One-Dimensional Generalized Thermoelastic Problem for a Half Space

Abstract

In this paper the theory of generalized thennoelasticity is used to solve a bormdary-value problem of an isotropic elastic half-space with its plane boundary held rigidly fired and subjected to a sudden temperature increase. Approximate small time solution is obtained by using the Laplace transform method. Numerical values of stress and temperature have been obtained. It hav been noticed that the displacement is continuour and that there are two discontinuities in both the stress and temperature jiuictions.

One-dimensional thermoelastic waves in elastic half-space with dual phase-lag effects

“…The finite jumps are not constants but they decay exponentially with distance from the boundary. The same results are observed to occur in ETE, TRDTE [Dhaliwal and Rokne 1988;, but not in TEWOED where the jumps are all constants [Chandrasekhariah and Srinath 1996;1997]. However the discontinuity in temperature and stress at both the wave fronts is a situation common in the context of ETE, TRDTE and TEWOED [Norwood and Warren 1969;Sherief and Dhaliwal 1981;Dhaliwal and Rokne 1988;Chandrasekhariah and Srinath 1996].…”

“…The first term of the solutions (23)- (28) represents the contribution of the E-wave near its wave front ξ = v 1 η and the second term represents the contribution of the T-wave near its wave front ξ = v 2 η. We observe also that both the waves experience decay exponentially with the distance (attenuation), which is also the case in CTE, ETE and TRDTE, but not the case in TEWOED where the waves do not experience attenuation (see [Dhaliwal and Rokne 1988;Chandrasekhariah and Srinath 1996;1997]. From (23)- (28), we further note that all of U, , τ are identically zero for ξ > v 2 η.…”

“…Further the waves suffer exponential attenuation at both the wave fronts as in ETE and TRDTE. Similar problems have been studied in [Dhaliwal and Rokne 1988; in the context of ETE and TRDTE, and in [Chandrasekhariah and Srinath 1996] in the context of TEWOED. The results of the present analysis are compared with those derived in the context of ETE, TRDTE, TEWOED and CTE.…”

“…Problems concerning generalized thermoelasticity theories and G-N theory have been studied by many authors [RoyChoudhuri and Debnath 1983;RoyChoudhuri 1984;1985;1987;Dhaliwal and Rokne 1988;RoyChoudhuri 1990;Chandrasekharaiah and Murthy 1993;Chandrasekhariah and Srinath 1996;RoyChoudhuri and Banerjee 2004;RoyChoudhuri and Bandyopadhyay 2005;RoyChoudhuri and Dutta 2005;. Tzou [1995a;1995b] and Ozisik and Tzou [1994] have developed a new model called dual phase-lag model for heat transport mechanism in which Fourier's law is replaced by an approximation to a modification of Fourier's law with two different time translations for the heat flux and the temperature gradient.…”

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“…Problems concerning generalized thermoelasticity theories and G-N theory have been studied by many authors [RoyChoudhuri and Debnath 1983;RoyChoudhuri 1984;1985;Dhaliwal and Rokne 1988;RoyChoudhuri 1990;Chandrasekharaiah and Murthy 1993;Chandrasekhariah and Srinath 1996;RoyChoudhuri and Banerjee 2004;RoyChoudhuri and Bandyopadhyay 2005;RoyChoudhuri and Dutta 2005;. Tzou [1995a;1995b] and Ozisik and Tzou [1994] have developed a new model called dual phase-lag model for heat transport mechanism in which Fourier's law is replaced by an approximation to a modification of Fourier's law with two different time translations for the heat flux and the temperature gradient.…”