The ray method is used to solve the problem of the propagation of discontinuous (weak shock) waves in inhomogeneous elastic media. A procedure for drawing the fronts of reflected and refracted waves at interfaces and calculating their intensities is proposed. The effect of shielding discontinuous waves by one or two interfaces is studied. The cases of slipping and non-slipping contact are examined
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References
A. N. Guz, Elastic Waves in Bodies with Initial (Residual) Stresses [in Russian], A.S.K., Kyiv (2004).
V. I. Gulyaev and G. M. Ivanchenko, “Diffraction of a plane discontinuous wave in layered anisotropic elastic media,” Mech. Comp. Mater., 39, No. 1, 27–36 (2003).
V. I. Gulyaev, P. Z. Lugovoi, G. M. Ivanchenko, and E. V. Yakovenko, “The diffraction of a shock wave at the curvilinear interface of transversely isotropic elastic media,” J. Appl. Mat. Mech., 64, No. 3, 379–386 (2000).
V. I. Gulyaev, P. Z. Lugovoi, V. B. Kritskii, and G. M. Ivanchenko, “Reflection and refraction of plane discontinuous waves by paraboloidal interfaces between anisotropic elastic media,” Geofiz. Zh., 27, No. 3, 418–426 (2005).
V. I. Gulyaev, P. Z. Lugovoi, and G. M. Ivanchenko, “Diffraction of discontinuous waves by ellipsoidal interfaces of transversely isotropic elastic media,” Int. Appl. Mech., 40, No. 10, 1145–1151 (2004).
I. K. Kikoin, Tables of Physical Quantities [in Russian], Atomizdat, Moscow (1976).
Yu. A. Kravtsov and Yu. I. Orlov, Geometrical Optics of Inhomogeneous Media, Springer Verlag, Berlin (1990).
G. I. Petrashen’, Wave Propagation in Anisotropic Elastic Media [in Russian], Nauka, Leningrad (1980).
Yu. N. Podil’chuk and Yu. K. Rubtsov, “Application of the method of ray series to the investigation of axisymmetric nonstationary problems of the dynamical theory of elasticity,” Int. Appl. Mech., 22, No. 3, 201–207 (1986).
Yu. N. Podil’chuk and Yu. K. Rubtsov, Ray Methods in the Theory of Propagation and Scattering of Waves [in Russian], Naukova Dumka, Kyiv (1988).
F. I. Fedorov, Theory of Elastic Waves in Crystals, Plenum, New York (1968).
R. D. Borcherdt, “Reflection–refraction of general P- and type-I S-waves in elastic and inelastic solids,” Geophys. J. Royal Astron. Soc., 70, 621–638 (1982).
C. Chapman, Fundamentals of Seismic Wave Propagation, Cambridge Univ. Press, Cambridge (2004).
J. M. Crichlow, “The effect of underground structure on seismic motions of the ground surface,” Geophys. J. Royal Astron. Soc., 70, 563–575 (1982).
O. K. Ersoy, Diffraction, Fourier Optics and Imaging, Wiley, Blackwell (2007).
V. V. Gaydachuk, V. I. Koshel’, and P. Z. Lugovoi, “Stress distribution around mine working,” Int. Appl. Mech., 46, No. 9, 981–986 (2010).
A. Ya. Grigorenko, I. I. Dyyak, S. I. Matysyak, and I. I. Prokopyshyn, “Domain decomposition methods applied to solve frictionless-contact problems for multilayer elastic bodies,” Int. Appl. Mech., 46, No. 4, 388–399 (2010).
V. I. Gulyaev, P. Z. Lugovoi, Yu. A. Zaets, and M. Nabil, “Evolution of the fronts of quasi-compressional and quasi-discontinuous waves in inhomogeneous transversely isotropic elastic media,” Int. Appl. Mech., 47, No. 1, 55–61 (2011).
A. N. Norris and G. R. Wickham, “Elastic waves in inhomogeneously oriented anisotropic materials,” Wave Motion, 33, No. 1, 97–108 (2001).
D. M. Pai, “Wave propagation in inhomogeneous media: A planewave layer interaction method,” Wave Motion, 13, No. 3, 205–306 (1991).
O. N. Panasyuk, “Propagation of quasishear waves in prestressed materials with unbonded layers,” Int. Appl. Mech., 47, No. 3, 276–282 (2011).
A. L. Virovlyansky, A. Yu. Kazarova, and L. Ya. Lyubavin, “Ray-based description of normal mode amplitudes in a range-dependent waveguide,” Wave Motion, 42, No. 4, 317–334 (2005).
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Translated from Prikladnaya Mekhanika, Vol. 48, No. 4, pp. 67–77, July–August 2012.
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Gulyaev, V.I., Lugovoi, P.Z. & Zayets, Y.A. Shielding of elastic nonstationary waves by interfaces. Int Appl Mech 48, 414–422 (2012). https://doi.org/10.1007/s10778-012-0528-8
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DOI: https://doi.org/10.1007/s10778-012-0528-8