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Nonstationary Love waves of \(SH\) type in an anisotropic elastic medium. A kinematic approach. II. (English. Russian original) Zbl 0973.74584

J. Math. Sci., New York 86, No. 3, 2793-2801 (1997); translation from Zap. Nauchn. Semin. POMI 218, 206-219 (1994).
Summary: [For part I see the author, J. Math. Sci., New York 83, No. 2, 334-343 (1997); translation from Zap. Nauchn. Semin. POMI 210, 262-276 (1994; Zbl 0872.73008)]
We study high-frequency Love waves (similar to the well-known transverse waves of the SH type) near the surface of an anisotropic elastic body. The formulation of the boundary value problem, independent of a specific form of the elasticity tensor, provides a kinematic approach which is essential for constructing the asymptotics of these high-frequency waves. To this end, an algorithm is proposed that allows one to relate the transversality of the polarization of surface waves to the directions of their propagation on the surface, and to obtain the necessary conditions for the generation of such waves. The algorithm suggested makes it possible to indicate those types of symmetry of media (special cases of anisotropy), for which the directions obtained correspond to the field of rays of Love waves. In these cases, the space-time ray method provides a mathematical tool for constructing uniform asymptotics of the surface waves.

MSC:

74J15 Surface waves in solid mechanics

Citations:

Zbl 0872.73008
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References:

[1] Yanson, Z. A., Nonstationary Love waves of the SH type in an anisotropic elastic medium. A kinematic approach, Zap. Nauchn. Semin. POMI, 210, 262-276 (1994) · Zbl 0872.73008
[2] Yanson, Z. A., On nonstationary Love waves near the surface of an anisotropic elastic body, Zap. Nauchn. Semin. POMI, 203, 166-172 (1992) · Zbl 0844.73017
[3] Z. A. Yanson, “Nonstationary Love waves near the surface of a transversally isotropic elastic body,” in:Vopr. Dinam. Teor. Raspr. Seismich. Voln, No. 30, Leningrad State Univ. (1990), pp. 113-125.
[4] Azhotkin, V. D.; Babich, V. M., On wave propagation along the surface of an anisotropic body of arbitrary shape, Zap. Nauchn. Semin. LOMI, 165, 9-14 (1987) · Zbl 0662.73020
[5] Babich, V. M.; Yanson, Z. A., On propagation of Love waves along the surface of an elastic body of arbitrary shape, Izv. Akad. Nauk SSSR, Fizika Zemli, 5, 17-27 (1985)
[6] G. I. Petrashen,Wave Propagation in Anisotropic Elastic Media [in Russian], Leningrad (1990).
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