The basic equations for the wave on the surface of an initially stressed transversely isotropic dual-phase-lag thermoelastic body subjected to the action of a magnetic field were solved. Particular solutions were applied to the thermally insulated free surface of a half-space to obtain the frequency equation for the Rayleigh wave. This equation was approximated for calculating the numerical values of the dimensionless velocity of the Rayleigh wave. The Rayleigh-wave velocity was represented graphically for the cases of coupled, Lord–Shulman, and dual-phaselag thermoelasticities. The influence of the dual-phase-lag and the initial stress of a body, the value of the magnetic field, and the frequency of the Rayleigh wave on the velocity of this wave were determined.
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References
M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys., 2, 240–253 (1956).
H. Lord and Y. Shulman, A generalised dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15, 299–309 (1967).
A. E. Green and K. A. Lindsay, Thermoelasticity, J. Elast., 2, 1–7 (1972).
J. Ignaczak and M. Ostoja-Starzewski, Thermoelasticity with Finite Wave Speeds, Oxford University Press, Oxford (2009).
R. B. Hetnarski and J. Ignaczak, Generalized thermoelasticity, J. Therm. Stresses, 22, 451–476 (1999).
H. Deresiewicz, Effect of boundaries on waves in a thermoelastic solid: Reflection of plane waves from plane boundary, J. Mech. Phys. Solids, 8, 164–172 (1960).
A. N. Sinha and S. B. Sinha, Reflection of thermoelastic waves at a solid half space with thermal relaxation, J. Phys. Earth, 22, 237–244 (1974).
M. I. A. Othman and Y. Song, Reflection of plane waves from an elastic solid half-space under hydrostatic initial stress without energy dissipation, Int. J. Solids Struct., 44, 5651–5664 (2007).
B. Singh, Effect of hydrostatic initial stresses on waves in a thermoelastic solid half-space. Appl. Math. Comp., 198, 494–505 (2008).
B. Singh, Reflection of plane waves at the free surface of a monoclinic thermoelastic solid half-space. Euro. J. Mech. A-Solids, 29, 911–916 (2010).
D. Y. Tzou, A unified approach for heat conduction from macro to microscales, J. Heat Transf., 117, 8–16 (1995).
D. Y. Tzou, Experimental support for the lagging behavior in heat propagation, J. Thermophys. Heat Transf., 9, 686–693 (1995).
D. Y. Tzou, Macro-to-Microscale Heat Transfer: The Lagging Behavior, Taylor and Francis, Washington, DC (1996).
A. E. Abouelregal, Rayleigh waves in athermoelastic solid half space using dual-phase-lag model. Int. J. Eng. Sci., 49, 781–791 (2011).
J. Wang, R. S. Dhaliwal, and S. R. Majumdar, Some theorems in the generalized theory of thermoelasticity for prestressed bodies, Indian J. Pure Appl. Math., 28, 267–276 (1997).
P. Chadwick and L. T. C. Seet, Wave propagation in a transversely isotropic heat conducting elastic material, Mathematica, 17, 255–274 (1970).
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Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 87, No. 6, pp. 1472–1479, November–December, 2014.
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Singh, B., Kumari, S. & Singh, J. Propagation of the Rayleigh Wave in an Initially Stressed Transversely Isotropic Dual-Phase-Lag Magnetothermoelastic Half-Space. J Eng Phys Thermophy 87, 1539–1547 (2014). https://doi.org/10.1007/s10891-014-1160-8
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DOI: https://doi.org/10.1007/s10891-014-1160-8