Technical Papers
Apr 30, 2015

Propagation of Torsional Waves in a Fiber Composite Layer Lying over an Initially Stressed Viscoelastic Half-Space

Publication: International Journal of Geomechanics
Volume 16, Issue 1

Abstract

The present study investigates the possibility of torsional surface wave propagation in a fiber composite layer lying over an initially stressed viscoelastic half-space. The closed-form expression for the dispersion relation and damping equation has been obtained. Viscoelasticity of the lower half-space, reinforcement, wave number, and horizontal compressive/tensile initial stress acting in an initially stressed lower half-space have substantial effect on the dispersion curve. For the sake of comparative study, numerical computation and graphical demonstration have been carried out by considering some of the special cases of the problem in addition to the problem itself. A remarkable finding is that reinforcement in the superficial layer favors more the phase velocity and damped velocity of a torsional surface wave as compared with the reinforced free superficial layer. As a special case of the problem, it is found that the obtained dispersion relation is well in agreement with the classical Love wave equation.

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Acknowledgments

The authors convey their sincere thanks to the Indian School of Mines, Dhanbad, for providing JRF to Mr. Santan Kumar and also for facilitating them with its best facility for research.

References

Achenbach, J. D. (1976). Wave propagation in elastic solid, North Holland, New York.
Belfield, A. J., Rogers, T. G., and Spencer, A. J. M. (1983). “Stress in elastic plates reinforced by fibres lying in concentric circles.” J. Mech. Phys. Solids, 31(1), 25–54.
Biot, M. A. (1940). “The influence of initial stress on elastic waves.” J. Appl. Phys., 11, 522–530.
Biot, M. A. (1965). Mechanics of incremental deformation, Wiley, New York.
Chattopadhyay, A., and Singh, A. K. (2012a). “Propagation of a crack due to magnetoelastic shear waves in a self-reinforced medium.” J. Vib. Control, 20(3), 406–420.
Chattopadhyay, A., and Singh, A. K. (2012b). “Propagation of magnetoelastic shear waves in an irregular self-reinforced layer.” J. Eng. Math., 75(1), 139–155.
Chattopadhyay, A., Gupta, S., Chattopadhyay, A., and Singh, A. K. (2010b). “The dispersion of shear wave in multilayered magnetoelastic self-reinforced media.” Int. J. Sol. Struct., 47(9), 1317–1324.
Chattopadhyay, A., Gupta, S., Kumari, P., and Sharma, V. K. (2011). “Propagation of torsional waves in an inhomogeneous layer over an inhomogeneous half space.” Meccanica, 46(4), 671–680.
Chattopadhyay, A., Gupta, S., Kumari, P., and Sharma, V. K. (2012c). “Effect of point source and heterogeneity on the propagation of SH-waves in a viscoelastic layer over a viscoelastic half-space.” Acta Geophys., 60(1), 119–139.
Chattopadhyay, A., Gupta, S., Sahu, S. A., and Dhua, S. (2013). “Torsional surface waves in heterogeneous anisotropic half-space under initial stress.” Arch. Appl. Mech., 83(3), 357–366.
Chattopadhyay, A., Gupta, S., Sahu, S. A., and Singh, A. K. (2012a). “Torsional wave in self- reinforced medium over a heterogeneous half space.” Int. J. Geomech., 193–197.
Chattopadhyay, A., Gupta, S., Sahu, S. A., and Singh, A. K. (2012b). “Dispersion of horizontally polarized shear waves in an irregular non-homogeneous self-reinforced crustal layer over a semi-infinite self-reinforced medium.” J. Vib. Control, 19(1), 109–119.
Chattopadhyay, A., Gupta, S., Samal, S. K., and Sharma, V. K. (2009). “Torsional wave in self-reinforced medium.” Int. J. Geomech., 9–13.
Chattopadhyay, A., Gupta, S., Sharma, V. K., and Kumari, P. (2010a). “Propagation of shear waves in viscoelastic medium at irregular boundaries.” Acta Geophys., 58(2), 195–214.
Chattopadhyay, A., Singh, A. K., and Dhua, S. (2014). “Effect of heterogeneity and reinforcement on propagation of a crack due to shear waves.” Int. J. Geomech., 04014013.
Chaudhary, S., Kaushik, V. P., and Tomar, S. K. (2005). “Transmission of shear waves through a self-reinforced layer sandwiched between two inhomogeneous viscoelastic half-spaces.” Int. J. Mech. Sci., 47(9), 1455–1472.
Dey, S., Gupta, S., and Gupta, A. K. (1993). “Torsional surface wave in elastic half space with void pores.” Int. J. Numer. Anal. Methods Geomech., 17(3), 197–204.
Dhua, S., Singh, A. K., and Chattopadhyay, A. (2013). “Propagation of torsional wave in a composite layer overlying an anisotropic heterogeneous half-space with initial stress.” J. Vib. Control,.
Ewing, W. M., Jardetzky, W. S., and Press, F. (1957). Elastic waves in layered media, McGraw-Hill, New York.
Georgiadis, H. G., Vardoulakis, I., and Lykotrafitis, G. (2000). “Torsional surface waves in a gradient-elastic half-space.” Wave Motion, 31(4), 333–348.
Gubbins, D. (1990). Seismology and plate tectonics, Cambridge University Press, Cambridge.
Kaur, T., Singh, A. K., Chattopadhyay, A., and Sharma, S. K. (2014). “Dynamic response of normal moving load on an irregular fibre-reinforced half-space.” J. Vib. Control,.
Kumari, P., and Sharma, V. K. (2014). “Propagation of torsional waves in a viscoelastic layer over an inhomogeneous half space.” Acta Mech., 225(6), 1673–1684.
Love, A. E. H. (1944). A treatise on mathematical theory of elasticity, Dover Publications, New York.
Markham, M. F. (1970). “Measurements of elastic constants of fiber composites by ultrasonics.” Composites, 1(3), 145–149.
Singh, A. K., Kumar, S., and Chattopadhyay, A. (2014). “Effect of irregularity and heterogeneity on the stresses produced due to a normal moving load on a rough monoclinic half-space.” Meccanica, 49(12), 2861–2878.
Udias, A. (1999). Principles of seismology, Cambridge University Press, Cambridge, U.K.
Vardoulakis, I. (1984). “Torsional surface waves in inhomogeneous elastic media.” Int. J. Numer. Anal. Methods Geomech., 8(3), 287–296.
Vishwakarma, S. K., and Gupta, S. (2012). “Torsional surface wave in a homogeneous crustal layer over a viscoelastic mantle.” Int. J. Appl. Math. Mech., 8(16), 38–50.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 16Issue 1February 2016

History

Received: May 21, 2014
Accepted: Nov 13, 2014
Published online: Apr 30, 2015
Discussion open until: Sep 30, 2015
Published in print: Feb 1, 2016

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Authors

Affiliations

Abhishek Kumar Singh [email protected]
Assistant Professor, Dept. of Applied Mathematics, Indian School of Mines, Dhanbad-826004, Jharkhand, India. E-mail: [email protected]
Santan Kumar [email protected]
Ph.D. Student, Dept. of Applied Mathematics, Indian School of Mines, Dhanbad-826004, Jharkhand, India (corresponding author). E-mail: [email protected]
Amares Chattopadhyay [email protected]
Professor, Dept. of Applied Mathematics, Indian School of Mines, Dhanbad-826004, Jharkhand, India. E-mail: [email protected]

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