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Effect of Impedance Boundary on Reflection of Plane Waves from Free Surface of a Rotating Thermoelastic Solid Half Space


Affiliations
1 Department of Mathematics, Post Graduate Government College, Sector 11, Chandigarh, India
2 Department of Mathematics, School of Chemical Engineering and Physical Science, Lovely Professional University, Phagwara-Punjab, India
     

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The coupled partial differential equations governing a rotating thermoelastic medium in context of Lord and Shulman theory are solved for plane wave solutions. A cubic velocity equation is obtained, which correspond to the speeds of propagation of three coupled plane waves. A reflection phenomenon is considered in a rotating thermoelastic solid half-space for incidence of a coupled plane wave. The plane surface of the half-space is subjected to impedance boundary conditions, where normal and tangential tractions are proportional to normal and tangential displacement components time frequency, respectively. The expressions for energy ratios of all reflected waves are obtained and computed numerically for a particular material representing the medium. The dependence of energy ratios on rotation parameter, impedance parameters and angle of incidence is shown graphically.

Keywords

Generalized Thermoelasticity, Impedance Boundary, Reflection, Energy Ratios, Rotation.
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  • Achenbach J.D. (1973), Wave propagation in elastic solids, North Holland.

  • Ben-Menahem A. and Singh S.J. (1981), Seismic Waves and Sources, Springer.

  • Biot M.A. (1956), Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics, 2, 240-253.

  • Borcherdt R.D. (1982), Reflection-refraction of general P-and type-I S-waves in elastic and anelastic solids, Geophysical Journal International, 70, 621-638.

  • Bullen K.E. (1963), An Introduction to the Theory of Seismology, Cambridge University Press.

  • Cagniard L. (1962), Reflection and refraction of progressive waves, translated and revised by E. A. Flinn and C. H. Dix., New York McGraw-Hill Book Company.

  • Chatterjee M., Dhua S.and Chattopadhyay A. (2016), Quasi-P and quasi-S waves in a self–reinforced medium under initial stresses and under gravity, Journal of Vibration and Control, 22, 3965-3985.

  • Chattopadhyay A., Kumari P. and Sharma V.K. (2015), Reflection and refraction at the interface between distinct generally anisotropic half spaces for three-dimensional plane quasi-P waves, Journal of Vibration and Control, 21, 493-508.

  • Christie D.G. (1955), Reflection of elastic waves from a free boundary, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 46, 527-541.

  • Deresiewicz H. (1960), The effect of boundaries on wave propagation in a liquid-filled porous solidI. Reflection of plane waves at a free plane boundary (non-dissipative case), Bulletin of the Seismological Society of America, 50, 599-607.

  • Dey S. and Addy S.K. (1977), Reflection of plane waves under initial stresses at a free surface, International Journal of Non-Linear Mechanics, 12, 371–381.

  • Ewing W.M., Jardetzky W.S. and Press F. (1957), Elastic Waves in Layered Media, New York, McGraw-Hill Book Company.

  • Green A.E. and Lindsay K.A. (1972), Thermoelasticity, J. Elasticity, 2, 1-7.

  • Godoy E., Durn M. and Ndlec J.C. (2012), On the existence of surface waves in an elastic half-space with impedance boundary conditions, Wave Motion, 49, 585-594.

  • Haskell N.A. (1962), Crustal reflection of plane P and SV waves, Journal of Geophysical Research, 67, 4751-4768.

  • Hetnarski R.B. and Ignaczak J. (1999), Generalized thermoelasticity, Journal of Thermal Stresses, 22, 451-476.

  • Ignaczak J. and Ostoja-Starzewski M. (2009), Thermoelasticity with Finite Wave Speeds, Oxford University Press.

  • Lord H. and Shulman Y. (1967), A generalized dynamical theory of thermoelasticity, Journal of Mechanics and Physics of the Solids, 15, 299-309.

  • Malischewsky P.G. (1987), Surface Waves and Discontinuities, Elsevier, Amsterdam.

  • Miklowitz J. (1966), Elastic wave propagation, Applied Mechanics Surveys, Spartan Books.

  • Ogden R.W. and Sotiropoulos D.A. (1998), Reflection of plane waves from the boundary of a pre-stressed compressible elastic half-space, IMA Journal of Applied Mathematics, 61, 61-90.

  • Parfitt V.R. and Eringen A.C. (1969), Reflection of plane waves from the flat boundary of a micropolar elastic half‐space, Journal of the Acoustical Society of America, 45, 1258-1272.

  • Rokhlin S.I., Bolland T.K. and Adler L. (1986), Reflection and refraction of elastic waves on a plane interface between two generally anisotropic media, Journal of the Acoustical Society of America, 79, 906-918.

  • Schoenberg M. and Censor D. (1973), Elastic waves in rotating media, Quarterly of Applied Mathematics, 31, 115-125.

  • Sharma J.N. (2001), On the propagation of thermoelastic waves in homogeneous isotropic plates, Indian Journal of Pure and Applied Mathematics, 32, 1329-1341.

  • Sidhu R.S. and Singh S.J. (1984), Reflection of P and SV waves at the free surface of a prestressed elastic half‐space, Journal of the Acoustical Society of America, 76, 594-598.

  • Singh B. (2005), Reflection of P and SV waves from free surface of an elastic solid with generalized thermodiffusion, Journal of Earth System Science, 114, 159-168.

  • Singh B. (2015), Rayleigh waves in an incompressible fibrereinforced elastic solid with impedance boundary conditions, Journal of the Mechanical Behaviour of Materials, 24, 183-186.

  • Singh B. (2016), Rayleigh wave in a thermoelastic solid half-space with impedance boundary conditions, Meccanica 51, 1135-1139.

  • Sinha A.N. and Sinha S.B.(1974), Reflection of thermoelastic waves at a solid half-space with thermal relaxation, Journal of Physics of the Earth, 22, 237-244.

  • Vinh P.C. and Hue T.T.T. (2014), Rayleigh waves with impedance boundary conditions in anisotropic solids, Wave Motion, 51, 1082-1092.

  • Wei P.J., Tang Q. and Lia Y. (2015), Reflection and transmission of elastic waves at the interface between two gradient-elastic solids with surface energy, European Journal of Mechanics - A/Solids, 52, 54-71.


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  • Effect of Impedance Boundary on Reflection of Plane Waves from Free Surface of a Rotating Thermoelastic Solid Half Space

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Authors

Baljeet Singh
Department of Mathematics, Post Graduate Government College, Sector 11, Chandigarh, India
Anand Kumar Yadav
Department of Mathematics, School of Chemical Engineering and Physical Science, Lovely Professional University, Phagwara-Punjab, India
Sachin Kaushal
Department of Mathematics, School of Chemical Engineering and Physical Science, Lovely Professional University, Phagwara-Punjab, India

Abstract


The coupled partial differential equations governing a rotating thermoelastic medium in context of Lord and Shulman theory are solved for plane wave solutions. A cubic velocity equation is obtained, which correspond to the speeds of propagation of three coupled plane waves. A reflection phenomenon is considered in a rotating thermoelastic solid half-space for incidence of a coupled plane wave. The plane surface of the half-space is subjected to impedance boundary conditions, where normal and tangential tractions are proportional to normal and tangential displacement components time frequency, respectively. The expressions for energy ratios of all reflected waves are obtained and computed numerically for a particular material representing the medium. The dependence of energy ratios on rotation parameter, impedance parameters and angle of incidence is shown graphically.

Keywords


Generalized Thermoelasticity, Impedance Boundary, Reflection, Energy Ratios, Rotation.

References