Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T06:39:01.526Z Has data issue: false hasContentIssue false
  • English
  • Français

Influence of Loosely-Bonded Sandwiched Initially Stressed Visco-Elastic Layer on Torsional Wave Propagation

Published online by Cambridge University Press:  28 October 2016

A. K. Singh ,
Z. Parween ,
A. Das  and
A. Chattopadhyay
A. K. Singh
Affiliation:
Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)Dhanbad, India
Z. Parween*
Affiliation:
Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)Dhanbad, India
A. Das
Affiliation:
Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)Dhanbad, India
A. Chattopadhyay
Affiliation:
Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)Dhanbad, India
*
*Corresponding author (zeenatparween.ism@gmail.com)
Get access

Abstract

Assumption that the common interfaces of the media are perfectly bonded may not be always true. Situation may arise that composition of the two medium may be responsible for weakening the contact between them. So, it becomes obligatory to consider a loosely bonded interface in such cases which may affect the propagation of elastic waves through them. This paper thrashes out the propagation of torsional surface wave in an initially stressed visco-elastic layer sandwiched between upper and lower initially stressed dry-sandy Gibson half-spaces, theoretically. Both the upper and lower dry-sandy Gibson half-spaces are considered to be loosely-bonded with the sandwiched layer. Mathematical model is proposed and solution in terms of Whittaker's and Bessel's function is obtained. Velocity equation is obtained in closed form, its real part deals with the dispersion phenomenon whereas its imaginary part provides the damping characteristics. Influence of heterogeneities, sandiness, gravity parameters, initial-stresses, loose-bonding and internal-friction on the phase and damped velocities of torsional wave are computed numerically and depicted graphically. Deduced dispersion equation and damped velocity equation matches with classical Love-wave equation and vanishes identically for the isotropic case respectively.

Keywords

Loosely-bondedVisco-elasticDry-sandy Gibson half-spaceTorsional wave
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 3 , June 2017 , pp. 351 - 368
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

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

1. Gupta, S. and Pramanik, A., “Torsional Surface Waves in an Inhomogeneous Layer over a Fluid Saturated Porous Half-Space,” Journal of Mechanics, pp. 1-9 (2015).Google Scholar
2. Vishwakarma, S. K., Gupta, S. and Kundu, S., “Torsional Wave Propagation in a Substratum over a Dry Sandy Gibson Half-Space,” International Journal of Geomechanics, DOI: 10.1061/(ASCE) GM.1943-5622.0000322 (2013).Google Scholar
3. Mukhopadhyay, A. K., Gupta, A. K., Kundu, S. and Manna, S. “Influence of initial stress and gravity on torsional surface wave in heterogeneous medium,” Journal of Vibration and Control, DOI: 1077546315587145 (2015).Google Scholar
4. Prasad, R. M., Kundu, S. and Gupta, S., “Propagation of torsional surface wave in sandy layer sandwiched between a non-homogeneous and a gravitating anisotropic porous semi-infinite media,” Journal of Vibration and Control, DOI: 1077546315600112 (2015).Google Scholar
5. Singh, A. K., Das, A., Kumar, S. and Chattopadhyay, A. “Influence of corrugated boundary surfaces, reinforcement, hydrostatic stress, heterogeneity and anisotropy on Love-type wave propagation,” Meccanica, 50, pp. 2977–2994 (2015).CrossRefGoogle Scholar
6. Vardoulakis, I., “Torsional surface waves in inhomogeneous elastic media,” International Journal of Numerical and Analytical Methods in Geomechanics, 8, pp. 287–296 (1984).Google Scholar
7. Sharma, M. D. and Gogna, M. L. “Seismic wave propagation in a visco-elastic porous solid saturated by viscous liquid,” Pure and Applied Geophysics, 135, pp. 383–400 (1991).Google Scholar
8. Garg, N., “Effect of initial stress on harmonic plane homogeneous waves in visco-elastic anisotropic media,” Journal of Sound and Vibration, 303, pp. 515–525 (2007).Google Scholar
9. Sahu, S. A., Saroj, P. K. and Dewangan, N., “SH-waves in viscoelastic heterogeneous layer over half-space with self-weight,” Archives of Applied Mechanics, 84, pp. 235–245 (2014).Google Scholar
10. Dey, S., Gupta, A. K. and Gupta, S., “Effect of gravity and initial stress on torsional surface waves in dry sandy medium,” Journal of Engineering Mechanics, 128, pp. 1115–1118 (2002).CrossRefGoogle Scholar
11. Sharma, M. D. and Gogna, M. L., “Propagation of Love waves in an initially stressed medium consisting of a slow elastic layer lying over a liquid-saturated porous solid half-space,” Journal of Acoustical Society of America, 89, pp. 2584–2588 (1991).Google Scholar
12. Chattaraj, R., Samal, S. K. and Debasis, S., “Dispersion of torsional surface waves in anisotropic layer over porous half space under gravity,” Journal of Applied Mathematics and Mechanics, 94, pp. 1017–1025 (2014).Google Scholar
13. Kumar, R. and Miglani, A., “Effect of Pore Alignment on Surface Wave Propagation in a Liquid-Saturated Layer over a Liquid-Saturated Porous Half-Space with Loosely bonded Interface,” Journal of Physics of the Earth, 44, pp. 153–172 (1996).Google Scholar
14. Dey, S., Gupta, A. K. and Gupta, S., “Propagation of Torsional Surface Waves in Dry Sandy Medium under Gravity,” Mathematics and Mechanics of Solids, 3, pp. 229–235 (1998).Google Scholar
15. 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
16. Murty, G. S., “A theoretical model for the attenuation and dispersion of Stoneley waves at the loosely-bonded interface of elastic half-spaces,” Physics of the Earth and Planetary Interiors, 11, pp. 65–79 (1975).Google Scholar
17. Murty, G. S. “Reflection, transmission and attenuation of elastic waves at a loosely bonded interface of two half-spaces,” Geophysical Journal of the Royal Astronomical Society, 44, pp. 389–404 (1976).Google Scholar
18. Borcherdt, R. D., Viscoelastic Waves in Layered Media, Cambridge University Press, Cambridge (2009).Google Scholar
19. Birch, F., Schairer, J. F. and Spicer, H. C., Handbook of Physical Constants, Geological Society of America, Boulder (1950).Google Scholar
20. Ewing, W. M., Jardetzky, W. S. and Press, F., Elastic Waves in Layered Media, McGraw-Hill, New York (1957).Google Scholar
21. Whittaker, E. T. and Watson, G. N., A Course of Modern Analysis, Universal Book Stall, New Delhi (1991).Google Scholar
22. Gubbins, D., Seismology and Plate Tectonics, Cambridge University Press, Cambridge (1990).Google Scholar
23. Zhang, L., Drilled Shafts in Rock: Analysis and Design, CRC press, Boca Raton (2004).Google Scholar