Technical Papers
Jun 24, 2015

Effect of Reinforcement and Inhomogeneity on the Propagation of Love Waves

Publication: International Journal of Geomechanics
Volume 16, Issue 2

Abstract

The aim of this paper is to investigate the propagation of Love waves in an anisotropic fiber-reinforced layer over an elastic inhomogeneous stratum. The inhomogeneity of the half-space has been taken as a linear variation of rigidity and density. The equations of motion have been formulated separately for layer and half-space under suitable boundary conditions. The frequency relation of phase velocity has been deduced in compact form using separation of variables by means of the Whittaker function. Some particular cases have also been investigated. As a special case when both the layer and half-space are homogeneous, the computed frequency relation coincides with the general equation of the Love wave. Numerical calculations of frequency relation have been performed for different values of parameters and plotted graphically to study the effect of different factors. The wave velocity is strongly influenced by the reinforcement and inhomogeneity parameters.

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References

Abd-Alla, A. M., and Ahmed, S. M. (1999). “Propagation of Love waves in a nonhomogeneous orthotropic elastic layer under initial stress overlying semi-infinite medium.” Appl. Math. Comput., 106(2), 265–275.
Abd-Alla, A. M., Nofal, T. A., Abo-Dahab, S. M., and Al-Mullise, A. (2013). “Surface waves propagation in fibre-reinforced anisotropic elastic media subjected to gravity field.” Int. J. Phys. Sci., 8(14), 574–584.
Belfield, A. J., Rogers, T. G., and Spencer, A. J. M. (1983). “Stress in elastic plates reinforced by fibers lying in concentric circles.” J. Mech. Phys. Solids, 31(1), 25–54.
Biot, M. A. (1965). Mechanics of incremental deformations, John Wiley & Sons, New York.
Chattaraj, R., and Samal, S. K. (2013). “Love waves in the fiber reinforced layer over a gravitating porous half-space.” Acta Geophys., 61(5), 1170–1183.
Chattaraj, R., Samal, S. K., and Mahanti, N. (2013). “Dispersion of Love wave propagating in irregular anisotropic porous stratum under initial stress.” Int. J. Geomech., 402–408.
Chattopadhyay, A. (1975). “On the dispersion equation for Love wave due to irregularity in the thickness of nonhomogeneous crustal layer.” Acta Geophys. Polon., 23, 307–317.
Chattopadhyay, A., and Choudhury, S. (1990). “Propagation, reflection and transmission of magnetoelastic shear waves in a self-reinforced medium.” Int. J. Eng. Sci., 28(6), 485–495.
Chattopadhyay, A., Gupta, S., Sahu, S. A., and Singh, A. K. (2012). “Torsional surface waves in a self-reinforced medium over a heterogeneous half space.” Int. J. Geomech., 193–197.
Chattopadhyay, A., and Michel, V. (2006). “A model for spherical SH-wave propagation in self-reinforced linearly elastic media.” Arch. Appl. Mech., 75(2–3), 113–124.
Chaudhary, S., Kaushik, V. P., and Tomar, S. K. (2004). “Reflection/transmission of plane SH wave through a self-reinforced elastic layer between two half-spaces.” Acta Geophys. Polon., 52(2), 219–235.
Ewing, W. M., Jardetzky, W. S., and Press, F. (1957). Elastic waves in layered media, McGraw-Hill, New York.
Ghorai, A. P., 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.” Appl. Math. Model., 34(7), 1873–1883.
Gubbins, D. (1990). Seismology and plate tectonics, Cambridge Univ. Press, Cambridge.
Gupta, S., Majhi, D. K., Kundu, S., and Vishwakarma, S. K. (2013). “Propagation of Love waves in nonhomogeneous substratum over initially stressed heterogeneous half-space.” Appl. Math. Mech. Engl. Ed., 34(2), 249–258.
Hashin, Z., and Rosen, W. B. (1964). “The elastic moduli of fiber reinforced materials.” J. Appl. Mech., 31, 223–232.
Kundu, S., Gupta, S., and Manna, S. (2014a). “Propagation of Love wave in fiber-reinforced medium lying over an initially stressed orthotropic half-space.” Int. J. Numer. Anal. Meth. Geomech., 38(11), 1172–1182.
Kundu, S., Gupta, S., and Manna, S. (2014b). “SH-type waves dispersion in an isotropic medium sandwiched between an initially stressed orthotropic and heterogeneous semi-infinite media.” Meccanica, 49(3), 749–758.
Markham, M. F. (1970). “Measurement of the elastic constants of fibre composites by ultrasonics.” Composites, 1(3), 145–149.
Pradhan, A., Samal, S. K., and Mahanti, N. C. (2003). “The influence of anisotropy on the Love waves in a self-reinforced medium.” Tamkang J. Sci. Eng., 6(3), 173–178.
Richter, C. F. (1958). Elementary seismology, W.H. Freeman and Company, San Francisco, and Bailey Bros. Swinfen Ltd., London.
Sengupta, P. R., and Nath, S. (2001). “Surface waves in fiber-reinforced anisotropic elastic medium.” Sãdhanã, 26(4), 363–370.
Sethi, M., Gupta, K. C., and Gupta, D. M. (2013). “Surface waves in fibre-reinforced anisotropic solid elastic media under the influence of gravity.” Int. J. Appl. Mech. Eng., 18(1), 177–188.
Singh, B. (2006). “Wave propagation in thermally conducting linear fibre-reinforced composite materials.” Arch. Appl. Mech., 75(8–9), 513–520.
Singh, B., and Singh, S. J. (2004). “Reflection of plane waves at the free surface of a fiber-reinforced elastic half-space.” Sãdhanã, 29(3), 249–257.
Singh, S. J. (2002). “Surface waves in fibre-reinforced anisotropic elastic media.” Sãdhanã, 27(3), 405–407.
Sinha, N. K. (1967). “Propagation of Love waves in a nonhomogeneous stratum of finite depth sandwiched between two semi-infinite isotropic media.” Pure Appl. Geophys., 67(1), 65–70.
Spencer, A. J. M. (1972). Deformation of fiber reinforced material, Oxford Univ. Press, London.
Verma, P. D. S. (1986). “Magnetoelastic shear waves in self-reinforced bodies.” Int. J. Eng. Sci., 24(7), 1067–1073.
Vishwakarma, S. K., Gupta, S., and Kundu, S. (2014). “Torsional wave propagation in a substratum over a dry sandy Gibson half-space.” Int. J. Geomech., 06014002.
Wang, Y. S., and Zhang, Z. M. (1998). “Propagation of Love waves in a transversely isotropic fluid-saturated porous layered half-space.” J. Acoust. Soc. Am., 103(2), 695–701.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 16Issue 2April 2016

History

Received: Jun 9, 2014
Accepted: Mar 10, 2015
Published online: Jun 24, 2015
Discussion open until: Nov 24, 2015
Published in print: Apr 1, 2016

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Authors

Affiliations

Santanu Manna [email protected]
Dept. of Earth Sciences, Indian Institute of Science Education and Research, Kolkata-741246, India; Dept. of Applied Mathematics, Indian School of Mines, Dhanbad-826004, India (corresponding author). E-mail: [email protected]
Santimoy Kundu [email protected]
Dept. of Applied Mathematics, Indian School of Mines, Dhanbad 826004, India. E-mail: [email protected]
Shishir Gupta [email protected]
Dept. of Applied Mathematics, Indian School of Mines, Dhanbad 826004, India. E-mail: [email protected]

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