119
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Fractional thermo-viscoelasticity theory with and without energy dissipation

Pages 1903-1922 | Received 26 Aug 2020, Accepted 19 Oct 2020, Published online: 05 Nov 2020

References

  • Pobedrya B. Coupled problems in thermoviscoelasticity. Mech Compos Mat. 1969;5:353–358.
  • Kartashov E. Dynamic thermoviscoelasticity in a thermal shock problem. Therm Eng. 2012;59:1051–1061.
  • Ezzat MA, Zakaria M, Shaker O, et al. State space formulation to viscoelastic fluid flow of magnetohydrodynamic free convection through a porous medium. Acta Mech. 1996;119:147–164.
  • Ezzat MA, Abd-Elaal MZ. Free convection effects on a viscoelastic boundary layer flow with one relaxation time through a porous medium. J Frank Inst. 1997;334:685–706.
  • Ezzat MA. Free convection effects on perfectly conducting fluid. Int J Eng Sci. 2001;39:799–819.
  • Ezzat MA, Youssef HM. Stokes' first problem for an electro-conducting micropolar fluid with thermoelectric properties. Can J Phys. 2010;88:35–48.
  • Palani G, Abbas IA. Free convection MHD flow with thermal radiation from an impulsively started vertical plate. Nonlinear Analys Model Control. 2009;14:73–84.
  • Belbachir N, et al. Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory. Smart Struct Sys. 2020;4:409–422.
  • Al-Furjan MSH, et al. A comprehensive computational approach for nonlinear thermal instability of the electrically FG-GPLRC disk based on GDQ method. Eng Compu. 2020. https://doi.org/https://doi.org/10.1007/s00366-020-01088-7
  • Matouk H, et al. Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory. Adv Nano Res. 2020;8:293–305.
  • Biot M. Thermoelasticity and irreversible thermodynamics. J Appl Phys. 1956;27:240–253.
  • Lord HW, Shulman YA. Generalized dynamical theory of thermo- elasticity. J Mech Phys Solids. 1967;15:299–309.
  • Ignaczak J, Ostoja-Starzewski M. Thermoelasticity with finite wave speeds. New York: Oxford University Press; 2009.
  • Wojnar R. Uniqueness of displacement-heat flux and stress-temperature problems in thermoelasticity with one relaxation time. J Therm Stress. 1985;8:351–364.
  • Sherief HS, Ezzat MA. Solution of the generalized problem of thermoelasticity in the form of series of functions. J Therm Stress. 1994;17:75–95.
  • Ezzat MA, Othman MI, El-Karamany AS. State space approach to generalized thermo-viscoelasticity with two relaxation times. Int J Eng Sci. 2001;40:283–302.
  • Marin M, Agarwal RP, Mahmoud SR. Nonsimple material problems addressed by the Lagrange’s identity. Bound Value Probl. 2013;135:1–14.
  • Lata P, Kaur I. Thermomechanical interactions in transversely isotropic magneto thermoelastic solid with two temperatures and without energy dissipation. Steel Compos Struct An Int J. 2019;32:779–793.
  • Othman MIA, Fekry M, Marin M. Plane waves in generalized magneto-thermo-viscoelastic medium with voids under the effect of initial stress and laser pulse heating. Struct Eng Mech. 2020;29:4788–4806.
  • Abbas IA. Natural frequencies of a poroelastic hollow cylinder. Acta Mech. 2006;186:229–237.
  • Abbas IA. Eigenvalue approach in a three-dimensional generalized thermoelastic interactions with temperature-dependent material properties. Comp Math Applic. 2014;68:2036–2056.
  • Abbas IA, Abd-Alla NA, Othman MI. Generalized magneto-thermoelasticity in a fiber-reinforced anisotropic half space. Int J Thermophys. 2011;32:1071–1085.
  • Hobiny A, Abbas IA. Analytical solutions of photo-thermo-elastic waves in a non-homogenous semiconducting material. Res. Phys. 2018;10:385–390.
  • Boussoula A, et al. A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates. Smart Struct Sys. 2020;25:197–218.
  • Refrafi S, et al. Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations. Compu Concre. 2020;25:311–325.
  • Tounsi A, et al. A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation. Steel Comps Struct. 2020;34:511–524.
  • Belbachir N, et al. Bending analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings. Steel Comps Struct. 2019;33:81–92.
  • Zarga D, et al. Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory. Steel Comps Struct. 2019;32:389–410.
  • Al-Furjan MSH, et al. Chaotic simulation of the multi-phase reinforced thermo-elastic disk using GDQM. Eng Compu. 2020. https://doi.org/https://doi.org/10.1007/s00366-020-01144-2
  • Ezzat MA, Abd-Elaal MZ. State space approach to viscoelastic fluid flow of hydromagnetic fluctuating boundary-layer through a porous medium. ZAMM. 1997;77:197–207.
