Shear Waves Through Non Planar Interface Between Anisotropic Inhomogeneous and Visco-Elastic Half-Spaces
محورهای موضوعی : Engineering
B Prasad
1
,
P Chandra Pal
2
,
S Kundu
3
1 - Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India
2 - Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India
3 - Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India
کلید واژه: Inhomogeneity, SH-waves, Anisotropy, Visco-elastic, Corrugated boundary,
چکیده مقاله :
A problem of reflection and transmission of a plane shear wave incident at a corrugated interface between transversely isotropic inhomogeneous and visco-elastic half-spaces is investigated. Applying appropriate boundary conditions and using Rayleigh’s method of approximation expressions for reflection and transmission coefficients are obtained for the first and second order approximation of the corrugation. Further, closed form formulae of these coefficients are presented for a corrugated interface of periodic shape (cosine law interface). Numerical computations for this particular type of corrugated interface are performed and a number of graphs are plotted to illustrate the effect of different parameters of the both half-spaces on the reflection and transmission coefficients. It is found that these coefficients depend upon the amplitude of corrugation of the boundary, angle of incidence and frequency of the incident wave and are strongly influenced by the anisotropy, inhomogeneity and visco-elasticity of the half-spaces. Some special cases are also derived.
[1] Rayleigh L., 1907, On the dynamical theory of gratings, The Royal Society Publishing 79: 399-416.
[2] Asano S., 1960, Reflection and refraction of elastic waves at a corrugated boundary surface part-I: The case of incidence of SH-wave, Bulletin of Earthquake Research Institute 38: 177-197.
[3] Asano S., 1961, Reflection and refraction of elastic waves at a corrugated boundary surface part-II, Bulletin of Earthquake Research Institute 39: 367-406.
[4] Asano S., 1966, Reflection and refraction of elastic waves at a corrugated interface, Bulletin of the Seismological Society of America 56: 201-221.
[5] Abubakar I., 1962, Scattering of plane elastic waves at rough surfaces, Proceedings of Cambridge Philosophical Society 58: 136-157.
[6] Dunkin J.W., Eringen A.C., 1962, The reflection of elastic waves from the wavy boundary of a half-space, Proceedings of the 4th U. S. National Congress on Applied Mechanics, University of California Press, Berkeley.
[7] Abubakar I., 1962, Reflection and refraction of plane SH-waves at irregular interface, Journal of Physics of the Earth 10: 1-14.
[8] Abubakar I., 1962, Reflection and refraction of plane SH-waves at irregular interfaces, Journal of Physics of the Earth 10: 15-20.
[9] Kaushik V.P., Chopra S.D., 1981, Reflection and transmission of plane SH-waves at an anisotropic elastic viscoelastic interface, Geophysical Research Bulletin 19: 1-12.
[10] Gogna M.L., Chander S., 1985, Reflection and refraction of SH-waves at an interface between anisotropic inhomogeneous elastic and viscoelastic half-spaces, Acta Geophysica Polonica 33: 357-375.
[11] Gupta S., 1987, Reflection and transmission of SH-waves in laterally and vertically heterogeneous media at an irregular boundary, Geophysical Transmission 33: 89-111.
[12] Kumar R., Tomar S.K., Chopra A., 2003, Reflection/refraction of SH-waves at a corrugated interface between two different anisotropic and vertically heterogeneous elastic solid half-spaces, Australia and New Zealand Industrial and Applied Mathematics Journal 44: 447-460.
[13] Tomar S.K., Kaur J., 2003, Reflection and transmission of SH-waves at a corrugated interface between two laterally and vertically heterogeneous anisotropic elastic half-spaces, Earth Planets and Space 55: 531-547.
[14] Kaur J., Tomar S.K., Kaushik V.P., 2005, Reflection and refraction of SH-waves at a corrugated interface between two laterally and vertically heterogeneous viscoelastic solid half-spaces, International Journal of Solids Structures 42(13): 3621-3643.
[15] Chattopadhyay A., Gupta S., Sharma V.K., Kumari P., 2008, Propagation of SH waves in an irregular monoclinic crustal layer, Archive of Applied Mechanics 78(12): 989-999.
[16] Chattopadhyay A., Gupta S., Sharma V.K., Kumari P., 2009, Reflection and refraction of plane quasi-P waves at a corrugated interface between distinct triclinic elastic half spaces, International Journal of Solids and Structures 46: 3241-3256.
[17] Chattopadhyay A., Gupta S., Sharma V.K., Kumari P., 2010, Propagation of shear waves in viscoelastic medium at irregular boundaries, Acta Geophysica 58(2): 195-214.
[18] Chattopadhyay A., Gupta S., Sahu S.A., Singh A.K., 2013, Dispersion of horizontally polarized shear waves in an irregular non-homogeneous self-reinforced crustal layer over a semi-infinite self-reinforced medium, Journal of Vibration and Control 19(1): 109-119.
[19] Kumar R., Garg S.K., Ahuja S., 2015, Wave propagation in fibre-reinforced transversely isotropic thermoelastic media with initial stress at the boundary, Journal of Solid Mechanics 7(2): 223-238.
[20] Prasad B., Pal P.C., Kundu S., 2017, Propagation of SH-waves through non planer interface between visco-elastic and fibre-reinforced solid half-spaces, Journal of Mechanics 33(4): 545-557.
[21] Kakar R., 2015, Rayleigh waves in a homogeneous magneto-thermo Voigt-type viscoelastic half-space under initial surface stress, Journal of Solid Mechanics 7(3): 255-267.
[22] Kumar S., Pal P.C., Majhi S., 2017, Reflection and transmission of SH-waves at a corrugated interface between two semi-infinite anisotropic magneto elastic half-spaces, Waves in Random and Complex Media 27(2): 339-358.
[23] Vaishnav P.K., Kundu S., Abo-Dahab S.M., Saha A., 2017, Torsional surface wave propagation in anisotropic layer sandwiched between heterogeneous half-space, Journal of Solid Mechanics 9(1): 213-224.
[24] Gupta R.N., 1965, Reflection of plane waves from a linear transition layer in liquid media, Geophysics 30(1): 122-132.
[25] Schoenberg M., 1971, Transmission and reflection of plane waves at an elastic-viscoelastic interface, Geophysical Journal of the Royal Astronomical Society 25: 35-47.
[26] Kaushik V.P., Rana A., 1997, Transmission of SH waves through a linear viscoelastic layer sandwiched between two anisotropic inhomogeneous elastic half spaces, Indian Journal of Pure and Applied Mathematics 28(6): 851-863.
[27] Savarensky E., 1975, Seismic Waves, Mir Publication, Moscow.
[28] Gubbins D., 1990, Seismology and Plate Tectonics, Cambridge University Press, Cambridge.
