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Geomechanics and Engineering Volume 15, Number 1, May20 2018 , pages 645-657 DOI: https://doi.org/10.12989/gae.2018.15.1.645 |
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Torsional waves in fluid saturated porous layer clamped between two anisotropic media |
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Shishir Gupta, Santimoy Kundu, Prasenjit Pati and Mostaid Ahmed
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| Abstract | ||
| The paper aims to analyze the behaviour of torsional type surface waves propagating through fluid saturated inhomogeneous porous media clamped between two inhomogeneous anisotropic media. We considered three types of inhomogeneities in upper anisotropic layer which varies exponentially, quadratically and hyperbolically with depth. The anisotropic half space inhomogeneity varies linearly with depth and intermediate layer is taken as inhomogeneous fluid saturated porous media with sinusoidal variation. Following Biot, the dispersion equation has been derived in a closed form which contains Whittaker\'s function and its derivative, for approximate result that have been expanded asymptotically up to second term. Possible particular cases have been established which are in perfect agreement with standard results and observe that when one of the upper layer vanishes and other layer is homogeneous isotropic over a homogeneous half space, the velocity of torsional type surface waves coincides with that of classical Love type wave. Comparative study has been made to identify the effects of various dimensionless parameters viz. inhomogeneity parameters, anisotropy parameters, porosity parameter, and initial stress parameters on the torsional wave propagation by means of graphs using MATLAB. The study has its own relevance in connection with the propagation of seismic waves in the earth where fluid saturated poroelastic layer is present. | ||
| Key Words | ||
| torsional surface wave; inhomogeneity; anisotropy; porosity; dispersion equation; group velocity | ||
| Address | ||
| Shishir Gupta, Santimoy Kundu and Prasenjit Pati: Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, India Mostaid Ahmed: 1.) Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, India 2.) Department of Mathematics, The Neotia University, Jhinga, West Bengal, India | ||