Abstract
The present paper is concerned with the propagation of torsional surface waves in a heterogeneous anisotropic half-space under the initial compressive stress. The heterogeneity in the half-space is caused by the linear variation in rigidity, initial compressive stress and density. The solution part of the problem involves the use of Whittaker function. The dispersion equation has been obtained in a closed form, which shows the variation of phase velocity with corresponding wave number. Effects of anisotropy and initial stress have been shown by the means of graphs for different anisotropic materials. It has found that the phase velocity of torsional waves decreases with increment in initial stress and inhomogeneity. Obtained phase velocity of torsional surface wave is found to be less than the shear wave velocity, which agrees with the standard result.
Similar content being viewed by others
References
Ewing W.M., Press W.S.F.: Elastic Waves in Layered Media. McGraw-Hill, New York, NY, USA (1957)
Meissner E.: Elastic oberflachenwellen mit dispersion in einem inhomogeneous medium. Viertelgahrsschriftden Naturforschender Ge-sellschaft in Zurich 66, 181–185 (1921)
Rayleigh L.: Theory of Sound. Dover, New York, NY, USA (1945)
Vardoulakis I.: Torsional surface wave in inhomogeneous elastic media. Int. J. Numer. Anal. Methods Geomech. 8, 287–296 (1984)
Dey S., Dutta D.: Torsional wave propagation in an initially stressed cylinder. Proc. Indian Nat. Sci. Acad. A 58, 425–429 (1992)
Dey S., Gupta S., Gupta A.K.: Torsional surface wave in an elastic half space with void pores. Int. J. Numer. Anal. Methods Geomech. 17, 197–204 (1993)
Chattopadhyay A., Gupta S., Kumari P., Sharma V.K.: Propagation of torsional waves in an inhomogeneous layer over an inhomogeneous half space. Meccanica 46(4), 671–680 (2011)
Dey S., Gupta A.K., Gupta S.: Torsional surface waves in non-homogeneous and anisotropic medium. J. Acoust. Soc. Am. 99(5), 2737–2741 (1996)
Fahmy M.A., El-Shahat T.M.: The effect of initial stress and inhomogeneity on the thermoelastic stresses in a rotating anisotropic solid. Arch. Appl. Mech. 78, 431–442 (2008)
Wang C., Lin Y., Jeng Y., Ruan Z.: Wave propagation in an inhomogeneous cross-anisotropic medium. Int. J. Numer. Anal. Methods Geomech. 34(7), 711–732 (2010)
Gupta S., Chattopadhyay A., Kundu S., Gupta A.K.: Effect of rigid boundary on the propagation of Torsional wave in a homogeneous layer over a heterogeneous half-space. Arch. Appl. Mech. 80, 143–150 (2010)
Biot M.A.: Non linear theory of elasticity and the linearized case for a body initial stress. Philos. Mag. 27(7), 468–489 (1939)
Whittaker E.T., Watson G.N.: A Course of Modern Analysis. Cambridge University Press, Cambridge (1991)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chattopadhyay, A., Gupta, S., Sahu, S.A. et al. Torsional surface waves in heterogeneous anisotropic half-space under initial stress. Arch Appl Mech 83, 357–366 (2013). https://doi.org/10.1007/s00419-012-0683-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-012-0683-8