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Dispersion Study of Propagation of Torsional Surface Wave in a Layered Structure

Published online by Cambridge University Press:  24 January 2017

S. Gupta  and
N. Bhengra
S. Gupta
Affiliation:
Department of Applied MathematicsIndian Institute of Technology (ISM)Dhanbad, India
N. Bhengra*
Affiliation:
Department of Applied MathematicsIndian Institute of Technology (ISM)Dhanbad, India
*
*Corresponding author ([email protected])
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Abstract

This paper presents the feasibility of torsional surface wave propagation in an anisotropic layer sandwiched between two anisotropic inhomogeneous media. The anisotropy considered in the upper layer and the lower half-space is of transversely isotropic kind while the sandwiched anisotropic layer is a porous layer. The directional rigidities and density have been considered linearly and exponentially varying in the half-space and in the upper layer respectively, while it is taken as a variable in the sandwiched layer. The compact form of dispersion equation governing the propagation of the torsional surface wave has been derived by using the Whittaker function under appropriate boundary conditions. The dispersion of the torsional wave and the effects of inhomogeneity parameters, initial stress and poroelastic constant have been calculated numerically and demonstrated through graphs.

Keywords

Torsional surface waveTransversely isotropic mediumPorous mediumWhittaker function
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 3 , June 2017 , pp. 303 - 315
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

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References

1. Ewing, W. M., Jardetzky, W. S. and Press, F., Elastic waves in layered media, McGraw-Hill, New York (1957).Google Scholar
2. Gubbins, D., Seismology and Plate Tectonics, Cambridge University Press, Cambridge (1990).Google Scholar
3. Udias, A., Principles of Seismology, Cambridge University Press, Cambridge (1999).Google Scholar
4. 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
5. Selim, M. M., “Propagation of torsional surface wave in heterogeneous half-space with irregular free surface,” Applied Mathematical Sciences, 1, pp. 1429–1437 (2007).Google Scholar
6. Ozturk, A. and Akbarov, S. D., “Torsional wave propagation in a pre-stressed circular cylinder embedded in a pre-stressed elastic medium,” Applied Mathematical Modeling, 33, pp. 3636–3649 (2009).Google Scholar
7. Akbarov, S. D., Kepceler, T. and Egilmez, M. M, “Torsional wave dispersion in a finitely pre-strained hollow sandwich circular cylinder,” Journal of Sound and Vibration, 330, pp. 4519–4537 (2011).CrossRefGoogle 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. 671–680 (2011).Google Scholar
9. Biot, M. A., “Theory of elastic waves in a fluid-saturated porous solid: I. Low frequency range,” The Journal of the Acoustical Society of America, 28, pp. 168–178 (1956).CrossRefGoogle Scholar
10. Biot, M. A., “Theory of elastic waves in a fluid-saturated porous solid: II. High frequency range,” The Journal of the Acoustical Society of America, 28, pp. 179–191 (1956).CrossRefGoogle Scholar
11. Biot, M. A., “Mechanics of deformation and acoustic propagation in porous media,” Journal of Applied Physics, 33, pp. 1482–1498 (1962).Google Scholar
12. Deresiewicz, H., “The effect of boundaries on wave propagation in a liquid-filled porous solid: II. The Love waves in a porous layer,” Bulletin of the Seismological Society of America, 51, pp. 51–59 (1961).Google Scholar
13. Deresiewicz, H., “The effect of boundaries on wave propagation in a liquid-filled porous solid: VI. The Love waves in a double surface layer,” Bulletin of the Seismological Society of America, 54, pp. 417–423 (1964).CrossRefGoogle Scholar
14. Deresiewicz, H., “The effect of boundaries on wave propagation in a liquid-filled porous solid: IX. Love waves in a porous internal stratum,” Bulletin of the Seismological Society of America, 55, pp. 919–923 (1965).CrossRefGoogle Scholar
15. Sharma, M. D. and Gogna, M. L., “Propagation of the Love waves in an initially stressed medium consist of a slow elastic lying over a liquid saturated porous solid half-space,” The Journal of the Acoustical Society of America, 89, pp. 2584–2588 (1991).Google Scholar
16. Wang, Y. S. and Zhang, Z. M., “Propagation of the Love waves in a transversely isotropic fluid-saturated porous layered half-space,” The Journal of the Acoustical Society of America, 103, pp. 695–701 (1998).Google Scholar
17. 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
18. Ke, L. L., Wang, Y. S. and Zhang, Z. M., “Love waves in an inhomogeneous fluid saturated porous layered half-space with linearly varying properties,” Soil Dynamics and Earthquake Engineering, 26, pp. 574–581 (2006).CrossRefGoogle Scholar
19. Bullen, K. E., “The problem of the Earth's density variation,” Bulletin of the Seismological Society of America, 30, pp. 235–250 (1940).Google Scholar
20. Gupta, S., Majhi, D. K. and Vishwakarma, S. K., “Torsional surface wave propagation in an initially stressed non-homogeneous layer over a non-homogeneous half-space.” Applied Mathematics and Computation, 219, pp. 3209–3218 (2012).CrossRefGoogle Scholar
21. Sari, C. and Salk, M., “Analysis of gravity anomalies with hyperbolic density contrast: An application to the gravity data of Western Anatolia,” Journal of the Balkan Geophysical Society, 5, pp. 87–96 (2002).Google Scholar
22. Biot, M. A., Mechanics of Incremental Deformation, John Willey and Sons, New York (1965).Google Scholar
23. Biot, M. A., “Non-linear theory of elasticity and the linearized case for a body under initial stress,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 27, pp. 468–489 (1939).CrossRefGoogle Scholar
24. Chattopadhyay, A. et al., “Torsional surface waves in heterogeneous anisotropic half-space under initial stress,” Archive of Applied Mechanics, 83, pp. 357–366 (2013).Google Scholar
25. Samal, S. and Chattaraj, R., “Surface wave propagation in fiber-reinforced anisotropic elastic layer between liquid saturated porous half space and uniform liquid layer,” Acta Geophysica, 59, pp. 470–482 (2011).Google Scholar
26. Tierstein, H. F., Linear Piezoelectric Plate Vibrations, Plenum Press, New York, (1969).Google Scholar