Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-25T06:37:24.940Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  15 July 2015

S. Gupta  and
A. Pramanik
S. Gupta
Affiliation:
Department of Applied Mathematics, Indian School of Mines, Jharkhand, India
A. Pramanik*
Affiliation:
Department of Applied Mathematics, Indian School of Mines, Jharkhand, India
*
*Corresponding author (abhijit_pramanik@yahoo.in)
Get access

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.

Keywords

Torsional Surface WavesInhomogeneityPorous Half-SpacePhase velocity
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 1 , February 2016 , pp. 113 - 121
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Achenbach, J.D., Wave Propagation in Elastic Solids, North Holland Publishing Company, Amsterdam (1973).Google Scholar
2.Ewing, W.M., Jardetzky, W.S. and Press, F., Elastic Waves in Layered Media, McGraw-Hill, New York (1957).Google Scholar
3.Rayleigh, L., “On Waves Propagated along Plane Surface of an Elastic Solid,” Proceedings of the London Mathematical Society, 17, pp. 4–11 (1885).Google Scholar
4.Georgiadis, H.G., Vardoulakis, I. and Lykotrafitis, G., “Torsional Surface Waves in a Gradient-Elastic Half Space,” Wave Motion, 31, pp. 333–348 (2000).Google Scholar
5.Meissner, E., “Elastic Oberflachenwellen Mit Dispersion in Einem Inhomogeneous Medium,” Viertlagahrsschriftder Naturforschenden Gesellschaft, Zurich, 66, pp. 181–195 (1921).Google Scholar
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. 287–294 (1996).Google Scholar
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. 1239–1252 (2012).Google Scholar
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. 71–680 (2011).CrossRefGoogle Scholar
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. 357–366 (2013).Google Scholar
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. 1120–1123 (2000).CrossRefGoogle Scholar
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).Google Scholar
12.Weiskopf, W.H., “Stresses in Soils Under Foundations,” Journal of the Franklin Institute-Engineering and Applied Mathematics, 239, p. 445 (1945).CrossRefGoogle Scholar
13.Biot, M.A., Mechanics of Incremental Deformation, Wiley, New York (1966).Google Scholar
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. 168–178 (1956a).CrossRefGoogle Scholar
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. 179–191 (1956b).Google Scholar
16.Dey, S. and Sarkar, M.G., “Torsional Surface Waves in an Initially Stressed Anisotropic Porous Medium,” Journal of Engineering Mechanics, 128, pp. 184–189 (2002).Google Scholar
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. 1873–1883 (2010).Google Scholar
18.Gupta, A.K. and Gupta, S., “Torsional Surface Waves in Gravitating Anisotropic Porous Half Space,” Mathematics and Mechanics of Solids, 16, pp. 445–450 (2011).Google Scholar
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. 50–62 (2010).Google Scholar
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. 3689–3697 (2014).CrossRefGoogle Scholar
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. 1673–1684 (2014).Google Scholar
22.Bullen, K.E., An Introduction to the Theory of Seismology, Cambridge University Press, London (1963).Google Scholar
23.Birch, F., “Symposium on the Interior of the Earth. The Earth’s Mantle. Elasticity and Constitution,” Transactions American Geophysical Union, 35, pp. 78–85 (1954).Google Scholar
24.Whittaker, E.T. and Watson, G.N., A Course of Modern Analysis, Cambridge University Press, Cambridge (1991).Google Scholar
25.Gubbins, D., Seismology and Plate Tectonics, Cambridge University Press, Cambridge (1990).Google Scholar