SH Wave Propagation in a Finite Thicker Layer of the Void Pore Sandwiched by Heterogeneous Orthotropic Media
Publication: International Journal of Geomechanics
Volume 17, Issue 5
Abstract
The present paper investigates the propagation of SH waves in a finite thicker layer of the void pore sandwiched by heterogeneous orthotropic media. In the upper semi-infinite medium initial stress, density and shear moduli are assumed to vary hyperbolically, whereas in the lower semi-infinite medium linear variation in initial stress, density and shear moduli are considered. The study reveals that, under assumed conditions, there may be two types of SH waves. The first front depends on the void parameter and velocity of shear wave of the medium, whereas the second kind of SH wave is affected only by the void parameter. The study also shows that SH waves propagate in an elastic homogeneous layer between two heterogeneous semi-infinite media. To study the effect of void parameter as well as heterogeneity and initial stress parameters, the velocities of SH waves are calculated numerically and presented in a number of graphs.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors gratefully acknowledge financial help from the Council of Scientific and Industrial Research, New Delhi, through Grant 25(227)/13/EMR-II(2). The authors also deeply acknowledge the contribution of Bappa Mukherjee, research scholar, Department of Applied Geophysics, Indian School of Mines, Dhanbad, India, for improvement of this paper.
References
Abd-Alla, A. M., Abo-Dahab, S. M., and Al-Thamali, T. A. (2013). “Love waves in a non-homogeneous orthotropic magneto-elastic layer under initial stress overlying a semi-infinite medium.” J. Comput. Theor. Nanosci., 10(1), 10–18.
Abd-Alla, A. M., and Ahmed, S. M. (1999). “Propagation of Love waves in a non-homogeneous orthotropic elastic layer under initial stress overlying semi-infinite medium.” Appl. Math. Comput., 106(2–3), 265–275.
Abd-Alla, A. M., Hammad, H. A. H., and Abo-Dahab, S. M. (2004). “Rayleigh waves in a magnetoelastic half-space of orthotropic material under influence of initial stress and gravity field.” Appl. Math. Comput., 154(2), 583–597.
Ahmed, S. M., and Abo-Dahab, S. M. (2010). “Propagation of Love waves in an orthotropic granular layer under initial stress overlying a semi-infinite Granular medium.” J. Vib. Control, 16(12), 1845–1858.
Biot, M. A. (1956a). “Theory of propagation of elastic waves in a fluid-saturated porous solid: I. Low frequency range.” J. Acoust. Soc. Am., 28(2), 168–178.
Biot, M. A. (1956b). “Theory of propagation of elastic waves in a fluid-saturated porous solid: II. Higher frequency range.” J. Acoust. Soc. Am., 28(2), 179–191.
Chandrasekharaiah, D. S. (1987). “Effect of surface stresses and voids on Rayleigh waves in an elastic solid.” Int. J. Eng. Sci., 25(2), 205–211.
Chattaraj, R., Samal, S. K., and Mahanti, N. C. (2013). “Dispersion of Love wave propagating in irregular anisotropic porous stratum under initial stress.” Int. J. Geomech., 402–408.
Chattopadhyay, A., Gupta, S., Kumari, P., and Sharma, V. K. (2013). “Torsional wave propagation in non-homogeneous layer between non-homogeneous half-spaces.” Int. J. Numer. Anal. Methods Geomech., 37(10), 1280–1291.
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., Gupta, S., Samal, S. K., and Sharma, V. K. (2009). “Torsional waves in self-reinforced medium.” Int. J. Geomech., 9–13.
Cowin, S. C., and Nunziato, J. W. (1983). “Linear elastic materials with voids.” J. Elast., 13(2), 125–147.
Dey, S., Gupta, S., and Gupta, A. K. (2004). “Propagation of Love waves in an elastic layer with void pores.” Sadhana, 29(4), 355–363.
Dey, S., Gupta, S., Gupta, A. K., Kar, S. K., and De, P. K. (2003). “Propagation of torsional surface waves in an elastic layer with void pores over an elastic half-space with void pores.” Tamkang J. Sci. Eng., 6(4), 241–249.
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. Modell., 34(7), 1873–1883.
Gupta, S., Chattopadhyay, A., and Majhi, D. K. (2011a). “Effect of rigid boundary on propagation of torsional surface waves in porous elastic layer.” Appl. Math. Mech., 32(3), 327–338.
Gupta, S., Chattopadhyay, A., Vishwakarma, S. K., and Majhi, D. K. (2011b). “Influence of rigid boundary and initial stress on the propagation of Love wave.” Appl. Math., 2, 586–594.
