Effects of Gravitational and Hydrostatic Initial Stress on a Two-Temperature Fiber-Reinforced Thermoelastic Medium for Three-Phase-Lag
الموضوعات :
1 - Department of Mathematics, Faculty of Science and Arts, Al-mithnab, Qassim University, P.O. Box 931, Buridah 51931, Al-mithnab, Kingdom of Saudi Arabia
2 - Department of Mathematics, Faculty of Science, Taif University 888, Saudi Arabia
الکلمات المفتاحية: Fiber-reinforced, Hydrostatic initial stress, Three-phase-lag model, Gravity field, Green-Naghdi theory, Two-temperature,
ملخص المقالة :
The three-phase-lag model and Green–Naghdi theory without energy dissipation are employed to study the deformation of a two-temperature fiber-reinforced medium with an internal heat source that is moving with a constant speed under a hydrostatic initial stress and the gravity field. The modulus of the elasticity is given as a linear function of the reference temperature. The exact expressions for the displacement components, force stresses, thermal temperature and conductive temperature are obtained by using normal mode analysis. The variations of the considered variables with the horizontal distance are illustrated graphically. A comparison is made with the results of the two theories for two different values of a hydrostatic initial stress. Comparisons are also made with the results of the two theories in the absence and presence of the gravity field as well as the linear temperature coefficient.
[1] Chen P.J., Gurtin M. E., 1968, On a theory of heat conduction involving two temperatures, Zeitschrift für Angewandte Mathematik und Physik 19: 614-627.
[2] Chen P.J., Williams W.O., 1968, A note on non simple heat conduction, Zeitschrift für angewandte Mathematik und Physik 19: 969-970.
[3] Chen P.J., Gurtin M. E., Williams W.O., 1969, On the thermodynamics of non-simple elastic materials with two-temperatures, Zeitschrift für Angewandte Mathematik und Physik 20: 107-112.
[4] Warren W. E., Chen P. J., 1973, Wave propagation in the two temperatures theory of thermoelasticity, Journal of Acta Mechcanica 16: 21-33.
[5] Youssef H. M., 2005, Theory of two-temperature generalized thermoelasticity, Journal of Applied Mathematics 71: 383-390.
[6] Puri P., Jordan P.M., 2006, On the propagation of harmonic plane wanes under the two temperature theory, International Journal of Engineering Science 44: 1113-1126.
[7] Abbas I. A., Youssef H. M., 2009, Finite element method of two-temperature generalized magneto-thermoelasticity, Journal Archive of Applied Mechanics 79: 917-925.
[8] Kumar R., Mukhopadhyay S., 2010, Effects of thermal relaxation time on plane wave propagation under two-temperature thermoelasticity, International Journal of Engineering Science 48: 128-139.
[9] Das P., Kanoria M., 2012, Two-temperature magneto-thermoelastic response in a perfectly conducting medium based on GN-III Model, International Journal of Pure and Applied Mathematics 81: 199-229.
[10] Abbas I. A., Zenkour A. M., 2014, Two-temperature generalized thermoplastic interaction in an infinite fiber-reinforced anisotropic plate containing a circular cavity with two relaxation times, Journal of Computational and Theoretical Nanoscience 11: 1-7.
[11] Othman M. I. A., Hasona W.M., Abd-Elaziz E.M., 2014, Effect of rotation on micropolar generalized thermoelasticity with two temperatures using a dual-phase-lag model, Canadian Journal of Physics 92: 149-158.
[12] Zenkour A. M., Abouelregal A. E., 2015, The fractional effects of a two-temperature generalized thermoelastic semi-infinite solid induced by pulsed laser heating, Archive of Mechanics 67: 53-73.
[13] Biot M. A., 1956, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics 27: 240-253.
[14] Lord H. W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal Mechanics Physics of Solid 15: 299-309.
[15] Green A. E., Lindsay K. A., 1972, Thermoelasticity, Journal of Elasticity 2: 1-7.
