Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-19T00:09:41.708Z Has data issue: false hasContentIssue false
  • English
  • Français

Impacts on the Propagation of SH-Waves in a Heterogeneous Viscoelastic Layer Sandwiched between an Anisotropic Porous Layer and an Initially Stressed Isotropic Half Space

Published online by Cambridge University Press:  24 May 2016

S. Kundu ,
P. Alam ,
S. Gupta  and
D. Kr. Pandit
S. Kundu*
Affiliation:
Department of Applied MathematicsIndian School of MinesDhanbad, India
P. Alam
Affiliation:
Department of Applied MathematicsIndian School of MinesDhanbad, India
S. Gupta
Affiliation:
Department of Applied MathematicsIndian School of MinesDhanbad, India
D. Kr. Pandit
Affiliation:
Department of Applied MathematicsIndian School of MinesDhanbad, India
*
*Corresponding author ([email protected])
Get access

Abstract

The present study deals with the affected behaviour of SH-wave propagation through a viscoelastic layer sandwiched between an anisotropic porous layer of finite thickness and an isotropic half space. The sandwiched viscoelastic layer is considered as heterogeneous medium of finite thickness and isotropic half-space is considered as initially stressed medium. The method of separation of variables has been applied to obtain the dispersion equation of SH-wave in their respective media. The obtained complex dispersion relation has been separated into real and imaginary parts. Moreover, the dispersion relation has been satisfied with the classical condition of Love waves. The effects of heterogeneity, attenuation constant, dissipation factor of viscoelasticity, initial stress (compressive), thickness ratio of two layers and porosity on the propagation of SH-waves have been shown by number of graphs. Graphs have been plotted for the dimensionless phase and damping velocity on the propagation of SH-waves with respect to the dimensionless real wave number. The results may be useful to explore the nature and peculiarity of SH-wave propagation in the viscoelastic structure.

Keywords

Attenuation coefficientDissipation factorPhase velocityDamping velocity
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 1 , February 2017 , pp. 13 - 22
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. Moresi, L., Mühlhaus, H.-B. and Dufour, F., “Viscoelastic Formulation for Modelling of Plate Tectonics,” Bifurcation and Localization in Soils and Rocks, Balkema, Rotterdam, pp. 337–344 (2001).Google Scholar
2. Carcione, J. M., “Wave Propagation in Anisotropic Linear Viscoelastic Media: Theory and Simulated Wavefields,” Geophysical Journal International, 101, pp. 739–750 (1990).Google Scholar
3. Biot, M. A., “Theory of Deformation of a Porous Viscoelastic Anisotropic Solid,” Journal of Applied Physics, 27, pp. 459–467 (1956).Google Scholar
4. Biot, M. A., “General Solution of the Equations of Elasticity and Consolidation for a Porous Material,” Journal of Applied Mechanics, 32, pp. 91–95 (1956).Google Scholar
5. Chattopadhyay, A., Gupta, S., Sharma, V. K. and Kumari, P., “Propagation of Shear Waves in Viscoelastic Medium at Irregular Boundaries,” Ada Geophysica, 58, pp. 195–214 (2010).Google Scholar
6. Cooper, H. F., “Reflection and Transmission of Oblique Plane Waves at a Plane Interface Between Viscoelastic Media,” The Journal of the Acoustical Society of America, 42, pp. 1064–1069 (1967).Google Scholar
7. Chaudhary, S., Kaushik, V. P. and Tomar, S. K., “Transmission of Shear Waves Through a Self-Reinforced Layer Sandwiched Between Two Inhomogeneous Viscoelastic Half-Spaces,” International Journal of Mechanical Science, 47, pp. 1455–1472 (2005).Google Scholar
8. Červený, V., “Inhomogeneous Harmonic Plane Waves in Viscoelastic Anisotropic Media,” Studia Geophysica Et Geodaetica, 48, pp. 167–186 (2004).Google Scholar
9. 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
10. Kumar, S., Pal, P. C. and Bose, S., “Propagation of SH-Type Waves in Inhomogeneous Anisotropic Layer Overlying an Anisotropic Viscoelastic Half-Space,” International Journal of Engineering, Science and Technology, 6, pp. 24–30 (2014).Google Scholar
11. Kumari, P. and Snarma, V. K., “Propagation of Torsional Waves in a Viscoelastic Layer Over an Inhomogeneous Half Space,” Acta Mechanica, 225, pp. 1673–1684 (2010).Google Scholar
12. Ke, L. L., Wang, Y. S. and Zhang, Z. M., “Propagation of Love Waves in an Inhomogeneous Fluid Saturated Porous Layered Half-Space with Properties Varying Exponentially,” Journal of Engineering Mechanics, 131, pp. 1322–1328 (2005).Google Scholar
13. 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
14. Sahu, S. A., Saroj, P. K. and Dewangan, N., “SH-Waves in Viscoelastic Heterogeneous Layer Over Half-Space with Self-Weight,” Archive of Applied Mechanics, 84, pp. 235–245 (2014).CrossRefGoogle Scholar
15. Singh, A. K., Kumar, S. and Chattopdhyay, C., “Propagation of Torsional Waves in a Fiber Composite Layer Lying Over an Initially Stressed Viscoelastic Half-Space,” International Journal of Geomechanics, DOI: 10.1061/(ASCE)GM.1943-5622. 0000469.Google Scholar
16. Gubbins, D., Seismology and Plate Tectonics, Cambridge University Press, Cambridge (1990).Google Scholar
17. Altenbach, H., Altenbach, J. and Kissing, W., Mechanics of Composite Structural Elements, Springer-Verlag Berlin Heidelberg, Berlin (2004).CrossRefGoogle Scholar
18. Biot, M. A., Mechanics of Incremental Deformations, Wiley, New York (1965).Google Scholar
19. Ewing, W. M., Jardetzky, W. S. and Press, F., Elastic Waves in Layered Media, McGraw-Hill, New York (1957).Google Scholar
20. Love, A. E. H., Mathematical Theory of Elasticity, Cambridge University Press, Cambridge (1920).Google Scholar
21. Bhattacharya, S. N., “Exact Solution of SH-Wave Equation for Inhomogeneous Media,” Bulletin of the Seismological Society of America, 60, pp. 1847–1859 (1970).Google Scholar