Gupta, S., Majhi, D. K., Kundu, S., and Vishwakarma, S. K. (2013). “Propagation of Love waves in a non-homogeneous substratum over initially stressed heterogeneous half-space.” Appl. Math. Mech., 34(2), 249–258.
Ieşan, D., and Nappa, L. (2003). “Axially symmetric problems for a porous elastic solid.” Int. J. Solid Struct., 40(20), 5271–5286.
Kundu, S., Gupta, S., Chattopadhyay, A., and Majhi, D. K. (2013). “Love wave propagation in porous rigid layer lying over an initially stressed half-space.” Int. J. Appl. Phys. Math., 3(2), 140–142.
Kundu, S., Gupta, S., and Manna, S. (2014a). “Propagation of Love wave in fibre-reinforced medium lying over an initially stressed orthotropic half-space.” Int. J. Numer. Anal. Methods 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.
Kundu, S., Manna, S., and Gupta, S. (2014c). “Love wave dispersion in pre-stressed homogeneous medium over a porous half-space with irregular boundary surfaces.” Int. J. Solid Struct., 51(21–22), 3689–3697.
Kundu, S., Manna, S., and Gupta, S. (2014d). “Propagation of SH-wave in an initially stressed orthotropic medium sandwiched by a homogeneous and an inhomogeneous semi-infinite media.” Math. Methods Appl. Sci., 38(9), 1926–1936.
Love, A. E. H. (1927). The mathematical theory of elasticity, Cambridge University Press, Cambridge, U.K.
Lowrie, W. (2007). Fundamentals of geophysics, Cambridge University Press, Cambridge, U.K.
Manna, S., Kundu, S., and Gupta, S. (2015). “Effect of reinforcement and inhomogeneity on the propagation of Love waves.” Int. J. Geomech., 04015045.
MATLAB [Computer software]. MathWorks, Natick, MA.
Midya, G. K. (2004). “On Love-type surface waves in homogeneous micropolar elastic media.” Int. J. Eng. Sci., 42(11–12), 1275–1288.
Nie, G., Liu, X., Liu, J., and Fang, X. (2015). “Effect of an inhomogeneous initial stress on Love wave propagation in 0.67Pb(Mg1∕3Nb2∕3)O3-0.33PbTiO3 single crystal layered structure poled along [011]c.” Meccanica, 50(1), 119–132.
Nunziato, J. W., and Cowin, S. C. (1979). “A nonlinear theory of elastic materials with voids.” Arch. Ration. Mech. Anal., 72(2), 175–201.
Puri, P., and Cowin, S. C. (1985). “Plane waves in linear elastic materials with voids.” J. Elast., 15(2), 167–183.
Sethi, M., Gupta, K. C., Kakar, R., and Gupta, M. P. (2011). “Propagation of Love waves in a non-homogeneous orthotropic layer under compression P overlying semi-infinite non-homogeneous medium.” Int. J. Appl. Math. Mech., 7(10), 97–110.
Singh, A. K., Parween, Z., Chatterjee, M., and Chattopadhyay, A. (2015). “Love-type wave propagation in a pre-stressed viscoelastic medium influenced by smooth moving punch.” Waves Random Complex Medium, 25(2), 268–285.
Singh, B., and Kumar, R. (1998). “Reflection and refraction of plane waves at an interface between micropolar elastic solid and viscoelastic solid.” Int. J. Eng. Sci., 36(2), 119–135.
Vishwakarma, S. K., and Gupta, S. (2013a). “Existence of torsional surface waves in an earth’s crustal layer lying over a sandy mantle.” J. Earth Syst. Sci., 122(5), 1411–1421.
Vishwakarma, S. K., Gupta, S., and Majhi, D. K. (2013b). “Influence of rigid boundary on the Love wave propagation in elastic layer with void pores.” Acta Mech. Solida Sin., 26(5), 551–558.
Whittaker, E. T., and Watson, G. N. (1990). A course in modern analysis, Cambridge University Press, Cambridge, U.K.
Zhu, J. B., et al. (2011). “Seismic response of a single and a set of filled joints of viscoelastic deformational behaviour.” Geophys. J. Int., 186(3), 1315–1330.
Zhu, J. B., Zhao, X. B., Wu, W., and Zhao, J. (2012). “Wave propagation across rock joints filled with viscoelastic medium using modified recursive method.” J. Appl. Geophys., 86, 82–87.
Information & Authors
Information
Published In
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Jun 16, 2015
Accepted: Aug 22, 2016
Published online: Oct 5, 2016
Discussion open until: Mar 5, 2017
Published in print: May 1, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.