Scattering of a plane sound waves by an elastic cylinder with an non-uniform coating situated near to a flat surface

L. A. Tolokonnikov ; D. Yu. Efimov

Čebyševskij sbornik, Tome 21 (2020) no. 4, pp. 369-381.

Résumé

In article the problem of the scattering of an obliquely incident plane monochromatic sound wave by an elastic cylinder with a radially non-uniform elastic coating in presence of a flat surface (absolutely rigid and acoustically soft) is considered. The analytical solution of the problem by the method of imaginary sources using addition theorems for cylindrical wave functions is received. Wave fields in a containing medium and homogeneous elastic cylinder are found in the form of expansions in wave cylindrical functions. The boundary-value problem for the system of ordinary second order differential equations is constructed for determination of the displacement fields in inhomogeneous coatings. Numerical calculations of frequency and angular characteristics of the scattered field for elastic homogeneous cylinders with and without coating located near the underlying plane are performed. Influence of continuously inhomogeneous elastic coatings on sound-reflecting properties of elastic cylindrical bodies are revealed.

Détail

Keywords: scattering, sound waves, elastic cylinder, non-uniform elastic coating, flat surface.

Bibliographie

[1] 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

[2] 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

[3] 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

[4] 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

[5] Larin N. V., “Difraktsiya ploskoi zvukovoi volny na termouprugom tsilindre s nepreryvno-neodnorodnym pokrytiem”, Izvestiya Tulskogo gos. un-ta. Tekhnicheskie nauki, 2017, no. 6, 154–173

[6] Larin N. V., Skobeltsyn S. A., Tolokonnikov L. A., “Ob opredelenii lineinykh zakonov neodnorodnosti tsilindricheskogo uprugogo sloya, imeyuschego naimenshee otrazhenie v zadannom napravlenii pri rasseyanii zvuka”, Izvestiya Tulskogo gos. un-ta. Estestvennye nauki, 2014, no. 4, 54–62

[7] Tolokonnikov L. A., Larin N. V., Skobeltsyn S. A., “Modelirovanie neodnorodnogo pokrytiya uprugogo tsilindra s zadannymi zvukootrazhayuschimi svoistvami”, Prikladnaya mekhanika i tekhnicheskaya fizika, 58:4 (2017), 189–199 | Zbl

[8] Tolokonnikov L. A., “Difraktsiya ploskoi zvukovoi volny na uprugom tsilindre s neodnorodnym pokrytiem, nakhodyaschemsya vblizi ploskoi poverkhnosti”, Izvestiya Tulskogo gos. un-ta. Tekhnicheskie nauki, 2018, no. 9, 276–289

[9] Tolokonnikov L. A., “Difraktsii ploskoi zvukovoi volny na dvukh uprugikh tsilindrakh s neodnorodnymi pokrytiyami”, Chebyshevskii sbornik, 19:1 (2018), 238–254 | DOI | MR | Zbl

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

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

[12] Sedov L. I., Mekhanika sploshnoi sredy, v. 2, Nauka, M., 1994, 560 pp. | MR

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

[14] Kantorovich L. V., Krylov V. I., Priblizhennye metody vysshego analiza, Fizmatlit, M., 1962, 708 pp. | MR

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