Abstract
A general model of equations of the three-phase-lag model and thermoelasticity without energy dissipation theory was used to study the effect of the gravity field on a fiber-reinforced thermoelastic half-space. The material is a homogeneous isotropic elastic half-space. Normal mode analysis was used to get the exact expressions for the displacement components, force stresses and temperature. The variations of the considered variables with the horizontal distance were illustrated graphically. Comparisons were made with the results of the two theories in the absence and presence of the gravity field as well as the reinforcement. A comparison was also made between the results of the two theories with and without temperature-dependent properties.
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References
Abbas IA (2012) Generalized magneto–thermoelastic interaction in a fiber-reinforced anisotropic hollow cylinder. Int J Thermophys 33(3):567–579
Abbas IA (2014a) Fractional order GN model on thermoelastic interaction in an infinite fibre-reinforced anisotropic plate containing a circular hole. J Comput Theor Nanosci 11(2):380–384
Abbas IA (2014b) Nonlinear transient thermal stress analysis of thick-walled FGM cylinder with temperature-dependent material properties. Meccanica 49(7):1697–1708
Abbas IA (2014c) A problem on functional graded material under fractional order theory of thermo-elasticity. Theoret Appl Fract Mech 74:18–22
Abbas IA (2014d) A GN model based upon two-temperature generalized thermoelastic theory in an unbounded medium with a spherical cavity. Appl Math Comput 245:108–115
Abbas IA (2014e) Three-phase-lag model on thermoelastic interaction in an unbounded fiber- reinforced anisotropic medium with a cylindrical cavity. J Comput Theor Nanosci 11(4):987–992
Abbas IA (2015) A dual phase lag model on thermoelastic interaction in an infinite fiber-reinforced anisotropic medium with a circular hole. Mech Based Des Struct Mach Int J 43(4):510–513
Abd-Alla AM, Mahmoud SR, Abo-Dahab SM, Helmy MI (2010) Influences of rotation, magnetic field, initial stress, and gravity on Rayleigh waves in a homogeneous orthotropic elastic half-space. Appl Math Sci 4(2):91–108
Abd-Alla AM, Abo-Dahab SM, Hammed HAH (2011) Propagation of Rayleigh waves in generalized magneto-thermoelastic orthotropic material under initial stress and gravity field. Appl Math Model 35(6):2981–3000
Belfield AJ, Rogers TG, Spencer AJM (1983) Stress in elastic plates reinforced by fibre lying in concentric circles. J Mech Phys Solids 31(1):25–54
Biot MA (1956) Thermoelasticity and irreversible thermodynamics. J Appl Phys 27(3):240–253
Bromwich TJJA (1898) On the influence of gravity on elastic waves and in particular on the vibrations of an elastic globe. Proc Lond Math Soc 30(1):98–120
Choudhuri SR (2007) On a thermoplastic three-phase-lag model. J Therm Stresses 30:231–238
Green AE, Naghdi PM (1991) A re-examination of the basic postulate of thermo-mechanics. Proc R Soc A Math Phys Eng Sci A 432(1885):171–194
Green AE, Naghdi PM (1992) On undamped heat waves in an elastic solid. J Therm Stresses 15(2):253–264
Green AE, Naghdi PM (1993) Thermoelasticity without energy dissipation. J Elast 31(3):189–208
Hetnarski RB, Ignaczak J (1999) Generalized thermoelasticity. J Therm Stresses 22(4–5):451–476
Hetnarski RB, Ignaczak J (2000) Nonclassical dynamical thermoelasticity. Int J Solids Struct 37(1):215–224
Jin ZH, Batra RC (1998) Thermal fracture of ceramics with temperature-dependent properties. J Therm Stresses 21(2):157–176
Kar A, Kanoria M (2009) Generalized thermo-visco-elastic problem of a spherical shell with three-phase-lag effect. Appl Math Model 33(8):3287–3298
Kumar A, Kumar R (2015) A domain of influence theorem for thermoelasticity with three- phase-lag model. J Therm Stresses 38(7):744–755
Kumar R, Chawla V, Abbas IA (2012) Effect of viscosity on wave propagation in anisotropic thermoelastic medium with three-phase-lag model. J Theor Appl Mech 39(4):313–341
Love AEH (1911) Some problems of geodynamics. Cambridge University Press, Cambridge
Noda N (1986) Thermal stresses in materials with temperature-dependent properties. In: Hetnaraski RB (ed) Thermal stresses I. North-Holland, Amsterdam
Othman MIA (2001) Lord-Shulman theory under the dependence of the modulus of elasticity on the reference temperature in two dimensional generalized thermoelasticity. J Therm Stresses 25(11):1027–1045
Othman MIA (2011) State-space approach to the generalized thermoelastic problem with temperature dependent elastic moduli and internal heat sources. J Appl Mech Tech Phys 52(4):644–656
Othman MIA, Said SM (2012) The effect of rotation on two-dimensional problem of a fibre-reinforced thermoelastic with one relaxation time. Int J Thermophys 33(1):160–171
Othman MIA, Said SM (2013) Plane waves of a fiber-reinforcement magneto-thermo- elastic comparison of three different theories. Int J Thermophys 34(2):366–383
Othman MIA, Said SM (2015) The effect of rotation on a fiber-reinforced medium under generalized magneto-thermoelasticity with internal heat source. Mech Adv Mater Struct 22(3):168–183
Othman MIA, Elmaklizi YD, Said SM (2013) Generalized thermoelastic medium with temperature dependent properties for different theories under the effect of gravity field. Int J Thermophys 34(3):521–537
Othman MIA, Atwa SY, Jahangir A, Khan A (2015) The effect of gravity on plane waves in a rotating thermo-microstretch elastic solid for a mode-I crack with energy dissipation. Mech Adv Mater Struct 22(11):945–955
Quintanilla R, Racke R (2008) A note on stability in three-phase-lag heat conduction. Int J Heat Mass Transf 51(1–2):24–29
Sengupta PR, Nath S (2001) Surface waves in fibre-reinforced anisotropic elastic media. Sãdhanã 26(4):363–370
Tzou DY (1995) A unified field approach for heat conduction from macro-to micro-scales. ASME J Heat Transf 117(1):8–16
Wang YZ, Liu D, Wang Q, Zhou JZ (2015) Fractional order theory of thermoelasticity for elastic medium with variable material properties. J Therm Stresses 38(6):665–676
Zenkour AM, Abbas IA (2014a) Thermal shock problem for a fiber-reinforced anisotropic half-space placed in a magnetic field via GN model. Appl Math Comput 246:482–490
Zenkour AM, Abbas IA (2014b) Nonlinear transient thermal stress analysis of temperature-dependent hollow cylinders using a finite element model. Int J Struct Stab Dyn 14(7):1450025
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Said, S.M., othman, M.I.A. Gravitational Effect on a Fiber-Reinforced Thermoelastic Medium with Temperature-Dependent Properties for Two Different Theories. Iran J Sci Technol Trans Mech Eng 40, 223–232 (2016). https://doi.org/10.1007/s40997-016-0014-8
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DOI: https://doi.org/10.1007/s40997-016-0014-8