This paper has been framed to study the propagation of torsional surface waves in an inhomogeneous layer of finite thickness over an initially stressed inhomogeneous half-space. Rigidity, density and initial stress of the half-space are assumed to have linear variation, and in layers linear variation in rigidity and density are also considered. It has been observed that the inhomogeneity parameter and the initial stress play an important role for the propagation of the torsional surface wave. The method of separation of variables is applied to find the displacement field. The dispersion equation of phase velocity is derived. The velocities of torsional waves are calculated numerically as a function of kH and presented in a number of graphs, where k is the wave number, and H is the thickness of the layer. Graphical user interface has been developed using MATLAB to generalize the effect of the various parameters discussed. As a particular case it has been seen that the dispersion equation is in agreement with the classical result of the Love wave when the initial stresses and inhomogeneity parameters are neglected.
AchenbachJD (1973) Wave Propagation in Elastic Solids, New York: North Holland Publishing Company.
2.
AkbarovSDKepcelerTEgilmezM (2011) Torsional wave dispersion in a finitely prestrained hollow sandwich circular cylinder. Journal of Sound and Vibration330: 4519–4537.
3.
BathM (1968) Mathematical Aspects of Seismology, New York: Elsevier Publishing Company.
4.
Bhattacharya RC (1975) On the torsional wave propagation in a two-layered circular cylinder with imperfect bonding. In: Proceedings of Indian National Science Academy vol. 41(6), pp. 613–619.
5.
BiotMA (1940) The influence of initial stress on elastic wave. Journal of Applied Physics11: 522–530.
6.
BiotMA (1965) Mechanics of Incremental Deformation, New York: John Wiley and Sons Inc.
7.
ChapmanC (2004) Fundamentals of Seismic Wave Propagation, Cambridge, UK: Cambridge University Press.
8.
ChattopadhyayAGuptaSKumariPSharmaVK (2011) Propagation of torsional waves in an inhomogeneous layer over an inhomogeneous half space. Meccanica46(4): 671–680.
9.
ChattopadhyayAGuptaSSahuSASinghAK (2012) Dispersion of horizontally polarized shear waves in an irregular non-homogeneous self-reinforced crustal layer over a semi-infinite self-reinforced medium. Journal of Vibration and Control19(1): 109–119.
10.
Dey S and Dutta A (1992) Torsional wave propagation in an initially stressed cylinder. In Proceedings of Indian National Science Academy vol. 58(5), pp. 425–429.
11.
DeySSarkarMG (2002) Torsional surface waves in an initially stressed anisotropic porous medium. Journal of Engineering Mechanics128: 184–194.
12.
DeySGuptaSGuptaAK (1996a) Propagation of torsional surface waves in a homogeneous substratum over a heterogeneous half space. International Journal of Numerical and Analytical Methods in Geomechanics20: 287–294.
13.
DeySGuptaSGuptaAK (1996b) Propagation of Rayleigh wave in a heterogeneous incompressible substratum over a homogeneous in compressible half space. International Journal of Numerical and Analytical Methods in Geomechanics20: 365–375.
14.
EwingWMJardetzkyWSPressF (1957) Elastic Waves in Layered Media, New York: McGraw-Hill.
15.
GeorgiadisHGVardoulakisILykotrafitisG (2000) Torsional surface waves in a gradient elastic half space. Wave Motion31(4): 333–348.
16.
GubbinsD (1990) Seismology and Plate Tectonics, Cambridge, UK: Cambridge University press.
17.
GuptaSChattopadhyayAKunduSGuptaAK (2010) Effect of rigid boundary on the propagation of Torsional wave in a homogeneous layer over a heterogeneous half-space. Archive of Applied Mechanics80: 143–150.
18.
GuptaSMajhiDKKunduSVishwakarmaSK (2012a) Propagation of torsional surfaces waves in a homogeneous layer of finite thickness over an initially stressed heterogeneous half-space. Journal of Applied Mathematics and Computation218: 5655–5664.
19.
GuptaSVishwakarmaSKMajhiDKKunduS (2012b) Influence of linearly varying density and rigidity on torsional surface waves in inhomogeneous crustal layer. Applied Mathematics and Mechanics33(10): 1239–1252.
20.
KepcelerT (2010) Torsional wave dispersion relations in a pre-stressed bi-material compounded cylinder with an imperfect interface. Applied Mathematical Modelling34: 4058–4073.
21.
MeissnerE (1921) Elastic surface-waves with dispersion in an inhomogeneous medium. The Quarterly Magazine Naturalist Society in Zurich66: 181–195.
22.
OzturkAAkbbarovSD (2009) Torsional wave propagation in a pre-stressed circular cylinder embedded in a pre-stressed elastic medium. Applied Mathematical Modelling33: 3636–3649.
23.
Rayleigh L (1985) On waves propagated along plane surface of an elastic solid. In Proceedings of the London Mathematics Society vol. 17(3), pp. 4–11.
24.
SelimMM (2007) Propagation of torsional surface waves in heterogeneous half-space with irregular free surface. Applied Mathematical Science1(29): 1429–1437.
25.
VardoulakisI (1984) Torsional surface waves in inhomogeneous elastic media. International Journal of Numerical and Analytical Methods in Geomechanics8: 287–296.
26.
VishwakarmaSKGuptaSVermaAK (2012) Torsional wave propagation in Earth’s crustal layer under the influence of imperfect interface. Journal of Vibration and Control00: 1–15. (accessed 9 May 2013).
27.
VrettosC (1990a) In plane vibrations of soil deposits with variable shear modulus parallel line load. International Journal of Numerical and Analytical Methods in Geomechanics14: 649–662.
28.
VrettosC (1990b) In plane vibrations of soil deposits with variable shear modulus: I. surface waves. International Journal of Numerical and Analytical Methods in Geomechanics14: 209–222.
29.
WhittakerETWatsonGN (1990) A Course in Modern Analysis, Cambridge, UK: Cambridge University Press.
