Abstract
The effect of gravity, heterogeneity and internal friction on propagation of SH-waves (horizontally polarised shear waves) in viscoelastic layer over a half-space has been studied. Using the method of separation of variables, dispersion equation has been obtained and used to recover the damped velocity of SH-waves. Both the real and imaginary parts of dispersion equation are in well agreement with the classical Love wave equation. It has been observed that heterogeneity of the medium affects the velocity profile of SH-wave significantly. Some other peculiarities have been observed and discussed in our study.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bhattacharya S.N.: Exact solution of SH-wave equation for inhomogeneous media. Bull. Seismol. Soc. Am. 60(6), 1847–1859 (1970)
Cooper H.F.: Reflection and transmission of oblique plane waves at an interface between viscoelasic media. J. Acoust. Soc. Am. 42, 1064–1069 (1967)
Schoenberg M.: Transmission and reflection of plane waves at an elastic–viscoelastic interface. Geophys. J. Int. 25, 35–47 (1971)
Shaw R.P., Bugl P.: The transmission of plane waves through layered linear viscoelastic media. J. Acoust. Soc. Am. 46(3B), 649–654 (1969)
Borcherdt R.D.: Viscoelastic Waves in Layered Media. Cambridge University Press, New York (2009)
Kaushik V.P., Chopra S.D.: Reflection and transmission of general plane SH-waves at the plane interface between two heterogeneous and homogeneous viscoelastic media. Geophys. Res. Bull. 20, 1–20 (1983)
Gogna, M.L., Chander, S.: Reflection and transmission of SH-waves at an interface between anisotropic inhomogeneous elastic and viscoelastic half-spaces. Acta Geophys. Pol. 33(4), 357–375 (1985)
Romeo M.: Interfacial viscoelastic SH-wave. Int. J. Solids Struct. 40(9), 2057–2068 (2003)
Kanai, K.: The effect of solid viscosity of surface layer on the earthquake movements. Bull. Earthq. Res. Inst. 28, 31 (1950)
Lockett, F.J.: The reflections and refractions of waves at an interface between visco-elastic materials. J. Mech. Phys. Solids 10, 53 (1962)
Červeny V.: Inhomogeneous harmonic plane waves in viscoelastic anisotropic media. Stud. Geod. 48, 167–186 (2004)
Chattopadhyay, A., Gupta, S., Sahu, S.A., Dhua, S.: Torsional surface waves in heterogeneous anisotropic half-space under initial stress. Arch. App. Mech. 83, 357–366 (2012)
Wang, C.-D., Wang, W.-J., Lin, Y.-T., Ruan, Z.-W.: Wave propagation in an inhomogeneous transversely isotropic material obeying the generalized power law model. Arch. App. Mech. 82, 919–936 (2012)
Roy A.: SH wave propagation in laterally heterogeneous medium. Springer Proc. Phys. 126, 335–338 (2009)
Ravindra Ravi: Usual assumptions in the treatment of wave propagation in heterogeneous elastic media. Pure Appl. Geophys. 70(1), 12–17 (1968)
Biot M.A.: Mechanics of Incremental Deformation. Wiley, New York (1965)
Whittaker E.T., Watson G.N.: A Course of Modern Analysis. Universal Book Stall, New Delhi (1991)
Gubbins, D.: Seismology and Plate Tectonics, p. 339. Cambridge University Press, Cambridge (1990)
Dey S., Mukherjee S.P.: Love waves in granular medium over a half-space under gravity. J. Acoust. Soc. Am. 72(5), 1626–1630 (1982)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sahu, S.A., Saroj, P.K. & Dewangan, N. SH-waves in viscoelastic heterogeneous layer over half-space with self-weight. Arch Appl Mech 84, 235–245 (2014). https://doi.org/10.1007/s00419-013-0796-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-013-0796-8