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http://dx.doi.org/10.12989/imm.2013.6.3.287

Influence of impulsive line source and non-homogeneity on the propagation of SH-wave in an isotropic medium  

Kakar, Rajneesh (DIPS Polytechnic College)
Publication Information
Interaction and multiscale mechanics / v.6, no.3, 2013 , pp. 287-300 More about this Journal
Abstract
In this paper, the effect of impulsive line on the propagation of shear waves in non-homogeneous elastic layer is investigated. The rigidity and density in the intermediate layer is assumed to vary quadratic as functions of depth. The dispersion equation is obtained by using the Fourier transform and Green's function technique. The study ends with the mathematical calculations for transmitted wave in the layer. These equations are in complete agreement with the classical results when the non-homogeneity parameters are neglected. Various curves are plotted to show the effects of non-homogeneities on shear waves in the intermediate layer.
Keywords
non-homogeneity; Green's function; Dirac-delta function; isotropic; shear waves;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Kakar, R. and Kakar, S. (2012), "Propagation of Love waves in a non-homogeneous elastic media", J. Acad. Indus. Res., 1(6), 323-328. 299
2 Kakar, R. and Gupta, K.C. (2012), "Propagation of Love waves in a non-homogeneous orthotropic layer under „P‟ overlying semi-infinite non-homogeneous medium", Global J. Pure Appl. Math., 8(4), 483-494.
3 Kakar, R. and Gupta, K.C. (2013), "Torsional surface waves in a non-homogeneous isotropic layer over viscoelastic half-space", Interact. Multiscale Mech., 6(1), 1-14.   DOI   ScienceOn
4 Kazumi, W. and Robert, G. (2002), "Green's function for SH-waves in a cylindrically monoclinic material", Payton J. Mech. Phys. Solids, 50(11), 2425-2439.   DOI   ScienceOn
5 Kazumi, W. and Robert, G. (2002), "Payton Green‟s function for torsional waves in a cylindrically monoclinic material", Int. J. Eng. Sci., 43, 1283-1291.
6 Kirpichnikova, N.Y. (2012), "The green‟s function of SH-polarized surface waves", J. Math. Sci., 185(4), 591-595.   DOI
7 Kumar, R. and Gupta, R.R. (2010), "Analysis of wave motion in micropolar transversely isotropic thermoelastic half space without energy dissipation", Interact. Multiscale Mech., 3(2), 145-156.   DOI   ScienceOn
8 Li, Y.L. (1994), "Exact analytic expressions of Green‟s functions for wave propagation in certain types of range-dependent inhomogeneous media", J. Acoust. Soc. Am., 96, 484-490.   DOI   ScienceOn
9 Li, W., Liu, S.B. and Yang, W. (2010), "A new approach of solving Green‟s function for wave propagation in an inhomogeneous absorbing medium", Chin. Phys. B, 19, 1-3.
10 Matsuda, O. and Glorieux, C. (2007), "A Green‟s function method for surface acoustic waves in functionally graded materials", J. Acoust. Soc. Am., 121(6), 3437-45.   DOI   ScienceOn
11 Ponnusamy, P. and Selvamani, R. (2012), "Wave propagation in a generalized thermo elastic plate embedded in elastic medium", Interact. Multiscale Mech., 5(1), 13-26.   DOI   ScienceOn
12 Chattopadhyay, A., Gupta, S., Abhishek, Singh, K. and Sanjeev, A. (2011), "Effect of point source, self-reinforcement and heterogeneity on the propagation of magnetoelastic shear wave", Appl. Math., 2(3), 271-282.   DOI
13 Chattopadhyay, A., Gupta, S., Sharma, V.K. and Kumari, P. (2010), "Effect of point source and heterogeneity on the propagation of SH-waves", Int. J. Appl. Math. Mech., 6(9), 76-89.
14 Daros, C.H. (2013), "Green‟s function for SH-waves in inhomogeneous anisotropic elastic solid with power-function velocity variation", Wave Motion, 50, 101-110.   DOI   ScienceOn
15 Ewing, W.M., Jardetzky, W.S. and Press, F. (1957), Elastic Waves in Layered Media, McGraw-Hill, New York.
16 Fedorov, F.I. (1968), Theory of Elastic Waves in Crystals, Plenum Press, NewYork.
17 Popov, M.M. (2002), "SH waves in a homogeneous transversely isotropic medium generated by a concentrated force", J. Math. Sci., 111(5), 3791-3798.   DOI
18 George, D., Manolis, Christos, Z. and Karakostas (2003), "Engineering analysis with boundary Elements", Eng. Anal. Bound. Elem, 27(2), 93-100.   DOI   ScienceOn
19 Gubbins, D. (1990), Seismology and Plate Tectonics, Cambridge University Press, Cambridge.
20 Jing, G.U.O., Hui, Q.I., Qingzhan, X.U. and Kirpichnikova, N.Y. (2008), "Scattering of SH-wave by interface cylindrical elastic inclusion with diametrical cracks", Proceeding of the14th World Conference on Earthquake Engineering, Beijing, China.
21 Rommel, B.E. (1990), Extension of the Weyl Integral for Anisotropic Medium, Fourth International Workshop on Seismic Anisotropy, Edinburgh.
22 Shaw, R.P. and Manolis, G. (1997), "Conformal mapping solutions for the 2D heterogeneous Helmholtz equation", Comput. Mech., 18, 411-418.
23 Stakgold, I. (1979), Green's Functions and Boundary Value Problems, John Wiley and Sons, New York, 51-55.
24 Symon, K.R. (1971), Mechanics, Addison Wesley Publishing Company, Reading, Massachusets.
25 Uscinski, B.J. (1977), The Elements of Wave Propagation Random Media, McGraw-Hill International Book Company, Great Britain.
26 Vaclav, V. and Kiyoshi, Y. (1996), "SH-wave Green tensor for homogeneous transversely isotropic media by higher-order approximations in asymptotic ray theory", Wave Motion, 23, 83-93.   DOI   ScienceOn