Love Waves in Voigt-Type Viscoelastic Inhomogeneous Layer Overlying a Gravitational Half-Space
Publication: International Journal of Geomechanics
Volume 16, Issue 3
Abstract
In this study, the author considers the propagation of Love waves in an inhomogeneous viscoelastic layer over a gravitational half-space when the upper boundary is assumed to be free. The proposed model is solved to obtain the dispersion relationship for Love waves in the Voigt-type layer under the effect of gravity, inhomogeneity, and initial stress. The relationship between the phase velocity and wave number of Love waves is expressed and then demonstrated with an interactive code. In the absence of various parameters of the medium, the results are in agreement with the classical results. They may be useful for understanding the nature of seismic wave propagation in geophysical applications and in the field of earthquake engineering.
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Acknowledgments
The author thanks GNA University for providing facilities for research and expresses his sincere thanks to the honorable reviewers for their useful suggestions and valuable comments.
References
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.
Bath, M. (1968). Mathematical aspects of seismology, Elsevier, New York.
Bhattacharya, J. (1969). “The possibility of the propagation of Love waves in an intermediate heterogeneous layer lying between two semi-infinite isotropic homogeneous elastic layers.” Pure Appl. Geophys., 72(1), 61–71.
Biot, M. A. (1965). Mechanics of incremental deformations, John Wiley & Sons, New York.
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. (1975). “On the propagation of Love types waves in an intermediate non-homogeneous layer lying between two semi-infinite homogeneous elastic media.” Gerlands Beitr. Geophys., 84(3–4), 327–334.
Dey, S., Gupta, A. K., and Gupta, S. (1996). “Propagation of torsional surface waves in a homogeneous substratum over a heterogeneous half-space.” Int. J. Numer. Anal. Methods Geomech., 20(4), 287–294.
Ewing, W. M., Jardetzky, W. S., and Press, F. (1957). Elastic waves in layered media, McGraw-Hill, New York.
Gubbins, D. (1990). Seismology and plate tectonics, Cambridge University Press, London.
Kadian, P., and Singh, J. (2010). “Effect of size of barrier on reflection of Love waves.” Int. J. Eng. Technol., 2(6), 458–461.
Kakar, R., and Gupta, M. (2014). “Love waves in an intermediate heterogeneous layer lying in between homogeneous and inhomogeneous isotropic elastic half-spaces.” Electron. J. Geotech. Eng. 19(Bund X), 7165–7185.
Kakar, R., and Kakar, S. (2012). “Propagation of Love waves in non-homogeneous elastic media.” J. Acad. Ind. Res., 1(6), 61–67.
Ke, L.-L., Wang, Y.-S., and Zhang, Z.-M. (2005). “Propagation of Love waves in an inhomogeneous fluid saturated porous layered half-space with properties varying exponentially.” J. Eng. Mech., 1322–1328.
Kundu, S., Gupta, S., and Majhi, D. K. (2013). “Love wave propagation in porous rigid layer lying over an initially stressed half space.” Appl. Phys. Math., 3(2), 140–142.
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. Methods Geomech., 38(11), 1172–1182.
Kundu, S., Gupta, S., Manna, S., and Dolai, P. (2014b). “Propagation of Love wave in fiber-reinforced medium over a nonhomogeneous half-space.” Int. J. Appl. Mech., 6(5), 1450050.
Love, A. E. H. (1911). Some problems of geo-dynamics, Cambridge University Press, London.
Madan, D. K., Kumar, R., and Sikka, J. S. (2014). “Love wave propagation in an irregular fluid saturated porous anisotropic layer with rigid boundary.” J. Appl. Sci. Res., 10(4), 281–287.
Manna, S., Kundu, S., and Gupta, S. (2013). “Love wave propagation in a piezoelectric layer overlying in an inhomogeneous elastic half-space.” J. Vib. Control, 21(13), 2553–2568.
MATLAB [Computer software]. MathWorks, Natick, MA.
Qian, Z., Jin, F., Wang, Z., and Kishimoto, K. (2004). “Love waves propagation in a piezoelectric layered structure with initial stresses.” Acta Mech., 171(1), 41–57.
Serón, F. J., and Badal, J. (1986). “A weak variational formulation for the propagation of Love waves.” Int. J. Numer. Methods Eng., 23(9), 1601–1613.
Singh, S. S. (2010). “Love wave at a layer medium bounded by irregular boundary surfaces.” J. Vib. Control, 17(5), 789–795.
Vashishth, A. K., and Sharma, M. D. (2008). “Propagation of plane waves in poroviscoelastic anisotropic media.” Appl. Math. Mech., 29(9), 1141–1153.
Whittaker, E. T., and Watson, G. N. (1990). A course in modern analysis, Cambridge University Press, London.
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© 2015 American Society of Civil Engineers.
History
Received: Jan 24, 2015
Accepted: Jul 9, 2015
Published online: Dec 3, 2015
Discussion open until: May 3, 2016
Published in print: Jun 1, 2016
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