomogeneous elastic coating, flat waveguide. 
@article{MM_2021_33_8_a5,
     author = {L. A. Tolokonnikov and N. V. Larin},
     title = {Scattering by a cylinder with an inhomogeneous coating of sound waves emitted by a linear source in a plane waveguide},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {97--113},
     publisher = {mathdoc},
     volume = {33},
     number = {8},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2021_33_8_a5/}
}
TY  - JOUR
AU  - L. A. Tolokonnikov
AU  - N. V. Larin
TI  - Scattering by a cylinder with an inhomogeneous coating of sound waves emitted by a linear source in a plane waveguide
JO  - Matematičeskoe modelirovanie
PY  - 2021
SP  - 97
EP  - 113
VL  - 33
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2021_33_8_a5/
LA  - ru
ID  - MM_2021_33_8_a5
ER  - 
%0 Journal Article
%A L. A. Tolokonnikov
%A N. V. Larin
%T Scattering by a cylinder with an inhomogeneous coating of sound waves emitted by a linear source in a plane waveguide
%J Matematičeskoe modelirovanie
%D 2021
%P 97-113
%V 33
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2021_33_8_a5/
%G ru
%F MM_2021_33_8_a5
L. A. Tolokonnikov; N. V. Larin. Scattering by a cylinder with an inhomogeneous coating of sound waves emitted by a linear source in a plane waveguide. Matematičeskoe modelirovanie, Tome 33 (2021) no. 8, pp. 97-113. http://geodesic.mathdoc.fr/item/MM_2021_33_8_a5/

[1] A. G. Romanov, L. A. Tolokonnikov, “The scattering of acoustic waves by a cylinder with a non-uniform elastic coating”, Journal of Applied Mathematics and Mechanics, 75:5 (2011), 595–600 | DOI | MR | Zbl

[2] L. A. Tolokonnikov, “Rasseianie naklonno padaiushchei ploskoi zvukovoi volny uprugim tsilindrom s neodnorodnym pokrytiem”, Izvestiia TulGU. Estestvennye nauki, 2013, no. 2-2, 265–274

[3] L. A. Tolokonnikov, N. V. Larin, S. A. Skobel'tsyn, “Modeling of inhomogeneous coating of an elastic cylinder with given sound-reflecting properties”, Journal of Applied Mechanics and Technical Physics, 58:4 (2017), 733–742 | DOI | MR | Zbl

[4] N. V. Larin, L. A. Tolokonnikov, “The scattering of a plane sound wave by an elastic cylinder with a discrete-layered covering”, Journal of Applied Mathematics and Mechanics, 79:2 (2015), 164–169 | DOI | MR | Zbl

[5] L. A. Tolokonnikov, “Difraktsiia tsilindricheskikh zvukovykh voln na tsilindre s neodnorodnym pokrytiem”, Izvestiia TulGU. Estestvennye nauki, 2013, no. 3, 202–208

[6] L. A. Tolokonnikov, “Difraktsiia sfericheskoi zvukovoi volny na uprugom tsilindre s neodnorodnym pokrytiem”, Chebyshevskii sbornik, 19:4 (2018), 215–226 | MR | Zbl

[7] V. E. Belov, S. M. Gorskii, A. Yu. Zinov'ev, A. I. Khil-ko, “Primenenie metoda integralnykh uravnenii k zadache o difraktsii akusticheskikh voln na uprugikh telakh v sloe zhidkosti”, Akusticheskii zhurnal, 40:4 (1994), 548–560

[8] T.A. Andrianova, V.E. Belov, A.A. Zalezsky, G.A. Sharonov, “An analysis of the mode composition and spatial distribution of acoustic fields for different localizations of inhomogeneities in a liquid layer”, Acoustical Physics, 42:4 (1996), 407–419

[9] V. E. Belov, S. M. Gorsky, A. A. Zalezsky, A. Yu. Zinovyev, “Application of the integral equation method to acoustic wave diffraction from elastic bodies in a fluid layer”, J. Acoust. Soc. Amer., 103:3 (1998), 1288–1295 | DOI

[10] R. H. Hackman, G. S. Sammelman, “Acoustic scattering in an inhomogeneous waveguide: Theory”, J. Acoust. Soc. Amer., 80:5 (1986), 1447–1458 | DOI

[11] R. H. Hackman, G. S. Sammelman, “Multiple-scattering analysis for a target in oceanic waveguide”, J. Acoust. Soc. Amer., 4:5 (1988), 1813–1825 | DOI

[12] V. M. Kuz'kin, “Sound scattering by a body in a planar layered waveguide”, Acoustical Physics, 49:1 (2003), 68–74 | DOI | MR

[13] B. P. Sharfarets, “Method for calculating the field of an opaque source and the field scattered by an inhomogeneous inclusion in a planar layered waveguide”, Acoustical Physics, 50:1 (2004), 107–111 | DOI

[14] E. L. Shenderov, Volnovye zadachi gidroakustiki, Sudostroenie, L., 1972, 352 pp.

[15] W. Nowacki, Teoria sprezystosci, PWN, Warszawa, 1973 | MR

[16] L. B. Felsen, N. Marcuvitz, Radiation, scattering of waves, Prentice-Hall, Inc, Englewood Cliffs, New Jersey, 1973 | MR

[17] L. M. Brekhovskikh, Waves in Layered Media, Nauka, M., 1973, 344 pp.

[18] V. T. Erofeenko, Teoremi slosheniya, Nauka i tehnika, Minsk, 1989, 255 pp. | MR

[19] Iu. S. Zav'ialov, B. I. Kvasov, V. L. Miroshnichenko, Metody splain-funktsii, Nauka, M., 1980, 352 pp. | MR