Shear Waves in an Inhomogeneous Viscoelastic Layer Resting over a Prestressed Orthotropic Substrate
Publication: International Journal of Geomechanics
Volume 17, Issue 6
Abstract
This paper intends to study the dispersive nature of shear waves transmitting in an inhomogeneous viscoelastic layer embedded over a prestressed orthotropic substrate. The frequency equations obtained under the combined effect of viscoelasticity and inhomogeneity were analyzed. It has been observed that the phase velocity of the shear wave is influenced by the prestress present in the half-space. The method of separation of variables has been incorporated to deduce the dispersion equation of the shear wave. Consequently, it has been found that the dispersion equations from the real and damped parts converged with the classical Love wave equation under certain suitable conditions. The graphical representations show that inhomogeneity, viscoelasticity, prestress, and shear moduli had a remarkable effect on the phase velocity of the shear wave.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The fellowship received from the University Grants Commission, New Delhi, through Grant F(0).7-79/2007(BSR) is gratefully acknowledged by the authors.
References
Abd-Alla, A., Hammad, H., and Abo-Dahab, S. (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.
Achenbach, J. D. (1973). Wave propagation in elastic solids, North-Holland, Amsterdam, Netherlands.
Bhattacharya, J. (1969). “The possibility of the propagation of Love type waves in an intermediate heterogeneous layer lying between two semi-infinite isotropic homogeneous elastic layers.” Pure Appl. Geophys., 72(1), 61–71.
Biot, M. (1965). Mechanics of incremental deformations, Wiley, New York.
Biswas, A. (1969). “Propagation of SH-waves in a heterogeneous viscoelastic layer overlying a homogeneous Voigt medium.” Pure Appl. Geophys., 76(1), 100–106.
Borcherdt, R. (1973). “Rayleigh-type surface wave on a linear viscoelastic half-space.” J. Acoust. Soc. Am., 54(6), 1651–1653.
Carcione, J. M. (1990). “Wave propagation in anisotropic linear viscoelastic media: Theory and simulated wavefields.” Geophys. J. Int., 101(3), 739–750.
Červený, V. (2004). “Inhomogeneous harmonic plane waves in viscoelastic anisotropic media.” Studia geophysica et geodaetica, 48(1), 167–186.
Chattopadhyay, A., Gupta, S., Kumari, P., and Sharma, V. (2012). “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., Sharma, V., and Kumari, P. (2010). “Propagation of shear waves in viscoelastic medium at irregular boundaries.” Acta Geophys., 58(2), 195–214.
Destrade, M. (2001). “Surface waves in orthotropic incompressible materials.” J. Acoust. Soc. Am., 110(2), 837–840.
Ewing, W., Jardetzky, W., and Press, F. (1957). Elastic waves in layered media, McGraw-Hill, New York.
Ghorai, A., Samal, S., and Mahanti, N. (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.
Gogna, M., and Chander, S. (1985). “Reflection and transmission of SH-waves at an interface between anisotropic inhomogeneous elastic and viscoelastic half-spaces.” Acta Geophys. Pol., 33(4), 357–375.
Gubbins, D. (1990). Seismology and plate tectonics, Cambridge University Press, London.
Kakar, R. (2015). “Love waves in Voigt-type viscoelastic inhomogeneous layer overlying a gravitational half-space.” Int. J. Geomech., 0401506.
Kanai, K. (1950). “The effect of solid viscosity of surface layer on the earthquake movements.” Bull. Earthquake Res. Inst., 28(1–2), 31–35.
Kaushik, V., and Chopra, S. (1983). “Reflection and transmission of general plane SH-waves at the plane interface between two heterogeneous and homogeneous viscoelastic media.” Geophys. Res. Bull., 20, 1–20.
Kumar, S., Pal, P. C., and Majhi, S. (2015). “Reflection and transmission of plane SH-waves through an anisotropic magnetoelastic layer sandwiched between two semi-infinite inhomogeneous viscoelastic half-spaces.” Pure Appl. Geophys., 172(10), 2621–2634.
Kundu, S., Gupta, S., and Manna, S. (2014). “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., Gupta, S., Vaishnav, P. K., and Manna, S. (2014). “Propagation of Love waves in a heterogeneous medium over an inhomogeneous half-space under the effect of point source.” J. Vib. Control.
Manolis, G., and Shaw, R. (1996). “Harmonic wave propagation through viscoelastic heterogeneous media exhibiting mild stochasticity. II: Applications.” Soil Dyn. Earthquake Eng., 15(2), 129–139.
Pilant, W. (1978). Elastic waves in the earth, Elsevier Scientific, New York.
Romeo, M. (2003). “Interfacial viscoelastic SH-waves.” Int. J. Solids Struct., 40(9), 2057–2068.
Sahu, S., Saroj, P., and Dewangan, N. (2014a). “SH-waves in viscoelastic heterogeneous layer over half-space with self-weight.” Arch. Appl. Mech., 84(11), 235–245.
Sahu, S., Saroj, P., and Paswan, B. (2014b). “Shear waves in a heterogeneous fiber-reinforced layer over a half-space under gravity.” Int. J. Geomech., 04014048.
Schoenberg, M. (1971). “Transmission and reflection of plane waves at an elastic-viscoelastic interface.” Geophys. J. Int., 25(1–3), 35–47.
Sethi, M., Gupta, K., Kakar, R., and Gupta, M. (2011). “Propagation of Love waves in a non-homogeneous orthotropic layer under compressive ‘P’ overlying semi-infinite non-homogeneous medium.” Int. J. Appl. Math. Mech., 7(10), 97–110.
Shaw, R., and Bugl, P. (1969). “Transmission of plane waves through layered linear viscoelastic media.” J. Acoust. Soc. Am., 46(3B), 649–654.
Singh, A. K., Das, A., Kumar, S., and Chattopadhyay, A. (2015a). “Influence of corrugated boundary surfaces, reinforcement, hydrostatic stress, heterogeneity and anisotropy on Love-type wave propagation.” Meccanica, 50(12), 2977–2994.
Singh, A. K., Kumar, S., and Chattopadhyay, A. (2015b). “Propagation of torsional waves in a fiber composite layer lying over an initially stressed viscoelastic half-space.” Int. J. Geomech., 04015014.
Singh, S. S. (2011). “Love wave at a layer medium bounded by irregular boundary surfaces.” J. Vib. Control, 17(5), 789–795.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 17 • Issue 6 • June 2017
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Jan 15, 2016
Accepted: Oct 11, 2016
Published online: Nov 17, 2016
Discussion open until: Apr 17, 2017
Published in print: Jun 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.