A Study on Propagation of Waves in a Transversely Isotropic Poroelastic Layer Bounded between Two Viscous Liquids
- 1 Department of Mathematics, BVRITH College of Engineering for Women, Hyderabad, India
- 2 Department of Mathematics, Deccan College of Engineering and Technology, Hyderabad, India
- 3 Department of Mathematics, University College of Technology, Osmania University, Hyderabad, India
- 4 Department of Mathematics, Osmania University, Hyderabad, India
Abstract
Propagation of Love waves in a transversely isotropic poroelastic layer bounded between two compressible viscous liquids is presented. The equations of motion in a transversely isotropic poroelastic solid are formulated in the framework of Biot’s theory. A closed-form solution for the propagation of Love waves is obtained in a transversely isotropic poroelastic layer. The complex frequency equation for phase velocity and attenuation of Love waves is derived for a transversely isotropic poroelastic layer when it is bounded between two viscous liquids and the results are compared with that of the poroelastic layer. The effect of viscous liquids on the propagation of Love waves is discussed. It is observed that the presence of viscous liquids decreases phase velocity in both transversely isotropic poroelastic layer and poroelastic layer. Results related to the case without viscous liquids have been compared with some of the earlier results and comparison shows good agreement.
- Deresiewicz, H. (1960) The Effect of Boundaries on Wave Propagation in a Liquid-Filled Porous Solid-I. Bulletin of the Seismological Society of America, 50, 599-607.
- Deresiewicz, H. and Rice, J.T. (1962) The Effect of Boundaries on Wave Propagation in a Liquid-Filled Porous Solid-II. Bulletin of the Seismological Society of America, 52, 595-626.
- Banghar, A.R. (1978) On Propagation and Attenuation of Love Waves. Proceedings of the Indian Academy of Sciences, 88, 133-146. https://doi.org/10.1007/BF02871610
- Nageswara Nath, C., Manoj Kumar, J. and Tajuddin, M. (2011) On the Parametric model of Loose Bonding between Two Poroelastic Half Spaces. Journal of Vibration and Control, 18, 1261-1274.
- Kielczynski, P., Szalewski, M.A. and Alcerzak, B. (2012) Effect of a Viscous Liquid Loading on Love Wave Propagation. International Journal of Solids and Structures, 49, 2314-2319. https://doi.org/10.1016/j.ijsolstr.2012.04.030
- Anjana, P.G., Samal, S.K. and Mahanti, N.C. (2010) 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, 1873-1883. https://doi.org/10.1016/j.apm.2009.10.004
- Wang, Y.S. and Zhang, Z.M. (1998) Propagation of Love Waves in a Transversely Isotropic Fluid Saturated Porous Layered Half-Space. Journal of the Acoustical Society of America, 103, 695-701. https://doi.org/10.1121/1.421196
- Nageswaranath, C., Manoj kumar, J. and Ahmed Shah, S. (2017) Effect of Viscosity on Waves Propagating in a Liquid Loaded on Poroelastic Layered Half-Space, Advanced Math. Models & Applications, 2, 144-154.
- Nageswara Nath C., Manoj Kumar, J. and Ahmed Shah, S. (2015) On Propagation of Love Waves in an Infinite Transversely Isotropic Poroelastic Layer. Journal of Physics: Conference Series, 662, Article ID: 012004. https://doi.org/10.1088/1742-6596/662/1/012004
- Kundu, S., Manna, S. and Gupta, S. (2014) Love Wave Dispersion in Pre-Stressed Homogeneous Medium over a Porous Half-Space with Irregular Boundary Surfaces. International Journal of Solids and Structures, 51, 3689-3697.
- Biot, M.A. (1956) The Theory of Propagation of Elastic Waves in Fluid-Saturated Porous Solid. Journal of the Acoustical Society of America, 28, 168-178. https://doi.org/10.1121/1.1908239
- Biot, M.A. and Willis, D.G. (1957) The Elastic Co-Efficients of the Theory of Consolidation. Journal of Applied Mechanics, 24, 594-601.