Diffraction of a spherical sound wave by an elastic cylinder with an non-uniform anisotropic coating

L. A. Tolokonnikov ; D. Yu. Efimov

Čebyševskij sbornik, Tome 23 (2022) no. 4, pp. 368-381.

Résumé

In paper the problem of the diffraction of a spherical monochromatic sound wave on a homogeneous isotropic elastic cylinder with a radially non-uniform anisotropic elastic coating. It is assumed that the body is located in a free space filled with an ideal liquid. The analytical solution of the problem is obtained. In the case of steady-state oscillations, the propagation of small perturbations in an ideal fluid is described by the Helmholtz scalar equation. The radiation field of a spherical source is written as a series expansion in cylindrical wave functions. The propagation of elastic waves in an isotropic elastic cylinder is described by the scalar and vector Helmholtz equations. The oscillations of an non-uniform anisotropic elastic cylindrical layer are described by the general equations of motion of a continuous medium. The asymptotic formula for the far field zone is obtained by the steepest descent method. Numerical calculations of the frequency characteristics of the scattered field are carried out for elastic cylinders with homogeneous and inhomogeneous transversally isotropic coatings, as well as for the case of a homogeneous isotropic coating. A significant influence and mutual influence of the inhomogeneity and anisotropy of the coating material on the acoustic properties of the scattering cylindrical body is revealed.

Détail

Keywords: diffraction, spherical sound wave, uniform elastic cylinder, inhomogeneous anisotropic coating.

Bibliographie

[1] Ivanov V. P., “Analiz polya difraktsii na tsilindre s perforirovannym pokrytiem”, Akusticheskii zhurn., 52:6 (2006), 791–798

[2] Bobrovnitskii Yu. I., “Nerasseivayuschee pokrytie dlya tsilindra”, Akusticheskii zhurn., 54:6 (2008), 879–889

[3] Kosarev O. I., “Difraktsiya zvuka na uprugoi tsilindricheskoi obolochke s pokrytiem”, Problemy mashinostroeniya i nadezhnosti mashin, 46:1 (2012), 34–37

[4] Romanov A. G., Tolokonnikov L. A., “Rasseyanie zvukovykh voln tsilindrom s neodnorodnym uprugim pokrytiem”, Prikladnaya matematika i mekhanika, 75:5 (2011), 850–857 | MR | Zbl

[5] Tolokonnikov L. A., “Rasseyanie naklonno padayuschei ploskoi zvukovoi volny uprugim tsilindrom s neodnorodnym pokrytiem”, Izvestiya Tulskogo gos. un-ta. Estestvennye nauki, 2013, no. 2-2, 265–274

[6] Larin N. V., Tolokonnikov L. A., “Rasseyanie ploskoi zvukovoi volny uprugim tsilindrom s diskretno-sloistym pokrytiem”, Prikladnaya matematika i mekhanika, 79:2 (2015), 242–250 | Zbl

[7] Tolokonnikov L. A., Larin N. V., Skobeltsyn S. A., “Modelirovanie neodnorodnogo pokrytiya uprugogo tsilindra s zadannymi zvukootrazhayuschimi svoistvami”, Prikladnaya mekhanika i tekhnicheskaya fizika, 2017, no. 4, 189–199 | Zbl

[8] Tolokonnikov L. A., “Difraktsiya tsilindricheskikh zvukovykh voln na tsilindre s neodnorodnym uprugim pokrytiem”, Izvestiya Tulskogo gos. un-ta. Estestvennye nauki, 2013, no. 3, 202–208

[9] Tolokonnikov L. A., Efimov D. Yu., “Difraktsiya tsilindricheskikh zvukovykh voln na uprugom tsilindre s radialno-neodnorodnym pokrytiem”, Chebyshevckii sbornik, 22:1 (2021), 460–472 | DOI | MR | Zbl

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

[11] Skobeltsyn S. A., Tolokonnikov L. A., “Rasseyanie zvukovykh voln transversalno-izotropnym neodnorodnym tsilindricheskim sloem”, Akusticheskii zhurn., 41:1 (1995), 134–138

[12] Tolokonnikov L. A., “Difraktsiya tsilindricheskikh voln na neodnorodnoi transversalno-izotropnoi tsilindricheskoi obolochke”, Oboronnaya tekhnika, 1998, no. 4-5, 9–11

[13] Larin N. V., Belkin A. E., “Rasseyanie zvuka na tverdom tsilindre s uprugim anizotropnym neodnorodnym pokrytiem”, Izvestiya Tulskogo gos. un-ta. Tekhnicheskie nauki, 2021, no. 11, 107–117

[14] Skobeltsyn S. A., “Zadacha o difraktsii ploskoi zvukovoi volny na uprugom tsilindre s transversalno-izotropnym neodnorodnym pokrytiem”, Izvestiya Tulskogo gos. un-ta. Tekhnicheskie nauki, 2021, no. 11, 230–239

[15] Tolokonnikov L. A., Efimov D. Yu., “Modelirovanie neodnorodnogo anizotropnogo pokrytiya uprugogo tsilindra, obespechivayuschego naimenshee otrazhenie zvuka”, Chebyshevckii sbornik, 23:1 (2022), 293–311 | DOI | MR

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

[17] Ivanov E. A., Difraktsiya elektromagnitnykh voln na dvukh telakh, Nauka i tekhnika, Minsk, 1968, 584 pp.

[18] Novatskii V., Teoriya uprugosti, Mir, M., 1975, 872 pp.

[19] Fedorov F. I., Teoriya uprugikh voln v kristallakh, Nauka, M., 1965, 388 pp.

[20] Ilin A. M., Danilin A. R., Asimptoticheskie metody v analize, Fizmatlit, M., 2009, 248 pp.

[21] Lebedev N. N., Spetsialnye funktsii i ikh prilozheniya, Fizmatgiz, M., 1963, 358 pp.

[22] Bkhatnagar P., Nelineinye volny v odnomernykh dispergiruyuschikh sistemakh, Mir, M., 1983, 136 pp.

[23] Zavyalov Yu. S., Kvasov B. I., Miroshnichenko V. L., Metody splain-funktsii, Nauka, M., 1980, 352 pp. | MR

[24] Samarskii A. A., Gulin A. V., Chislennye metody, Nauka, M., 1989, 432 pp.