Geodesic
Reflection of plane waves from a~rigid wall and a~free surface in a~transverse isotropic medium
Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 1, pp. 27-36.

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We provide a representation of the general solution to the two-dimensional equations of the dynamics of a transverse isotropic medium with the Carrier–Gassmann condition. The representation of the solution is based on two solving functions that satisfy two separate wave equations. The problem of the reflection of plane waves from a rigid wall and a free surface is solved. The reflection coefficients and transformations of plane waves are found. The obtained formulas imply the solution for an isotropic medium as well. Special cases are considered, where the forms (amplitudes) of the reflected waves are not determined uniquely but related to the form of a falling wave through a linear relation.
Mots-clés : transverse isotropy, coefficients of reflection and transformation.
Keywords: plane wave, Carrier–Gassmann condition 
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B. D. Annin; N. I. Ostrosablin. Reflection of plane waves from a~rigid wall and a~free surface in a~transverse isotropic medium. Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 1, pp. 27-36. http://geodesic.mathdoc.fr/item/SJIM_2016_19_1_a2/

[1] Annin B. D., “Transversalno-izotropnaya uprugaya model geomaterialov”, Sib. zhurn. industr. matematiki, 12:3 (2009), 5–14 | Zbl

[2] Payton R. G., Elastic Wave Propagation in Transversely Isotropic Media, Martinus Nijhoff Publ., The Hague–Boston–Lancaster, 1983 | Zbl

[3] Gassmann F., “Introduction to seismic travel time methods in anisotropic media”, Pure Appl. Geophys., 58 (1964), 63–113 | DOI

[4] Goldin S. V., Seismicheskie volny v anizotropnykh sredakh, Izd-vo SO RAN, Novosibirsk, 2008

[5] Ostrosablin N. I., “Obschie resheniya i privedenie sistemy uravnenii lineinoi teorii uprugosti k diagonalnomu vidu”, Prikl. mekhanika i tekhn. fizika, 34:5 (1993), 112–122 | MR | Zbl

[6] Ostrosablin N. I., “Diagonalizatsiya trekhmernoi sistemy uravnenii v smescheniyakh lineinoi teorii uprugosti transversalno-izotropnykh sred”, Prikl. mekhanika i tekhn. fizika, 54:6 (2013), 125–145 | MR | Zbl

[7] Ostrosablin N. I., “Uprugii anizotropnyi material s chistoprodolnymi i poperechnymi volnami”, Prikl. mekhanika i tekhn. fizika, 44:2 (2003), 143–151 | MR | Zbl

[8] Annin B. D., Belmetsev N. F., Chirkunov Yu. A., “Gruppovoi analiz uravnenii dinamicheskoi transversalno-izotropnoi uprugoi modeli”, Prikl. matematika i mekhanika, 78:5 (2014), 735–746 | MR

[9] Rabotnov Yu. N., Mekhanika deformiruemogo tverdogo tela, Nauka, M., 1979

[10] Novatskii V., Teoriya uprugosti, Mir, M., 1975 | MR

[11] Grinchenko V. T., Meleshko V. V., Garmonicheskie kolebaniya i volny v uprugikh telakh, Nauk. dumka, Kiev, 1981 | MR

[12] Parton V. V., Perlin P. I., Metody matematicheskoi teorii uprugosti, Nauka, M., 1981 | MR