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The model of the equations of two-dimensional coupled problem in thermo-elasticity for a thermally half-space solid whose surface is subjected to a thermal shock is established. The problem is in the context of the Green and Lindsay's generalized thermoelasticity theory with two relaxation times in an isotropic medium with the modulus of elasticity being dependent on the reference temperature. The normal mode analysis is used to obtain the exact expressions for the temperature, the displacement and thermal stress components. The resulting formulation is applied to two kinds of boundary conditions. Numerical results are illustrated graphically for each case considered. Comparison is carried out with the results predicted by the coupled theory and with the case where the modulus of elasticity is independent of temperature.
Czasopismo
Rocznik
Tom
Strony
49--63
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
- Department of Mathematics, Faculty of Education, P.O. Box 2801, Salalah- 211, Sultanate of Oman, m_i_othman@yahoo.com
Bibliografia
- [1] Nowacki, W. Thermoelasticity, Addison-Wesley Pub. Com. Inc. London, 1962.
- [2] Tanigawa, Y.: Some Basic Thermoelastic Problems for Non- homogeneous Structural Materials, Appl. Mech. Rev., 1995, 48, 115.
- [3] Ootao, Y., Akai, T., Tanigawa, Y.: Three-dimensional Transient Thermal Stress Analysis of a Non-homogeneous Hollow Circular Cylinder due to Moving Heat Source in the Axial Direction, J. Thermal Stresses, 1995, 18, 89.
- [4] Manson, S. S.: Behaviour of Material under Conditions of Thermal Stress. NACA Report, 1954, 1170, 317-350.
- [5] Biot, M.: Thermoelasticity and Irreversible Thermodynamics, J. Appl.Phys., 1956, 27, 240-253.
- [6] Müller, I.: The Coldness, A Universal Function in Thermoelastic Solids, Arch. Rat. Mech. Anal., 1971, 41, 319-332.
- [7] Green, A. E., Laws, N. : On the Entropy Production Inequality, Arch. Rat. Mech. Anal., 1972, 45, 47-53.
- [8] Green, A. E., Lindsay, K. A.: Thermoelasticity J. Elast., 1972, 2, 1-7.
- [9] Suhubi, E. S.: Themoelastic Solids. In Continuum Physics II, Chapter 2, ed. A. C. Eringen. Academic, Press, New York, 1975.
- [10] Lord, H., Shulman, Y.: A Generalized Dynamical Theory of Thermoelasticity. J. Mech. Phys. Solid, 1967, 15, 299-309.
- [11] Erbay, S., Suhubi, E. S.: Longitudinal Wave Propagation in Generalized Elastic Cylinder, J. Therm. Stresses, 1986, 9, 279-295.
- [12] Ignaczak, J.: A Strong Discontinuity Wave in Thermoelasticity with Relaxation Times, J. Therm. Stresses, 1985, 8, 25-40.
- [13] Ignaczak, J.: Decomposition Theorem for Thermoelasticity with Finite Wave Speeds, J. Therm. Stresses, 1978, 1, 41-52.
- [14] Dhaliwal, R., Sherief, H. H.: Generalized Thermoelasticity for an- Isotropic Media, Quart. Appl. Math., 1980, 33, 1-8.
- [15] Dhaliwal, R., Rokne: Thermal Shock Problem in Generalized Thermoelastic, J. Therm. Stresses, 1989, 12, 259.
- [16] Ezzat, M., Othman M. I. A.: Electromagneto-thermoelasticity Plane Waves with Two Relaxation Times in a Medium of Perfect Conductivity, Int. J. Engng Sci., 2000, 38, 107-120.
- [17] Ezzat, M., Othman, M. I. A., El-Karamany, A. S.: The Dependence of the Modulus of Elasticity on the Reference Temperature in Generalized Thermoelasticity, J. Therm. Stresses, 2001, 24, 1159-1176.
- [18] Ezzat, M., Othman, M. I. A., El-Karamany, A. S.: Electromagneto-thermoelasticity PlaneWaves with Thermal Relaxation in a Medium of Perfect Conductivity, J. Therm. Stresses, 2001, 24,411-432.
- [19] Sherief, H. H., Helmy, K. A.: A Two-Dimensional Problem for a Half-Space in Magneto-thermoelasticity with Thermal Relaxation, Int. J. Engng Sci., 2002, 40, 578-604 .
- [20] Nowacki, W.: Dynamic Problems of Thermoelasticity, Noordhoof Int., The Netherlands. 1975.
- [21] Othman, M. I. A.: Lord-Shulman Theory Under the Dependence of the Modulus of Elasticity on the Reference Temperature in Two-Dimensional Generalized Thermoelasticity, J. Thermal Stresses, 2002 25, 1027-1045.
- [22] Othman, M. I. A.: Electrohydrodynamic Stability in a Horizontal Viscoelastic Fluid Layer in the Presence of a Vertical Temperature Gradient, Int. J. Engng. Sci., 200139, 1217-1232 .
- [23] Othman M. I. A., M. Ezzat: Electromagneto-hydrodynamic Instability in Horizontal Viscoelastic Fluid Layer with One Relaxation Time, Acta Mech.,2001, 150, 1-2, 1-9 .
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Bibliografia
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bwmeta1.element.baztech-article-LOD9-0011-0016