[16] Hetnarski R. B., Ignaczak J., 1994, Generalized thermoelasticity: response of semi-space to a short laser pulse, Journal of Thermal Stresses 17: 377-396.
[17] Green A. E., Naghdi P. M., 1991, A reexamination of the basic postulate of thermo-mechanics, Proceedings of the Royal Society of London A 432: 171-194.
[18] Green A. E., Naghdi P. M., 1992, On undamped heat waves in an elastic solid, Journal of Thermal Stresses 15: 253-264.
[19] Green A. E., Naghdi P. M., 1993, Thermoelasticity without energy dissipation, Journal of Elasticity 31: 189-208.
[20] Tzou D.Y., 1995, A unified approach for heat conduction from macro-to micro-scales, ASME Journal of Heat Transfer 117: 8-16.
[21] Chandrasekharaiah D.S., 1998, Hyperbolic thermoelasticity: a review of recent literature, Journal of Applied Mechanics Review 51: 705-729.
[22] Roy Choudhuri S., 2007, On a thermoelastic three-phase-lag model, Journal of Thermal Stresses 30: 231-238.
[23] Quintanilla R., Racke R., 2008, A note on stability in three-phase-lag heat conduction, International Journal of Heat and Mass Transfer 51: 24-29.
[24] Kar A., Kanoria M., 2009, Generalized thermo-visco-elastic problem of a spherical shell with three-phase-lag effect, Journal of Applied Mathematical Modelling 33: 3287-3298.
[25] Quintanilla R., 2009, Spatial behaviour of solutions of the three-phase-lag heat equation, Journal of Applied Mathematics and Computation 213: 153-162.
[26] Abbas I. A., 2014, Three-phase-lag model on thermoelastic interaction in an unbounded fiber-reinforced anisotropic medium with a cylindrical cavity, Journal of Computational and Theoretical Nanoscience 11: 987-992.
[27] Othman M. I. A., Said S.M., 2014, 2D problem of magneto-thermoelasticity fiber-reinforced medium under temperature dependent properties with three-phase-lag model, Journal of Meccanica 49: 1225-1241.
[28] Kumar A., Kumar R., 2015, A domain of influence theorem for thermoelasticity with three-phase-lag model, Journal of Thermal Stresses 38: 744-755.
[29] Noda N., 1986, Thermal Stresses in Materials with Temperature-Dependent Properties, North-Holland, Amsterdam.
[30] Jin Z. H., Batra R.C., 1998, Thermal fracture of ceramics with temperature-dependent properties, Journal of Thermal Stresses 21: 157-176.
[31] Othman M. I. A., 2002, Lord-Shulman theory under the dependence of the modulus of elasticity on the reference temperature in two dimensional generalized thermoelasticity, Journal of Thermal Stresses 25: 1027-1045.
[32] Othman M. I. A., Song Y., 2008, Reflection of magneto-thermoelastic waves with two relaxation times and temperature dependent elastic moduli, Journal of Applied Mathematical Modelling 32: 483-500.
[33] Othman M. I. A., Lotfy Kh., Farouk R. M., 2010, Generalized thermo-micro-stretch elastic medium with temperature dependent properties for different theories, Engineering Analysis Boundary Elements 34: 229-237.
[34] Othman M. I. A., Elmaklizi Y. D., Said S. M., 2013, Generalized thermoelastic medium with temperature dependent properties for different theories under the effect of gravity Field, International Journal of Thermophysics 34: 521-553.
[35] Wang Y. Z., Liu D., Wang Q., Zhou J. Z., 2015, Fractional order theory of thermoelasticity for elastic medium with variable material properties, Journal of Thermal Stresses 38: 665-676.
[36] Belfield A. J., Rogers T. G., Spencer A. J. M., 1983, Stress in elastic plates reinforced by fibers lying in concentric circles, Journal Mechanics Physics of Solid 31: 25-54.
[37] Montanaro A., 1999, On singular surface in isotropic linear thermoelasticity with initial Stress, The Journal of the Acoustical Society of America 106: 1586-1588.
