Influence of linearly varying density and rigidity on torsional surface waves in inhomogeneous crustal layer

doi:10.1007/s10483-012-1618-7

Abstract

Abstract: The present work deals with the possibility of propagation of torsional surface wave in an inhomogeneous crustal layer over an inhomogeneous half space. The layer has inhomogeneity which varies linearly with depth whereas the inhomogeneous half space exhibits inhomogeneity of three types namely exponential, quadratic, and hyperbolic discussed separately. Dispersion equation is deduced for each case in a closed form. For a layer over a homogeneous half space, the dispersion equation agrees with the equation of the classical case. It is observed that the inhomogeneity factor due to linear variation in density in the inhomogeneous crustal layer decreases as the phase velocity increases, while the inhomogeneity factor in rigidity has the reverse effect on the phase velocity.

Key words: torsional wave, phase velocity, crustal layer, exponential, quadratic, hyperbolic, copmpoate compresson.backing GKRR maim comem

2010 MSC Number:

O347.4

S. GUPTA;S. K. VISHWAKARMA;D. K. MAJHI;S. KUNDU. Influence of linearly varying density and rigidity on torsional surface waves in inhomogeneous crustal layer. Applied Mathematics and Mechanics (English Edition), 2012, 33(10): 1239-1252.

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References

[1] Ewing, W. M., Jardetzky, W. S., and Press, F. Elastic Waves in Layered Media, McGraw-Hill,New York (1957)
[2] Vrettos, C. In plane vibrations of soil deposits with variable shear modulus: I. surface waves. Int.J. Numer. Anal. Meth. Geomech., 14, 209-222 (1990)
[3] Kennett, B. L. N. and Tkalcic, H. Dynamic Earth: crustal and mantle heterogeneity. Aust. J.Earth Sci., 55, 265-279 (2008)
[4] Reissner, E. and Sagoci, H. F. Forced torsional oscillations of an elastic half-space. Int. J. Appl.Phys. 15(9), 652-654 (1944)
[5] Rayleigh, L. On waves propagated along plane surface of an elastic solid. Proc. Lond. Math. Soc.,17(3), 4-11 (1885)
[6] Georgiadis, H. G., Vardoulakis, I., and Lykotrafitis, G. Torsional surface waves in a gradient-elastichalf space. Wave Motion, 31(4), 333-348 (2000)
[7] Meissner, E. Elastic oberflachenwellen mit dispersion in einem inhomogeneous medium (in Zurich).Viertlagahrsschriftder Naturforschenden Gesellschaft, 66, 181-195 (1921)
[8] Bhattacharya, R. C. On the torsional wave propagation in a two-layered circular cylinder withimperfect bonding. Proc. Indian Natn. Sci. Acad., 41(6), 613-619 (1975)
[9] Dey, S. and Dutta, A. Torsional wave propagation in an initially stressed cylinder. Proc. IndianNatn. Sci. Acad., 58(5), 425-429 (1992)
[10] Chattopadhyay, A., Gupta, S., Kumari, P., and Sharma, V. K. Propagation of torsional waves inan inhomogeneous layer over an inhomogeneous half space. Meccanica, 46(4), 671-680 (2011)
[11] Pujol, J. Elastic Wave Propagation and Generation in Seismology, Cambridge University Press,Cambridge (2003)
[12] Chapman, C. Fundamentals of Seismic Wave Propagation, Cambridge University Press, Cam-bridge (2004)
[13] Gupta, S., Chattopadhyay, A., Kundu, S., and Gupta, A. K. Effect of rigid boundary on thepropagation of torsional waves in a homogeneous layer over a heterogeneous half-space. Arch.Appl. Mech., 80, 143-150 (2010)
[14] Davini, C., Paroni, R., and Puntle, E. An asymptotic approach to the torsional problem in thinrectangular domains. Meccanica, 43(4), 429-435 (2008)
[15] Vardoulakis, I. Torsional surface waves in inhomogeneous elastic media. Int. J. Numer. Anal.Meth. Geomech., 8, 287-296 (1984)
[16] Akbarov, S. D., Kepceler, T., and Egilmez, M. M. Torsional wave dispersion in a finitely pre-strained hollow sandwich circular cylinder. Journal of Sound and Vibration, 330, 4519-4537 (2011)
[17] Ozturk, A. and Akbbarov, S. D. Torsional wave propagation in a pre-stressed circular cylinderembedded in a pre-stressed elastic medium. Applied Mathematical Modelling, 33, 3636-3649 (2009)
[18] Bullen, K. E. The problem of the Earth’s density variation. Bull. Seismol. Soc. Am., 30(3), 235-250 (1940)
[19] Sari, C. and Salk, M. Analysis of gravity anomalies with hyperbolic density contrast: an applicationto the gravity data of Western Anatolia. J. Balkan Geophys. Soc., 5(3), 87-96 (2002)
[20] Love, A. E. H. The Mathematical Theory of Elasticity, Cambridge University Press, Cambridge(1927)
[21] Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, Cambridge University Press,Cambridge (1990)
[22] Gubbins, D. Seismology and Plate Tectonics, Cambridge University press, Cambridge/New York(1990)
[23] Tierstein, H. F. Linear Piezoelectric Plate Vibrations, Plenum Press, New York (1969)