Abstract
The aim of the present work is to investigate the influence of magnetic field on wave propagation within a fiber-reinforced medium under the three-phase-lag theory and Green–Naghdi theory without energy dissipation. The modulus of the elasticity is given as a linear function of the reference temperature. The exact expression for the displacement components, temperature, and stress components are obtained by using normal mode analysis. Numerical results for the field quantities are given in the physical domain and illustrated graphically in the absence and presence of magnetic field. Comparisons are made between the results for the two different theories with and without temperature dependent properties as well as reinforcement. The results are a valuable contribution to the problem of practical design of such structures, for example to design stiffness, damping and so on into the right place of a structure by selecting the appropriate material properties.
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References
Lord HW, Shulman Y (1967) A generalized dynamic theory of thermoelasticity. J Mech Phys Solids 15:299–309
Green A, Lindsay K (1972) Thermoelasticity. J Elast 2:1–7
Hetnarski RB, Ignaczak J (1994) Generalized thermoelasticity: response of semi-space to a short laser pulse. J Therm Stress 17:377–396
Green A, Naghdi P (1991) A re-examination of the basic postulate of thermo-mechanics. Proc R Soc Lond 432:171–194
Green A, Naghdi P (1992) An unbounded heat wave in an elastic solid. J Therm Stress 15:253–264
Green A, Naghdi P (1993) Thermoelasticity without energy dissipation. J Elast 31:189–208
Othman MIA, Atwa SY, Farouk RM (2008) Generalized magneto-thermo-viscoelastic plane waves under the effect of rotation without energy dissipation. Int J Eng Sci 46:639–653
Othman MIA, Atwa SY, Farouk RM (2009) The effect of diffusion on two-dimensional problem of generalized thermoelasticity with Green–Naghdi theory. Int Commun Heat Mass Transf 36:857–864
Othman MIA, Atwa SY (2011) The effect of magnetic field on 2-D problem of generalized thermoelasticity without energy dissipation. Int J Ind Math 3:213–226
Othman MIA, Atwa SY (2012) Response of micropolar thermoelastic medium with voids due to various source under Green–Naghdi theory. Acta Mech Solida Sin 25:197–209
Othman MIA, Atwa SY (2012) Thermoelastic plane waves for an elastic solid half-space under hydrostatic initial stress of type III. Meccanica 47:1337–1347
Roychoudhuri S, Bandyopadhyay N (2004) Thermoelastic wave propagation in a rotating elastic medium without energy dissipation. Int J Math Math Sci 1:99–107
Chandrasekharaiah D (1996) Thermoelastic plane waves without energy dissipation. Mech Res Commun 23:549–555
Tzou D (1995) An unified field approach for heat conduction from macro to micro scales. ASME J Heat Transf 117:8–16
Chandrasekharaiah D (1998) Hyperbolic thermoelasticity. Appl Mech Rev 51:8–16
Roychoudhuri S (2007) On a thermoelastic three-phase-lag model. J Therm Stress 30:231–238
Lekhnitskii S (1980) Theory of elasticity of an anisotropic body. Mir publication, Moscow
Belfield AJ, Rogers TG, Spencer AJM (1983) Stress in elastic plates reinforced by fiber lying in concentric circles. J Mech Phys Solids 31:25–54
Othman MIA, Saied SM (2012) The effect of rotation on two-dimensional problem of a fibre-reinforced thermoelastic with one relaxation time. Int J Thermophys 33:160–171
Othman MIA, Lotfy Kh, Saied SM, Osman B (2012) Wave propagation of fiber-reinforced micropolar thermoelastic medium with voids under three theories. Int J Appl Math Mech 8:52–69
Othman MIA, Saied SM (2012) The effect of mechanical force on generalized thermoelasticity in a fiber-reinforced under three theories. Int J Thermophys 33:1082–1099
Othman MIA, Saied SM (2013) Two-dimensional problem of thermally conducting fiber-reinforced under Green–Naghdi theory. J Thermoelast 1:13–20
Othman MIA, Singh B (2007) The effect of rotation on generalized micropolar thermoelasticity for a half-space under five theories. Int J Solids Struct 44:2748–2762
Othman MIA (2001) Electrohydrodynamic stability in a horizontal viscoelastic fluid layer in the presence of a vertical temperature gradient. Int J Eng Sci 39:1217–1232
Othman MIA, Sweilam NH (2002) Electrohydrodynamic instability in a horizontal viscoelastic fluid layer in the presence of internal heat generation. Can J Phys 80:697–705
Othman MIA (2002) Lord–Shulman theory under the dependence of the modulus of elasticity on the reference temperature in two dimensional generalized thermoelasticity. J Therm Stress 25:1027–1045
Singh B (2006) Wave propagation in thermally conducting linear fibre-reinforced composite materials. Arch Appl Mech 75:513–520
Singh B, Singh SJ (2004) Reflection of planes waves at the free surface of a fibre-reinforced elastic half-space. Sãdhanã 29:249–257
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Othman, M.I.A., Said, S.M. 2D problem of magneto-thermoelasticity fiber-reinforced medium under temperature dependent properties with three-phase-lag model. Meccanica 49, 1225–1241 (2014). https://doi.org/10.1007/s11012-014-9879-z
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DOI: https://doi.org/10.1007/s11012-014-9879-z