Geodesic
Diffraction of a plane sound wave on two elastic cylinders with
Čebyševskij sbornik, Tome 19 (2018) no. 1, pp. 238-254.

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In paper the analytical solution of a problem about diffraction of a plane sound wave on two uniform elastic cylinders with radially non-uniform coatings is received. Analytic expressions are obtained which describe the wave fields in the containing medium and the homogeneous elastic bodies. The boundary-value problem for the system of ordinary differential equations of the second order is constructed for determination of the displacement fields in non-uniform coatings. By means of an continuous-non-uniform elastic coatings it is possible to change effectively scattering performances of bodies in determinate directions if to pick up corresponding the inhomogeneity laws for mechanical parametres of a coating. The problem is of interest for analysis of sound diffraction on a lattice of cylindrical bodies and also serves as a necessary element of solution by a method of imaginary sources of a problem about sound diffraction on the single homogeneous elastic cylinder with the non-uniform covering which is close to acoustically soft or absolutely rigid flat surfaces.
Keywords: diffraction, sound waves, uniform elastic cylinder, non-uniform coating. 
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L. A. Tolokonnikov. Diffraction of a plane sound wave on two elastic cylinders with. Čebyševskij sbornik, Tome 19 (2018) no. 1, pp. 238-254. http://geodesic.mathdoc.fr/item/CHEB_2018_19_1_a16/

[1] Faran J. J., “Sound scattering by solid cylinders and spheres”, J. Acoust. Soc. Amer., 23:4 (1951), 405–418 | DOI | MR

[2] Doolittle R. D., Uberall H., “Sound scattering by elastic cylindrical shells”, J. Acoust. Soc. Amer., 39:2 (1966), 272–275 | DOI | Zbl

[3] Flax L., Varadan V. K., Varadan V. V., “Scattering of an obliquely incident acoustic wave by an infinite cylinder”, J. Acoust. Soc. Amer., 68:6 (1980), 1832–1835 | DOI | MR | Zbl

[4] Vexler N. D., Korsunskii V. M., Rybak S. A., “Scattering of an sloping incident plane wave by a circular cylindrical shell”, Akust. Zhurnal, 36:1 (1990), 12–16

[5] Bezrukov A. V., Prihod'ko V. Yu., Tyutekin V. V., “Scattering of sound waves by elastic radially-layered cylindrical bodies”, Akust. Zhurnal, 32:6 (1986), 762–766

[6] Kovalenko G. P., “About a problem of diffraction of acoustic wave by an inhomogeneous solid body”, Akust. Zhurnal, 33:6 (1987), 1060–1063

[7] Skobel'tsyn S. A., Tolokonnikov L. A., “Scattering of sound waves by a transversely isotropic inhomogeneous cylinder layer”, Acoustical Physics, 41:1 (1995), 114–117

[8] Tolokonnikov L. A., “Diffraction of sound waves by an inhomogeneous non-isotropic hollow cylinder”, Oboron. Tekh., 1998, no. 4–5, 11–14

[9] Romanov A. G., Tolokonnikov L. A., “Scattering of a plane sound wave by an inhomogeneous elastic hollow cylinder in a viscous fluid”, Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, 2009, no. 1, 61–70

[10] Tolokonnikov L. A., Romanov A. G., “Diffraction of cylindrical sound waves by an inhomogeneous hollow cylinder in a viscous fluid”, Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, 2008, no. 2, 151–160

[11] Larin N. V., Tolokonnikov L. A., “Diffraction of a plane acoustic wave by a non-uniform thermoelastic cylindrical layer bounded by inviscid heat-conducting fluids”, J. Appl. Math. Mech., 73:3 (2009), 336–343 | DOI | Zbl

[12] Tolokonnikov L. A., “Diffraction of cylindrical waves by an inhomogeneous transversely-isotropic cylindrical shell”, Oboron. Tekh., 1998, no. 4–5, 9–11

[13] Tolokonnikov L. A., “The resonant sound scattering by a transversely-isotropic inhomogeneous cylindrical shell”, Izv. Tul. Gos. Univ., Ser. Geodinam., Phiz., Matem., Termodinam., Geoekolog., 2006, no. 3, 106–114

[14] Larin N. V., Skobel'tsyn S. A., Tolokonnikov L. A., “About definition of linear laws of heterogeneity of the cylindrical elastic layer having the least reflexion in the set direction at sound scattering”, Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, 2014, no. 4, 54–62

[15] Ivanov V. P., “Analysis of the field diffracted by a cylinder with a perforated coating”, Acoustical Physics, 52:6 (2006), 683–690 | DOI

[16] Bobrovnitskii Yu. I., “A nonscattering coating for a cylinder”, Acoustical Physics, 54:6 (2008), 758–768 | DOI

[17] Bobrovnitskii Yu. I., Morozov K. D., Tomilina T. M., “A periodic surface structure with extreme acoustic properties”, Acoustical Physics, 56:2 (2010), 127–131 | DOI

[18] Kosarev O. I., “Diffraction of sound by an elastic cylindrical shell with a coating”, Probl. Mashinostr. Nadezh. Mashin, 46:1 (2012), 34–37

[19] Romanov A. G., Tolokonnikov L. A., “The scattering of acoustic waves by a cylinder with a non-uniform elastic coating”, J. Appl. Math. Mech., 75:5 (2011), 595–600 | DOI | MR | Zbl

[20] Tolokonnikov L. A., “Diffraction of cylindrical sound waves by an cylinder with a non-uniform elastic coating”, Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, 2013, no. 3, 202–208

[21] Tolokonnikov L. A., “Scattering of an obliquely incident plane sound wave by an elastic cylinder with a non-uniform covering”, Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, 2013, no. 2-2, 265–274

[22] Larin N. V., Tolokonnikov L. A., “The scattering of a plane sound wave by an elastic cylinder with a discrete-layered covering”, J. Appl. Math. Mech., 79:2 (2015), 164–169 | DOI | MR | Zbl

[23] Larin N. V., “Diffraction of a plane acoustic wave on the thermoelastic cylinder with the continuously inhomogeneous covering”, Izv. Tul. Gos. Univ., Ser. Tekh. Nauki, 2017, no. 6, 154–173

[24] Larin N. V., “Influence of the continuously inhomogeneous coating jn the thermoelastic cylinder sound-reflecting properties”, Izv. Tul. Gos. Univ., Ser. Tekh. Nauki, 2017, no. 9-1, 395–403

[25] Tolokonnikov L. A., Larin N. V., Skobel'tsyn S. A., “Modeling of inhomogeneous coating of an elastic cylinder with given sound-reflecting properties”, J. Appl. Mech. and Techn. Physics, 2017, no. 4, 733–742 | DOI | MR | Zbl

[26] Tolokonnikov L. A., “Determination of the inhomogeneity laws for an covering of an elastic cylinder with cylindrical cavity,providing minimum sound reflexion”, Izv. Tul. Gos. Univ., Ser. Tekh. Nauki, 2017, no. 4, 67–81

[27] Tolokonnikov L. A., Logvinova A. L., “Diffraction of a plane sound wave on two non-uniform cylinders with rigid inserts”, Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, 2015, no. 1, 54–66

[28] Shenderov E. L., Wave problems of underwater acoustics, Sudostroenie, L., 1972, 352 pp.

[29] Ivanov E. A., Diffraction of electromagnetic waves by two bodies, Nauka i tekhnika, Minsk, 1968, 584 pp.

[30] Sedov L. I., Mechanics of a continuous medium, v. 2, Nauka, M., 1994, 560 pp.

[31] Nowacki W., Teoria sprezystosci, Mir, M., 1975, 872 pp.