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Torsional Surface Waves in an Inhomogeneous Layer over a Fluid Saturated Porous Half-Space

  • S. Gupta (a1) and A. Pramanik (a1)

Abstract

In the present paper the propagation of torsional surface waves is discussed in an inhomogeneous elastic layer lying over a fluid saturated porous half space. The inhomogeneity in rigidity and density in the inhomogeneous layer plays an important role in the propagation of torsional surface waves. The presence of fluid in the pores diminishes the velocity. Further, it is seen that if the layer becomes homogeneous and the porous half space is replaced by a homogeneous half space, the velocity of the torsional surface waves coincides with that of Love wave. The effect of inhomogeneity factors and porosity factor on the phase velocity of torsional surface wave is delimitated by means of graphs.

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*Corresponding author (abhijit_pramanik@yahoo.in)

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1.Achenbach, J.D., Wave Propagation in Elastic Solids, North Holland Publishing Company, Amsterdam (1973).
2.Ewing, W.M., Jardetzky, W.S. and Press, F., Elastic Waves in Layered Media, McGraw-Hill, New York (1957).
3.Rayleigh, L., “On Waves Propagated along Plane Surface of an Elastic Solid,” Proceedings of the London Mathematical Society, 17, pp. 411 (1885).
4.Georgiadis, H.G., Vardoulakis, I. and Lykotrafitis, G., “Torsional Surface Waves in a Gradient-Elastic Half Space,” Wave Motion, 31, pp. 333348 (2000).
5.Meissner, E., “Elastic Oberflachenwellen Mit Dispersion in Einem Inhomogeneous Medium,” Viertlagahrsschriftder Naturforschenden Gesellschaft, Zurich, 66, pp. 181195 (1921).
6.Dey, S., Gupta, A.K. and Gupta, S., “Propagation of Tor-sional Surface Waves in a Homogeneous Substratum over a Heterogeneous Half-Space,” International Journal for Numerical and Analytical Methods in Geomechanics, 20, pp. 287294 (1996).
7.Gupta, S., Vishwakarma, S.K., Majhi, D.K. and Kundu, S., “Influence of Linearly Varying Density and Rigidity on Torsional Surface Waves in Inhomogeneous Crustal Layer,” Applied Mathematics and Mechanics, 33, pp. 12391252 (2012).
8.Chattopadhyay, A., Gupta, S., Kumari, P. and Sharma, V.K., “Propagation of Torsional Waves in an Inhomogeneous Layer Over an Inhomogeneous Half-Space,” Meccanica, 46, pp. 71680 (2011).
9.Chattopadhyay, A., Gupta, S., Sahu, S.A. and Dhua, S., “Torsional Surface Waves in Heterogeneous An-isotropic Half-Space Under Initial Stress,” Archive of Applied Mechanics, 83, pp. 357366 (2013).
10.Dey, S., Gupta, A.K., Gupta, S. and Prasad, A.M., “Torsional Surface Waves in Nonhomogeneous An-isotropic Medium Under Initial Stress,” Journal of Engineering Mechanics, 126, pp. 11201123 (2000).
11.Dhua, S., Singh, A.K. and Chattopadhyay, A., “Propagation of Torsional Wave in a Composite Layer Overlying an Anisotropic Heterogeneous Half-Space with Initial Stress,” Journal of Vibration and Control, DOI: 10.1177/1077546313505124 (2013).
12.Weiskopf, W.H., “Stresses in Soils Under Foundations,” Journal of the Franklin Institute-Engineering and Applied Mathematics, 239, p. 445 (1945).
13.Biot, M.A., Mechanics of Incremental Deformation, Wiley, New York (1966).
14.Biot, M.A., “Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid: I. Low-Frequency Range,” Journal of the Acoustical Society of American, 28, pp. 168178 (1956a).
15.Biot, M.A., “Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid: II. Higher-Frequency Range,” Journal of the Acoustical Society of American, 28, pp. 179191 (1956b).
16.Dey, S. and Sarkar, M.G., “Torsional Surface Waves in an Initially Stressed Anisotropic Porous Medium,” Journal of Engineering Mechanics, 128, pp. 184189 (2002).
17.Ghorai, A.P., Samal, S.K. and Mahanti, N.C., “Love Waves in a Fluid-Saturated Porous Layer Under a Rigid Boundary and Lying Over an Elastic Half-Space Under Gravity,” Applied Mathematical Modelling, 34, pp. 18731883 (2010).
18.Gupta, A.K. and Gupta, S., “Torsional Surface Waves in Gravitating Anisotropic Porous Half Space,” Mathematics and Mechanics of Solids, 16, pp. 445450 (2011).
19.Gupta, S., Chattopadhyay, A. and Majhi, D.K., “Effect of Initial Stress on Propagation of Love Waves in an Anisotropic Porous Layer,” Journal of Solid Mechanics, 2, pp. 5062 (2010).
20.Kundu, S., Manna, S. and Gupta, S., “Love Wave Dispersion in Pre-Stressed Homogeneous Medium Over a Porous Half-Space with Irregular Boundary Surfaces,” International Journal of Solids and Structures, 51, pp. 36893697 (2014).
21.Kumari, P. and Sharma, V.K., “Propagation of Tor-sional Waves in a Viscoelastic Layer Over an Inho-mogeneous Half Space,” Acta Mechanica, 225, pp. 16731684 (2014).
22.Bullen, K.E., An Introduction to the Theory of Seismology, Cambridge University Press, London (1963).
23.Birch, F., “Symposium on the Interior of the Earth. The Earth’s Mantle. Elasticity and Constitution,” Transactions American Geophysical Union, 35, pp. 7885 (1954).
24.Whittaker, E.T. and Watson, G.N., A Course of Modern Analysis, Cambridge University Press, Cambridge (1991).
25.Gubbins, D., Seismology and Plate Tectonics, Cambridge University Press, Cambridge (1990).

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