- Volume 21 Issue 4
In this article, the problem of a two-dimensional thermoelastic half-space are studied using mathematical methods under the purview of the generalized thermoelastic theory with one relaxation time is studied. The surface of the half-space is taken to be thermally insulated and traction free. Accordingly, the variations of physical quantities due to by laser pulse given by the heat input. The nonhomogeneous governing equations have been written in the form of a vector-matrix differential equation, which is then solved by the eigenvalue approach. The analytical solutions are obtained for the temperature, the components of displacement and stresses. The resulting quantities are depicted graphically for different values of thermal relaxation time. The result provides a motivation to investigate the effect of the thermal relaxation time on the physical quantities.
Eigenvalue approach;exact solution;Lord and Shulman theory;relaxation time;laser pulse
- Abbas, I.A. (2014a), "Eigenvalue approach for an unbounded medium with a spherical cavity based upon two-temperature generalized thermoelastic theory", J. Mech. Sci. Technol., 28(10), 4193-4198. https://doi.org/10.1007/s12206-014-0932-6
- Abbas, I.A. (2014b), "Eigenvalue approach in a three-dimensional generalized thermoelastic interactions with temperature-dependent material properties", Comput. Math. Appl., 68(12), 2036-2056. https://doi.org/10.1016/j.camwa.2014.09.016
- Abbas, I.A. (2014c), "The effects of relaxation times and moving heat source on a two-temperature generalized thermoelastic thin slim strip", Can. J. Phys., 93(5), 585-590.
- Abbas, I.A. (2015a), "A dual phase lag model on thermoelastic interaction in an infinite fiber-reinforced anisotropic medium with a circular hole", Mech. Based Des. Struct. Mach., 43(4), 501-513. https://doi.org/10.1080/15397734.2015.1029589
- Abbas, I.A. (2015b), "Eigenvalue approach to fractional order generalized magneto-thermoelastic medium subjected to moving heat source", J. Magnet. Magnet. Mater., 377, 452-459. https://doi.org/10.1016/j.jmmm.2014.10.159
- Abbas, I.A. (2015c), "The effects of relaxation times and a moving heat source on a two-temperature generalized thermoelastic thin slim strip", Can. J. Phys., 93(5), 585-590.
- Abbas, I.A. and Kumar, R. (2016), "2D deformation in initially stressed thermoelastic half-space with voids", Steel Compos. Struct., Int. J., 20(5), 1103-1117. https://doi.org/10.12989/scs.2016.20.5.1103
- Abbas, I.A. and Youssef, H.M. (2015), "Two-dimensional fractional order generalized thermoelastic porous material", Latin Am. J. Solid. Struct., 12(7), 1415-1431. https://doi.org/10.1590/1679-78251584
- Abbas, I.A. and Zenkour, A.M. (2013), "LS model on electro-magneto-thermoelastic response of an infinite functionally graded cylinder", Compos. Struct., 96, 89-96. https://doi.org/10.1016/j.compstruct.2012.08.046
- Abbas, I.A. and Zenkour, A.M. (2014), "Dual-ohase-lag model on thermoelastic interactions in a semiinfinite medium subjected to a ramp-type heating", J. Computat. Theor. Nanosci., 11(3), 642-645. https://doi.org/10.1166/jctn.2014.3407
- Agarwal, V.K. (1978), "On surface waves in generalized thermoelasticity", J. Elast., 8(2), 171-177. https://doi.org/10.1007/BF00052480
- Agarwal, V.K. (1979a), "On electromagneto-thermoelastic plane waves", Acta Mechanica, 34(3-4), 181-191. https://doi.org/10.1007/BF01227983
- Agarwal, V.K. (1979b), "On plane waves in generalized thermoelasticity", Acta Mechanica, 31(3-4), 185-198. https://doi.org/10.1007/BF01176847
- Al-Qahtani, H.M. and Datta, S.K. (2008), "Laser-generated thermoelastic waves in an anisotropic infinite plate: Exact analysis", J. Therm. Stress., 31(6), 569-583. https://doi.org/10.1080/01495730801978380
- Biot, M.A. (1956), "Thermoelasticity and irreversible thermodynamics", J. Appl. Phys., 27(3), 240-253. https://doi.org/10.1063/1.1722351
- Bouchafa, A., Bouiadjra, M.B., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., Int. J., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493
- Das, N.C., Lahiri, A. and Giri, R.R. (1997), "Eigenvalue approach to generalized thermoelasticity", Ind. J. Pure Appl. Math., 28(12), 1573-1594.
