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IssuesArchive of Issues2008-1pp.34-61

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I. O. Osipov, "Reflection and refraction of plane waves on the interface of two anisotropic media," Mech. Solids. 43 (1), 34-61 (2008)
Year 2008 Volume 43 Number 1 Pages 34-61
DOI 10.3103/S0025654408010056
Title Reflection and refraction of plane waves on the interface of two anisotropic media
Author(s) I. O. Osipov (Petrozavodsk, Russia)
Abstract We use generalized functionally invariant solutions [1] of the equations of motion to obtain and analytically study solutions of the plane problem of reflection and refraction of plane waves on the interface of two anisotropic media with four elastic constants depending on the angles of incidence of primary waves for various relations between the elastic constants of the contacting media. For the primary waves, we find the ranges of incidence angles for which real and complex secondary waves are excited. We study all possible combinations of the distribution of phase velocities and reflection and refraction angles in detail and obtain conditions characterizing the directions of the energy flux vectors for the primary and secondary waves depending on the incidence angles of the primary waves for different relations between the elastic constants of the contacting media, which satisfy the necessary and sufficient conditions for the elastic energy form to be positive definite.
References
1.  I. O. Osipov, "Generalization of the Method of Functionally Invariant Solutions for Dynamic Problems of the Plane Theory of Elasticity of Anisotropic Media," Prikl. Mat. Mekh. 64(6), 1004-1019 (2000) [J. Appl. Math. Mech. (Engl. Transl.) 64 (6), 967-980 (2000)].
2.  V. I. Smirnov and S. L. Sobolev, "New Method for Solving a Plane Problem of Elastic Oscillations," Trudy Seismol. Inst. AN SSSR 20, 37-42 (1932).
3.  S. L. Sobolev, "Some Questions of the Propagation Theory of Oscillations," in Differential and Integral Equations of Mathematical Physics, Ed. by F. Frank and R. Mises (ONTI, Moscow-Leningrad, 1937), pp. 468-617 [in Russian].
4.  V. A. Sveklo, "Elastic Oscillations of an Anisotropic Body," Uch. Zap. Leningr. Gos. Univ., Ser. Mat., No. 17, 28-71 (1949).
5.  I. O. Osipov, "Reflections and Refraction of Plane Elastic Waves on the Interface of Two Anisotropic Media," Izv. Akad. Nauk SSSR, Ser. Geofiz., No. 5, 649-665 (1961).
6.  I. O. Osipov, "On the Two-Dimensional Problem of Propagation of Elastic Waves due to a Point Source in an Anisotropic Medium," Prikl. Mat. Mekh. 33(3), 548-555 (1969) [J. Appl. Math. Mech. (Engl. Transl.) 33 (3), 534-542 (1969)].
7.  I. O. Osipov, "On Wave Fields and Acute-Angled Edges on Wave Fronts in an Anisotropic Medium from a Point Source," Prikl. Mat. Mekh. 36(5), 927-934 (1972) [J. Appl. Math. Mech. (Engl. Transl.) 36 (5), 874-882 (1972)].
8.  G. I. Petrashen’, Wave Propagation in Anisotropic Media (Nauka, Leningrad, 1980) [in Russian].
9.  G. I. Petrashen’ and B. M. Kashtan, "An Elementary Theory of Propagation of Bulk Waves in Anisotropic Elastic Media," in Propagation of Bulk Waves and Methods for Computation of Wave Fields in Anisotropic Elastic Media (Nauka, Leningrad, 1984), pp. 15-107 [in Russian].
10.  I. O. Osipov, "The Propagation of the Energy of Elastic Waves in Anisotropic Media," Prikl. Mat. Mekh. 67(3), 482-502 (2003) [J. Appl. Math. Mech. (Engl. Transl.) 67 (3), 435-452 (2003)].
11.  I. O. Osipov, "Character of Variations in the Rates of Propagation of Elastic Waves in Anisotropic Media," Izv. Akad. Nauk SSSR. Ser. Geofiz., No. 1, 3-10 (1962).
Received 03 March 2005
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