Diffraction of a plane elastic wave by a gradient layer
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 4, pp. 116-125 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article, the problem of diffraction of a plane elastic wave by a gradient layer isotropic in a transverse direction is investigated. A system of second-order ordinary differential equations with boundary conditions of the third kind is obtained using an overdetermined boundary-value problem. This system is solved by the grid method. The calculation results for the case of piecewise linear scaling of elastic wave velocities are given.
Mots-clés : diffraction, gradient layer.
Keywords: elastic wave
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     title = {Diffraction of a~plane elastic wave by a~gradient layer},
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A. V. Anufrieva; D. N. Tumakov. Diffraction of a plane elastic wave by a gradient layer. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 4, pp. 116-125. http://geodesic.mathdoc.fr/item/UZKU_2012_154_4_a8/

[1] Slawinski M. A., Seismic Waves and Rays in Elastic Media, Pergamon, Amsterdam, 2003, 402 pp.

[2] Wen W., Sheng P., “Two- and three-dimensional ordered structures formed by electro-magnetorheological colloids”, Physica B, 338:1 (2003), 343–346 | DOI

[3] Milton G. W., Briane M., Willis J. R., “On cloaking for elasticity and physical equations with a transformation invariant form”, New J. Phys., 8:10 (2006), 248-1–248-20 | DOI

[4] Chen H., Chan C. T., “Acoustic cloaking in three dimensions using acoustic metamaterials”, Appl. Phys. Lett., 91:18 (2007), 183518-1–183518-3 | DOI

[5] Lee S.-J., Moon S. E., Ryu H.-C., Kwak M.-H., Kim Y.-T., Han S.-K., “Microwave properties of compositionally graded $\mathrm{(Ba,Sr)TiO}_3$ thin films according to the direction of the composition gradient for tunable microwave applications”, Appl. Phys. Lett., 82:13 (2003), 2133–2135 | DOI

[6] Chakraborty A. J., “Prediction of negative dispersion by a nonlocal poroelastic theory”, Acoust. Soc. Am., 123 (2008), 56–67 | DOI

[7] Brekhovskikh L. M., Godin O. A., Akustika sloistykh sred, Nauka, M., 1989, 416 pp.

[8] Epstein P., “Reflection of waves in an inhomogeneous absorbing medium”, Proc. Natl. Acad. Sci. USA, 16:10 (1930), 627–637 | DOI | Zbl

[9] Brekhovskikh L. M., Akustika okeanskoi sredy, Nauka, M., 1989, 222 pp.

[10] Yaroshenko A. A., Lastovenko O. R., Lisyutin V. A., Kalinyuk I. V., “O vliyanii profilya skorosti zvuka i techenii na rasprostranenie akusticheskikh voln v more”, Visnik Sumskogo derzhavnogo universitetu. Seriya Fizika, matematika, mekhanika, 2007, no. 1, 178–186

[11] Shvartsburg A. B., Erokhin N. S., “Gradientnye akusticheskie barery (tochno reshaemye barery)”, Usp. fiz. nauk, 181:6 (2011), 627–646 | DOI

[12] Anufrieva A. V., Tumakov D. N., Kipot V. L., “Elastic wave propagation through a layer with graded-index distribution of density”, Proc. Int. Conf. “Days on Diffraction 2012”, St. Petersburg, Russia, 2012, 21–26 | DOI

[13] Prikhodko V. Yu., Tyutekin V. V., “Raschet koeffitsienta otrazheniya zvukovykh voln ot tverdykh sloisto-neodnorodnykh sred”, Akust. zhurn., 32:2 (1986), 122–129

[14] Pleschinskaya I. E., Pleschinskii N. B., “Pereopredelennye granichnye zadachi dlya ellipticheskikh uravnenii s chastnymi proizvodnymi i ikh primenenie v teorii difraktsii voln”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 147, no. 3, 2005, 4–32 | Zbl

[15] Vdovina K. N., Pleschinskii N. B., Tumakov D. N., “Ob ortogonalnosti sobstvennykh voln poluotkrytogo uprugogo volnovoda”, Izv. vuz. Matem., 2008, no. 9, 69–75 | MR | Zbl