Reflection of plane waves is studied at a free surface of a perfectly conducting transversely isotropic elastic solid half-space with initial stress. The governing equations are solved to obtain the velocity equation which indicates the existence of two quasi planar waves in the medium. Reflection coefficients and energy ratios for reflected qP and qSV waves are derived and computed numerically for a particular material. Effects of the initial stress and magnetic field are shown graphically on these reflection coefficients and energy ratios.
Similar content being viewed by others
References
Acharya H K 1970 Reflection from the free surface of inhomogeneous media; Bull. Seismol. Soc. Am. 60 1101–1104.
Achenbach J D 1976 Wave propagation in elastic solids; North Holland Publishing Company, New York.
Ahmad F and Khan A 2001 Effect of rotation on wave propagation in a transversely isotropic medium; Math. Probab. Eng. 7 147–154.
Auld B A 1973 Acoustic Field and waves in solids; Wiley, New York.
Biot M A 1965 Mechanics of Incremental Deformations; Wiley, New York.
Chattopadhyay A and Rogerson G A 2001 Wave reflection in slightly compressible, finitely deformed elastic media; Archives of Applied Mechanics 71 307–316.
Das S C, Sengupta S and Acharya 1994 D P Magneto-visco-elastic waves in an initially stressed conducting layer including strain rate and stress rate; Bull. Tech. Univ. Island 47 243–255.
De S N and Sengupta P R 1972 Magneto elastic waves and disturbances in initially stressed conducting media; Pure Appl. Geophys. 93 41–54.
Dey S and Addy S K 1979 Reflection and refractional plane waves under initial stresses at an interface; Int. J. Non-Linear. Mech. 14(2) 101–110.
Gutenberg B 1944 Energy ratio of reflected and refracted seismic waves; Bull. Seismol. Soc. Am. 34 85–112.
Keith C M and Crampin S 1977 Seismic body waves in anisotropic media, reflection and refraction at a plane interface; Geophys. J. Roy. Astron. Soc. 49 181–208.
Knott C G 1899 Reflection and refraction of elastic waves with seismological applications; Phil. Mag. 48 64–97.
Love A E H 1942 A treaties on the mathematical theory of elasticity; Cambridge Univ. Press, London.
Norris A N 1983 Propagation of planes in a pre-stressed elastic medium; J. Acoust. Soc. Am. 74 1642–1643.
Pal A K and Chattopadhyay A 1984 The reflection phenomena of plane waves at a free boundary in a pre-stressed elastic medium; J. Acoust. Soc. Am. 76 924–925.
Rakshit A K and Sengupta P R 1998 Magneto-thermo-elastic waves in initially stressed conducting layer; Sadhana 23 233–246.
Selim M M and Ahmed M K 2006 Propagation and attenuation of seismic body waves in dissipative medium under initial and couple stresses; Appl. Math. 182 1064–1074.
Sharma M D 2007 Effect of initial stress on reflection at the free surfaces of anisotropic elastic medium; J. Earth Syst. Sci. 116(6) 537–551.
Singh B 2010 Wave propagation in a prestressed piezoelectric half-space; Acta Mech. 211 337–344.
Tolstoy I 1982 On elastic waves in pre-stressed solids; J. Geophys. Res. 87 6823–6827.
Tooly R D, Spancer T W and Sagoci H F 1965 Reflection and transmission of plane compression waves; Geophysics 30 552–570.
Yu C P and Tang S 1966 Magneto-elastic waves in initially stressed conductors; Z. Angew. Math. Phys. 17 766–775.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
SINGH, B., YADAV, A.K. Reflection of plane waves in an initially stressed perfectly conducting transversely isotropic solid half-space. J Earth Syst Sci 122, 1045–1053 (2013). https://doi.org/10.1007/s12040-013-0323-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12040-013-0323-x