- Deresiewicz, H. (1975), "Thermal coupling of waves in a plate", Acta Mechanica, 21(4), 329-342. https://doi.org/10.1007/BF01303074
- Dhaliwal, R.S. and Sherief, H.H. (1980), "Generalized thermoelasticity for anisotropic media", Quart. Appl. Math., 38(1), 1-8. https://doi.org/10.1090/qam/575828
- Ezzat, M.A. (2011), "Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer", Physica B: Condensed Matter, 406(1), 30-35. https://doi.org/10.1016/j.physb.2010.10.005
- Ezzat, M. and Awad, E. (2010), "Analytical aspects in the theory of thermoelastic bodies with microstructure and two temperatures", J. Therm. Stress., 33(7), 674-693. https://doi.org/10.1080/01495731003776069
- Ezzat, M.A. and El-Karamany, A.S. (2003), "The relaxation effects of the volume properties of viscoelastic material in generalized thermoelasticity", Int. J. Eng. Sci., 41(19), 2281-2298. https://doi.org/10.1016/S0020-7225(03)00108-3
- Ezzat, M.A. and Youssef, H.M. (2005), "Generalized magneto-thermoelasticity in a perfectly conducting medium", Int. J. Solid. Struct., 42(24-25), 6319-6334. https://doi.org/10.1016/j.ijsolstr.2005.03.065
- Green, A.E. and Lindsay, K.A. (1972), "Thermoelasticity", J. Elastic., 2(1), 1-7. https://doi.org/10.1007/BF00045689
- Isavand, S., Shakeri, B.M. and Mohandesi, J.A. (2015), "Dynamic response of functionally gradient austenitic-ferritic steel composite panels under thermo-mechanical loadings", Steel Compos. Struct., Int. J., 18(1), 1-28. https://doi.org/10.12989/scs.2015.18.1.001
- Kakar, S. and Kakar, R. (2014), "Electro-magneto-thermoelastic surface waves in non-homogeneous orthotropic granular half space", Geomech. Eng., Int. J., 7(1), 1-36. https://doi.org/10.12989/gae.2014.7.1.001
- Kumar, R. and Rupender (2010), "The effect of rotation in a magneto-micropolar thermoelastic layer with one relaxation time", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 224(3), 661-673. https://doi.org/10.1243/09544062JMES1725
- Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solid., 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5
- Mallik, S.H. and Kanoria, M. (2008), "A two dimensional problem for a transversely isotropic generalized thermoelastic thick plate with spatially varying heat source", Euro. J. Mech., A/Solids, 27(4), 607-621. https://doi.org/10.1016/j.euromechsol.2007.09.002
- Othman, M.I.A. and Abbas, I.A. (2012), "Generalized thermoelasticity of thermal-shock problem in a nonhomogeneous isotropic hollow cylinder with energy dissipation", Int. J. Thermophys., 33(5), 913-923. https://doi.org/10.1007/s10765-012-1202-4
- Othman, M.I. and Abbas, I.A. (2014), "Effect of rotation on plane waves in generalized thermomicrostretch elastic solid: Comparison of different theories using finite element method", Can. J. Phys., 92(10), 1269-1277. https://doi.org/10.1139/cjp-2013-0482
- Saadatfar, M. and Aghaie-Khafri, M. (2015), "Electromagnetothermoelastic behavior of a rotating imperfect hybrid functionally graded hollow cylinder", Smart Struct. Syst., Int. J., 15(6), 1411-1437. https://doi.org/10.12989/sss.2015.15.6.1411
- Verma, K. and Hasebe, N. (1999), "On the propagation of generalized thermoelastic vibrations in plates", Eng. Transact., 47(3), 300-319.
- Zenkour, A.M. and Abbas, I.A. (2015a), "Electro-magneto-thermo-elastic response of infinite functionally graded cylinders without energy dissipation", J. Magnet. Magnet. Mater., 395, 123-129. https://doi.org/10.1016/j.jmmm.2015.07.038
- Zenkour, A.M. and Abouelregal, A.E. (2015b), "Thermoelastic interaction in functionally graded nanobeams subjected to time-dependent heat flux", Steel Compos. Struct., Int. J., 18(4), 909-924. https://doi.org/10.12989/scs.2015.18.4.909
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