  • Abd-Alla NA, Abbas IA. A problem of generalized magnetothermoelasticity for an infinitely long, perfectly conducting cylinder. J Therm Stress. 2002;25:1009–1025.
  • Abbas IA, Marin M. Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating. Phys E: Low-dim Sys Nanostruct. 2017;87:254–260.
  • Green AE, Naghdi PM. Thermoelasticity without energy dissipation. J Elast. 1993;31:189–208.
  • Chandrasekharaiah D. One-dimensional wave propagation in the linear theory of thermoelasticity without energy dissipation. J Therm Stress. 1996;19:695–710.
  • Chiriă S, Ciarletta M. Reciprocal and variational principles in linear thermoelasticity without energy dissipation. Mech Res Commu. 2010;37:271–275.
  • Ciarletta M. A theory of micropolar thermoelasticity without energy dissipation. J Therm Stress. 1999;22:581–594.
  • Ezzat MA, Zakaria M, El-Bary AA. Generalized thermoelasticity with temperature dependent modulus of elasticity under three theories. J Appl Math Compu. 2004;14:193–212.
  • Choudhuri R, K S. On a thermoelastic three-phase-lag model. J Therm Stress. 2007;30:231–238.
  • Shereif HH, Raslan WE. Thermoelastic interactions without energy dissipation in an unbounded body with a cylindrical cavity. J Therm Stress. 2016;39:326–332.
  • Lata P, Zakhami H. Fractional order generalized thermoelastic study in orthotropic medium of type GN-III. Geomech Eng. 2019;19:295–305.
  • El-Attar SI, Hendy MH, Ezzat MA. On phase-lag Green–naghdi theory without energy dissipation for electro-thermoelasticity including heat sources. Mech Based Des Struct Mach. 2019;47:769–786.
  • Hendy MH, El-Attar SI, Ezzat MA. Two-temperature fractional Green–naghdi of type III in magneto-thermo-viscoelasticity theory subjected to a moving heat source. Ind J Phys. 2020. doi: https://doi.org/10.1007/s12648-020-01719-1.
  • Gorenflo R, Mainardi F. Fractional calculus: integral and differential equations of fractional orders. Wien: Fract. Frac. Calcu. Cont. Mech, Springer; 1997.
  • Podlubny I. Fractional differential Equations. New York: Academic Press; 1999.
  • Sherief H, El-Sayed AMA, Abd El-Latief AM. Fractional order theory of thermoelasticity. Int J Solids Struct. 2010;47:269–275.
  • Ezzat MA. Thermoelectric MHD with modified Fourier’s law. Int J Therm Sci. 2011;50:449–455.
  • Youssef HM. Theory of fractional order generalized thermoelasticity. J Heat Trans. 2010;132:1–7.
  • Ezzat MA, Alsowayan NS, Al-Muhiameed ZIA, et al. Fractional modelling of Pennes' bioheat transfer equation. Heat Mass Trans. 2014;50:907–914.
  • Yang X-J, Gao F, Ju Y. General fractional derivatives with applications in viscoelasticity. New York: Academic Press; 2020.
  • Hendy MH, Amin MM, Ezzat MA. Two-dimensional problem for thermoviscoelastic materials with fractional order heat transfer. J Therm Stress. 2019;42:1298–1315.
  • Ezzat MA. Fractional thermo-viscoelastic response of biological tissue with variable thermal material properties. J Therm Stress. 2020;43:1120–1137.
  • Cattaneo C. Sur une forme de l’équation de la Chaleur éliminant le paradoxe d’une propagation instantaneée. C R L'Académie Sciences Paris. 1958;247:431–433.
  • Kimmich R. Strange kinetics, porous media, and NMR. Chem Phys. 2002;284:1–2.
  • Mainardi F, Gorenflo R. On Mittag-Lettler-type function in fractional evolution processes. J Comput Appl Math. 2002;118:283–299.
  • Weeks ER, Weitz DA. Subdiffusion and the cage effect studied near the colloid glass transition. Chem Phys. 2002;284:361–367.
  • Li X, Xue Z, Tian X. A modified fractional order generalized bio-thermoelastic theory with temperature-dependent thermal material properties. Int J Therm Sci. 2018;132:249–256.
  • Ghazizadeh HR, Azimi A, Maerefat M. An inverse problem to estimate relaxation parameter and order of fractionality in fractional single-phase-lag heat equation. Int J Heat Mass Trans. 2012;55:2095–2101.
  • Ezzat MA, El-Bary AA, Al-Sowayan NS. Tissue responses to fractional transient heating with sinusoidal heat flux condition on skin surface. Anim Sci J. 2016;87:1304–1311.
  • Ezzat MA, El-Bary AA. Fractional magneto-thermoelastic materials with phase-lag Green-Naghdi theories. Steel Compos Struct. 2017;24:297–307.
  • Ezzat MA. The relaxation effects of the volume properties of electrically conducting viscoelastic material. Mat Sci Eng B. 2006;130:11–23.
  • Honig G, Hirdes U. A method for the numerical inversion of the Laplace transform. J Comp Appl Math. 1984;10:113–132.
  • Tzou D. Macro-to-Micro heat transfer. Washington (DC): Taylor & Francis; 1996.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.