Torsional Surface Waves in a Self-Reinforced Medium over a Heterogeneous Half Space
Publication: International Journal of Geomechanics
Volume 12, Issue 2
Abstract
This paper aims to study the dispersion of torsional surface waves in a self-reinforced layer over a half-space with linearly varying rigidity and density. Dispersion equation has been obtained in closed form. Dispersion relation for isotropic layer lying over a heterogeneous half-space has been deduced. As a result, the velocity equation for reinforced layer over a half-space of constant density has also been obtained. It has been observed that for isotropic upper layer over a homogeneous half-space, the velocity of torsional surface waves coincides with that of Love waves. This study shows that the increment in inhomogeneity decreases the phase velocity but the presence of reinforcement increases it significantly. Effects of different inhomogeneity parameters on the phase velocity have been depicted by means of graphs. Dispersion curves have been plotted for both reinforced and reinforcement free cases.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors convey their sincere thanks to Department of Science and Technology, New Delhi, for providing financial support to Mr. Sanjeev Anand Sahu through Project No. SR/S4/MS: 436/07, Project title: “Wave propagation in anisotropic media”.
References
Achenbach, J. D. (1976). Wave propagation in elastic solid, North Holland, NY.
Bao, L., Yuan, H., Sakurai, M., Nakazawa, M., and Kemmochi, K. (2006). “A study on the torsional wave of fibre reinforced composite materials.” J. Compos. Mater.JCOMBI, 40(4), 338–391.
Belfield, A. J., Rogers, T. G., and Spencer, A. J. M. (1983). “Stresses in elastic plates reinforced by fibres lying in concentric circles.” J. Mech. Phys. SolidsJMPSA8, 31(1), 25–34.
Chattopadhyay, A. (1978). “On the generation of G type seismic waves.” Acta Geophys. Pol.AGPOAP, 26(2), 131–138.
Chattopadhyay, A., and Choudhury, S. (1990). “Propagation, reflaction and transmission of magnetoelastic shear waves in self-reinforced medium.” Int. J. Eng. Sci.IJESAN, 28(6), 485–495.
Chattopadhyay, A., and Choudhury, S. (1995). “Magneto elastic shear waves in self-reinforced medium.” Int. J. Numer. Anal. Methods Geomech.IJNGDZ, 19(4), 289–304.
Chattopadhyay, A., Gupta, S., Samal, S. K., and Sharma, V. K. (2009). “Torsional waves in self-reinforced medium.” Int. J. Geomech.IJGNAI, 9(1), 9–13.
Damm, S. V., and Franchois, A. (2006). “A full-wave homogenization technique for steel fiber reinforced concrete.” ElectromagneticsETRMDV, 26(3–4), 301–314.
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.IJNGDZ, 20, 287–294.
Diaz, R. G., Castillero, J. B., Ramos, R. R., Rosado, R. M., Serranía, F., and Navarrete, M. (2002). “Modeling of elastic transversely isotropic composite using the asymptotic homogenization method. Some comparisons with other models.” Mater. Lett.MLETDJ, 56(6), 889–894.
Georgiadis, H. G., Vardoulakis, I., and Lykotrafitis, G. (2000). “Torsional surface waves in a gradient-elastic half-space.” Wave MotionWAMOD9, 31(4), 333–348.
Gubbins, D. (1990). Seismology and plate tectonics, Cambridge University Press, Cambridge.
Hool, G. A., and Kinne, W. S. (1924). Reinforced concrete and masonry structure, McGraw-Hill, NY.
Meissner, E. (1921). “Elastische Oberflachenwellen mit Dispersion in einem inhomogenen Medium.” Vierteljahrsschr. Naturforsch. Ges. ZuerichVNGZAL, 66, 181–195.
Meissner, R. (2002). The little book of planet earth, Springer-Verlag, NY.
Rayleigh, J. W. S. (1945). Theory of sound, Dover, NY.
Spencer, A. J. M. (1974). “Boundary layers in highly anisotropic plane elasticity.” Int. J. Solids Struct.IJSOAD, 10, 1103–1123.
Vardoulakis, I. (1984). “Torsional surface waves in inhomogeneous elastic media.” Int. J. Numer. Anal. Methods Geomech.IJNGDZ, 8(3), 287–296.
Whittaker, E. T., and Watson, G. N. (1991). A course of modern analysis, Cambridge University Press, Cambridge.
Information & Authors
Information
Published In
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Apr 7, 2010
Accepted: Jan 7, 2011
Published online: Jan 10, 2011
Published in print: Apr 1, 2012
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.