Mathematical modeling of torsional surface wave propagation in a non-homogeneous transverse isotropic elastic solid semi-infinite medium under a layer

• Autorzy: Sethi M. , Sharma A. , Vasishth A.

Identyfikatory

DOI

10.1515/ijame-2017-0025

• Języki publikacji: EN

Abstrakty

EN

The present paper deals with the mathematical modeling of the propagation of torsional surface waves in a non-homogeneous transverse isotropic elastic half-space under a rigid layer. Both rigidities and density of the half-space are assumed to vary inversely linearly with depth. Separation of variable method has been used to get the analytical solutions for the dispersion equation of the torsional surface waves. Also, the effects of nonhomogeneities on the phase velocity of torsional surface waves have been shown graphically. Also, dispersion equations have been derived for some particular cases, which are in complete agreement with some classical results.

Słowa kluczowe

EN

non-homogeneous media; torsional surface waves; rigidity

PL

fala powierzchniowa; propagacja fal; modelowanie matematyczne

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2017
• Tom: Vol. 22, no. 2
• Strony: 415--426
• Opis fizyczny: Bibliogr. 27 poz., wykr.

Twórcy

autor

Sethi M.

• Department of Applied Sciences Govt. Polytechnic College for Girls Jalandhar, India

autor

Sharma A.

• Department of Applied Sciences Cchandigarh Engg. College Landran, Mohali, India

autor

Vasishth A.

• Department of Applied Sciences Cchandigarh Engg. College Landran, Mohali, India

Bibliografia

• [1] Stoneley R. (1924): Elastic waves at surface of separation of two solids. - Proc. R. Soc. A 806. pp.416-428.
• [2] Bullen K.E. (1965): Theory of Seismology. - Cambridge University Press.
• [3] Ewing W.M., Jardetzky W.S. and Press F. (1957): Elastic Waves in Layered Media. - New York: Mcgraw-Hill.
• [4] Hunter S.C. (1970): Viscoelastic Waves, Progress in Solid Mechanics, I. - (ed: Sneddon IN and Hill R) Cambridge University Press.
• [5] Jeffreys H. (1970): The Earth. - Cambridge University Press.
• [6] Sezawa K. (1927): Dispersion of elastic waves propagated on the surface of stratified bodies and on curved surfaces. - Bull. Earthq. Res. Inst. Tokyo, vol.3. pp.1-18.
• [7] Thomson W.J. (1950): Transmission of elastic waves through a stratified elastic medium. - Appl. Phys., vol.21, pp.89-93.
• [8] Haskell N.A. (1953): The dispersion of surface waves in multilayered media. - Bull. Seis. Soc. Amer., vol.43. pp.17-34.
• [9] Biot M.A. (1965): Mechanics of Incremental Deformations. J. Willy.
• [10] Sinha N. (1967): Propagation of Love waves in a non-homogeneous stratum of finite depth sandwiched between two semi-infinite isotropic media. - Pure Applied Geophysics, vol.67, pp.65-70.
• [11] Roy P.P. (1984): Wave propagation in a thin two layered medium with stress couples under initial stresses. - Acta Mechanics, vol.54. pp.1-21.
• [12] Belfield A.J., Rogers T.G. and Spencer A.J.M. (1983): Stress in elastic plates reinforced by fibers lying in concentric circles. - Journal of the Mechanics and Physics of Solids, vol.31, No.1, pp.25-54.
• [13] Datta B.K. (1986): Some observation on interactions of Rayleigh waves in an elastic solid medium with the gravity field. - Rev. Roumaine Sci. Tech. Ser. Mec. Appl., vol.31. pp.369-374.
• [14]Chattopadhyay A., Chakraborty M. and Pal A.K. (1983): Effects of irregularity on the propagation of guided SH waves. - Jr. de Mecanique Theo. et appl, Vol.2 No.2. pp.215-225.
• [15] Goda M.A. (1992): The effect of inhomogeneity and anisotropy on Stoneley waves. - Acta Mech., vol.93, No.1-4. pp.89-98.
• [16] Gupta S., Vishwakarma S.K., Majhi D.K. and Kundu S. (2012): Influence of linearly varying density and rigidity on torsional waves in inhomogeneous crustal layer. - Appl. Math. Mech.-Engl. Ed., vol.33, No.10. pp.1239-1252.
• [17] Georgiadis H.G., Vardaulakis I. and lykotrafitis G. (2000): Torsional surface wave in gradient-elastic half-space. - Wave Motion, vol.31, No.4, pp.333-348.
• [18] Dey S. and Sarkar M.G. (2002): Torsional surface waves in an initially stressed anisotropic porous medium. - J. Eng. Mech., vol.128, No.2, pp.184-189.
• [19] Selim M.M. (2007): Propagation of torsional surface wave in heterogeneous half-space with irregular free surface. - Appl. Math. Sci., vol.1, No.29-32, pp.1429-1437.
• [20] Ozturk A. and Akbbarov S.D. (2009): Torsional wave propagation in a pre-stressed circular cylinder embedded in a pre-stressed elastic medium. - Appl. Math. Model., vol.33. pp.3636-3649.
• [21] Gupta S., Majhi D.K., Kundu S. and Vishwakarma S.K. (2012): Propagation of torsional surface waves in a homogeneous layer of finite thickness over an initially stressed heterogeneous half-space. - Appl. Math. Comput., vol.218. pp.5655-5664.
• [22] Davini C., Paroni R. and Puntle E. (2008): An asymptotic approach to the torsional problem in thin rectangular domains. - Meccanica, vol.43, No.4, pp.429-435.
• [23] Dey S., Gupta S., Gupta A.K., Kar S.K. and De P.K. (2003): Propagation of torsional surface waves in an elastic layer with void pores over an elastic half-space with void pores. - Tamkang J. Sci. Eng., vol.6, No.4, pp.241-249.
• [24] Sethi M., Gupta K.C., Rani Monika and Vasudeva A. (2013): Surface waves in homogeneous viscoelastic media of higher order under the influence of surface stresses. - J. Mech. Behav. Mater., vol.22, No.5-6, pp.185-191.
• [25] Sethi M., Sharma Arvind and Sharma Anupamdeep (2016): Propagation of SH waves in a double homogeneous crustal layers of finite depth lying over an homogeneous half-space. - Latin American journal of Solids and Structures, vol.13, No.14, pp.2328-2342.
• [26] Sethi M. and Sharma Anupamdeep (2016): Propagation of SH waves in an regular non homogeneous monoclinic crustal layer lying over a non-homogeneous semi-infinite medium. - International Journal of Applied Mechanics and Engineering, vol.21, No.1, pp.447-459.
• [27] Whittaker E.T. and Watson G.N. (1990): A Course in Modern Analysis. - 4th Edn, Cambridge: CambridgeUniversity Press.