The governing equations for a homogeneous and isotropic thermoelastic medium are formulated in the context of coupled thermoelasticity, Lord and Shulman theory of generalized thermoelasticity with one relaxation time, Green and Lindsay theory of generalized thermoelasticity with two relaxation times, Green and Nagdhi theory of thermoelasticity without energy dissipation and Chandrasekharaiah and Tzou theory of thermoelasticity. These governing equations are solved to obtain general surface wave solutions. The particular solutions in a half-space are obtained with the help of appropriate radiation conditions. The two types of boundaries at athe surface of a half-space are considered namely, the stress free thermally insulated boundary and stress free isothermal boundary. The particular solutions obtained in a half-space satisfy the relevant boundary conditions at the free surface of the half-space and a frequency equation for the Rayleigh wave speed is obtained for both thermally insulated and isothermal cases. The non-dimensional Rayleigh wave speed is computed for aluminium metal to observe the effects of frequency, thermal relaxation time and different theories of thermoelasticity.
[1] Biot M.A. (1956): Thermoelasticity and irreversible thermodynamics. – J. Appl. Phys. vol.2 pp.240-253.
[2] Green A.E. and Lindsay K.A. (1972): Thermoelasticity. – J. Elasticity vol.2 pp.1-7.
[3] Lord H. and Shulman Y. (1967): A generalised dynamical theory of thermoelasticity. – J. Mech. Phys. Solids vol.15 pp.299-309.
[4] Green A.E. and Naghdi P.M. (1993): Thermoelasticity without energy dissipation. – J. Elast. vol.31 pp.189-208.
[5] Hetnarski R.B. and Ignaczak J. (1999): Generalized thermoelasticity. – J. Thermal Stresses vol.22 pp.451-476.
[6] Ignaczak J. and Ostoja-Starzewski M. (2009): Thermoelasticity with Finite Wave Speeds. – Oxford University Press.
[7] Deresiewicz H. (1960): Effect of boundaries on waves in a thermo-elastic solid: Reflection of plane waves from plane boundary. – J. Mech. Phys. Solids vol.8 pp.164-172.
[8] Sinha A.N. and Sinha S.B. (1974): Reflection of thermoelastic waves at a solid half space with thermal relaxation. – J. Phys. Earth vol.22 pp.237-244.
[9] Sinha S.B. and Elsibai K.A. (1996): Reflection of thermoelastic waves at a solid half-space with two thermal relaxation times. – J. Thermal Stresses vol.19 pp.763-777.
[10] Sinha S.B. and Elsibai K.A. (1997): Reflection and refraction of thermoelastic waves at an interface of two semi-infinite media with two thermal relaxation times. – J. Thermal Stresses vol.20 pp.129-146.
[11] Sharma J.N. Kumar V. and Chand D. (2003): Reflection of generalized thermoelastic waves from the boundary of a half-space. – J. Thermal Stresses vol.26 pp.925-942.
[12] Singh B. (2008): Effect of hydrostatic initial stresses on waves in a thermoelastic solid half-space. – Applied Math. Comp. vol.198 pp.494-505.
[13] Singh B. (2010): Reflection of plane waves at the free surface of a monoclinic thermoelastic solid half-space. – European J. Mech. A-Solids vol.29 pp.911-916.
[14] Singh M.C. and Chakraborty N. (2015): Reflection of a plane magneto-thermoelastic wave at the boundary of a solid half-space in presence of initial stress. – Appl. Math. Modelling vol.39 pp.1409-1421.
[15] Wei W. Zheng R. Liu G. and Tao H (2016): Reflection and refraction of P wave at the interface between thermoelastic and porous thermoelastic medium. – Transport in Porous Media vol.113 pp.1-27.
[16] Li Y. Li L. Wei P. and Wang C. (2018): Reflection and refraction of thermoelastic waves at an interface of two couple-stress solids based on Lord-Shulman thermoelastic theory. – Appl. Math. Modelling vol.55 pp.536-550.
[17] Rayleigh L. (1885): On waves propagated along the plane surface of an elastic solid. – Proc. R. Soc. London Ser. A vol.17 pp.4-11.
[18] Lockett F.J. (1958): Effect of the thermal properties of a solid on the velocity of Rayleigh waves. – J. Mech. Phys. Solids vol.7 pp.71-75.
[19] Flavin J.N. (1962): Thermoelastic Rayleigh waves in a prestressed medium. – Math. Proc. Cambridge Phil. Soc. vol.58 pp.532-538.
[20] Chadwick P. and Windle D.W. (1964): Propagation of Rayleigh waves along isothermal and insulated boundaries. – Proc. R. Soc. Lond. A vol.280 pp.47-71.
[21] Tomita S. and Shindo Y. (1979): Rayleigh waves in magneto-thermoelastic solids with thermal relaxation. – Int. J. Eng. Sci vol.17 pp.227-232.
[22] Dawn N.C. and Chakraborty S.K. (1988): On Rayleigh wave in Green-Lindsay’s model of generalized thermoelastic media. – Ind. J. Pure Appl. Math vol.20 pp.273-286.
[23] Abd-Alla A.M. and Ahmed M. (1996): Rayleigh waves in an orthotropic thermoelastic medium under gravity field and initial stress. – Earth Moon and Planets vol.75 pp.185-197.
[24] Ahmed S.M. (2000): Rayleigh waves in a thermoelastic granular medium under initial stress. – Int. J. Math. Math. Sci. vol.23 pp.627-637.
[25] Sharma J.N. Walia V. and Gupta S.K. (2008): Effect of rotation and thermal relaxation on Rayleigh waves in piezothermoelastic half space. – Int. J. Mech. Sci. vol.50 pp.433-444.
[26] Abouelregal A. E. (2011): Rayleigh waves in a thermoelastic solid half space using dual-phase-lag model. – Int. J. Eng. Sci. vol.49 pp.781-791.
[27] Mahmoud S.R. (2012): Influence of rotation and generalized magneto-thermoelastic on Rayleigh waves in a granular medium under effect of initial stress and gravity field. – Meccanica vol.47 pp.1561-1579.
[28] Chirita S. (2013): On the Rayleigh surface waves on an anisotropic homogeneous thermoelastic half-space. – Acta Mech. vol.224 pp.657-674.
[29] Singh B. (2014): Propagation of Rayleigh wave in a thermoelastic solid half-space with microtemperatures. – Int. J. Geophys. Article ID 474502 6 pages http://dx.doi.org/10.1155/2014/474502 (2014)
[30] Bucur A.V. Passarella F. and Tibullo V. (2014): Rayleigh surface waves in the theory of thermoelastic materials with voids. – Meccanica vol.49 pp.2069-2078.
[31] Passarella F. Tibullo V. and Viccione G. (2017): Rayleigh waves in isotropic strongly elliptic thermoelastic materials with microtemperatures. – Meccanica vol.52 pp.3033-3041.
[32] Biswas S. Mukhopadhyay B. and Shaw S. (2017): Rayleigh surface wave propagation in orthotropic thermoelastic solids under three-phase-lag model. – J. Thermal Stresses vol.40 pp.403-419.
[33] Vashishth A.K. and Sukhija H. (2017): Coupled Rayleigh waves in a 2-mm piezoelectric layer over a porous piezo-thermoelastic half-space. – Acta Mechanica vol.228 pp.773-803.
[34] Tzou D.Y. (1995): A unified approach for heat conduction from macro to micro-scales. – J. Heat Transfer vol.117 pp.8-16.