This paper is concerned with the propagation of plane waves in a transversely isotropic generalized thermoelastic solid half-space with diffusion. The governing equations are modified in the context of the Lord and Shulman theory of generalized thermoelasticity and are solved to show the existence of four plane waves in the xz plane. Reflection of these plane waves from a thermally insulated free surface is studied, and a system of four nonhomogeneous equations for the reflection coefficients is obtained. For numerical computations of the speed and reflection coefficients, a particular material is modeled as a transversely isotropic generalized thermoelastic solid half-space. The speeds of plane waves are calculated against the angle of propagation to reveal the effects of anisotropy and diffusion. The reflection coefficients of various reflected waves are also obtained that demonstrate the effect of diffusion parameters.
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A. E. Green and K. A. Lindsay, Thermoelasticity, J. Elasticity, 2, 1–7 (1972).
H. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15, 299–309 (1967).
J. Ignaczak and M. Ostoja-Starzewski, Thermoelasticity with Finite Wave Speeds, Oxford University Press (2009).
R. B. Hetnarski and J. Ignaczak, Generalized thermoelasticity, J. Thermal 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).
S. B. Sinha and K. A. Elsibai, Reflection of thermoelastic waves at a solid half-space with two thermal relaxation times, J. Thermal Stresses, 19, 763–777 (1996).
S. B. Sinha and K. A. Elsibai, Reflection and refraction of thermoelastic waves at an interface of two semi-infinite media with two thermal relaxation times, J. Thermal Stresses, 20, 129–146 (1997).
J. N. Sharma, V. Kumar, and D. Chand, Reflection of generalized thermoelastic waves from the boundary of a half-space, J. Thermal Stresses, 26, 925–942 (2003).
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. Comput., 198, 494–505 (2008).
B. Singh, Reflection of plane waves at the free surface of a monoclinic thermoelastic solid half-space, Eur. J. Mech. A/Solids, 29, 911–916 (2010).
W. Nowacki, Dynamical problems of thermoelastic diffusion in solids, I and II, Bull. Acad. Pol. Sci., Ser. Tech., 22, 55–64, 129–135 (1974).
W. Nowacki, Dynamical problems of diffusion in solids, Eng. Fract. Mech., 8, 261–266 (1976).
H. H. Sherif, F. Hamza, and H. Saleh, The theory of generalized thermoelastic diffusion, Int. J. Eng. Sci., 42, 591–608 (2004).
B. Singh, Reflection of P and SV waves from the free surface of an elastic solid with generalized thermodiffusion, J. Earth Syst. Sci., 114, 159–168 (2005).
B. Singh, Reflection of SV waves from the free surface of an elastic solid in generalized thermoelastic diffusion, J. Sound Vibr., 291, 764–778 (2006).
S. M. Abo-Dahab and B. Singh, Influences of magnetic field on wave propagation in generalized thermoelastic solid with diffusion, Arch. Mech., 61, 121–136 (2009).
M. Aoudai, Variable electrical and thermal conductivity in the theory of generalized thermoelastic diffusion, Z. Angew. Math. Phys., 57, 350–366 (2006).
M. Aoudai, Uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion, J. Thermal Stresses, 30, 665–678 (2007).
M. Aoudai, Qualitative aspects in the coupled theory of thermoelastic diffusion, J. Thermal Stresses, 31, 706–727 (2008).
M. I. A. Othman, S. Y. Atwa, and R. M. Farouk, The effect of diffusion on two-dimensional problem of generalized thermoelasticity with Green–Naghdi theory, Int. Commun. Heat Mass Transfer, 36, 857–864 (2009).
M. Aoudai, Generalized theory of thermoelastic diffusion for anisotropic media, J. Thermal Stresses, 31, 270–285 (2008).
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. 85, No. 2, pp. 442–448, March–April, 2012
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Bijarnia, R., Singh, B. Propagation of plane waves in an anisotropic generalized thermoelastic solid with diffusion. J Eng Phys Thermophy 85, 478–486 (2012). https://doi.org/10.1007/s10891-012-0676-z
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DOI: https://doi.org/10.1007/s10891-012-0676-z