Effects of phase-lags in a thermoviscoelastic orthotropic continuum with a cylindrical hole and variable thermal conductivity

• Autorzy: Zenkour A. M. , Abouelregal A. E.
• Języki publikacji: EN

Abstrakty

EN

This article presents an analytical solution for the effect of phase-lags on a generalized plane strain thermoviscoelastic orthotropic medium with a cylindrical cavity subjected to a thermal shock from varying heat. It is assumed that the cylindrical cavity is made of Kelvin–Vogt type material. The general solutions for field quantities are obtained using the method of Laplace transforms. The results are graphically presented to illustrate the effect of phase-lags, viscoelasticity and variability of thermal conductivity on the studied fields. Comparisons are also presented with those in the absence of viscosity and variability of thermal conductivity.

Słowa kluczowe

EN

thermoviscelasticity; orthotropic medium; cylindrical hole; variable thermal conductivity; dual-phase-lags

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2015
• Tom: Vol. 67, nr 6
• Strony: 457--475
• Opis fizyczny: Bibliogr. 36 poz.

Twórcy

autor

Zenkour A. M.

• Faculty of Science, Department of Mathematics King Abdulaziz University P.O. Box 80203, Jeddah 21589, Saudi Arabia
• Faculty of Science, Department of Mathematics Kafrelsheikh University Kafr El-Sheikh 33516, Egypt

autor

Abouelregal A. E.

• Faculty of Science, Department of Mathematics Mansoura University Mansoura 35516, Egypt
• College of Science and Arts Department of Mathematics Aljouf University, Al-Qurayat, Saudi Arabia

Bibliografia

• 1. M.A. Biot, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics, 27, 240–253, 1956.
• 2. H.W. Lord, Y. Shulman, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids, 15, 299–307, 1967.
• 3. A.E. Green, K.A. Lindsay, Thermoelasticity, Journal of Elasticity, 2, 1–7, 1972.
• 4. D.S. Chandarasekharaia, Hyperbolic thermoelasticity: a review of recent literature, Applied Mechanics Reviews, 51, 705–729, 1998.
• 5. M. Aouadi, Generalized thermoelastic-piezoelectric problem by hybrid Laplace transform-finite element method, International Journal for Computational Methods in Engineering Science and Mechanics, 8, 137–147, 2007.
• 6. R.B. Hetnarski, M.R. Eslami, Thermal Stresses–Advanced Theory and Applications, Springer Science & Business Media, 158, 2009.
• 7. A.M. Zenkour, Three-dimensional thermal shock plate problem within the framework of different thermoelasticity theories, Composite Structures, 132, 1029–1042, 2015.
• 8. D.Y. Tzou, A unified approach for heat conduction from macro- to micro-scales, Journal of Heat Transfer, 117, 8–16, 1995.
• 9. D.Y. Tzou, Macro- to Microscale Heat Transfer: the Lagging Behavior, Series in Chemical and Mechanical Engineering, Taylor & Francis, Washington, DC, 1997.
• 10. D.Y. Tzou, Experimental support for the Lagging behavior in heat propagation, Journal of Thermophysics Heat Transfer, 9, 686–693, 1995.
• 11. S.K. Roychoudhuri, One-dimensional thermoelastic waves in elastic half-space with dual-phase-lag effects, Journal of Mechanics of Materials and Structures, 2, 489–503, 2007.
• 12. S.K. Roychoudhuri, On a thermoelastic three-phase-lag model, Journal of Thermal Stresses, 30, 231–238, 2007.
• 13. A.H. Akbarzadeh, D. Pasini, Phase-lag heat conduction in multilayered cellular media with imperfect bonds, International Journal of Heat and Mass Transfer, 75, 656–667, 2014.
• 14. R. Lakes, Viscoelastic Materials, Cambridge University Press, UK, 2009.
• 15. R. Quintanilla, Existence and exponential decay in the linear theory of viscoelastic mixtures, European Journal of Mechanics A/Solids, 24, 311–324, 2005.
• 16. D. Iesan, L. Nappa, On the theory of viscoelastic mixtures and stability, Mathematics and Mechanics of Solids, 13, 55–80, 2008.
• 17. M.M. Svanadze, Potential method in the linear theories of viscoelasticity and thermo-viscoelasticity for Kelvin–Voigt materials, Technische Mechanik, 32, 554–563, 2012.
• 18. A.A. Ilioushin, B.E. Pobedria, Fundamentals of the Mathematical Theory of Thermal Viscoelasticity, Nauka, Moscow, 1970.
• 19. R.I. Tanner, Engineering Rheology, Oxford University Press, Oxford, 1988.
• 20. R. Huilgol, N. Phan-Thien, Fluid Mechanics of Viscoelasticity, Elsevier, Amsterdam, 1997.
• 21. A.D. Kovalenko, V.G. Karanaukhov, A linearized theory of thermoviscoelasticity, Polymer Mechanics, 8, 194–199, 1972.
• 22. A.D. Drozdov, A constitutive model in finite thermoviscoelasticity based on the concept of transient networks, Acta Mechanica, 133, 13–37, 1999.
• 23. M.R. Kundu, B. Mukhopadhyay, A thermoviscoelastic problem of an infinite medium with a spherical cavity using generalized theory of thermoelasticity, Mathematical and Computer Modelling, 41, 25–32, 2005.
• 24. A. Baksi, B.K. Roy, R.K. Bera, Eigenvalue approach to study the effect of rotation and relaxation time in generalized magneto-thermo-viscoelastic medium in one dimension, Mathematical and Computer Modelling, 44, 1069–1079, 2006.
• 25. M. Kanoria, S.H. Mallik, Generalized thermoviscoelastic interaction due to periodically varying heat source with three-phase-lag effect, European Journal of Mechanics A/Solids, 29, 695–703, 2010.
• 26. M.A. Ezzat, A.S. El-Karamany, A.A. El-Bary, M.A. Fayik, Fractional calculus in one-dimensional isotropic thermo-viscoelasticity, Comptes Rendus Mecanique, 341, 553–566, 2013.
• 27. A. Kar, M. Kanoaria, Generalized thermo-visco-elastic problem of a spherical shell with three-phase-lag effect, Applied Mathematical Modelling, 33, 3287–3298, 2009.
• 28. S. Deswal, K.K. Kalkal, Three-dimensional half-space problem within the framework of two-temperature thermo-viscoelasticity with three-phase-lag effects, Applied Mathematical Modelling, In press, 2015.
• 29. A.E. Abouelregal, Generalized thermoelasticity for an isotropic solid sphere indualphase-lag of heat transfer with surface heat flux, International Journal for Computational Methods in Engineering Science and Mechanics, 12, 96–105, 2011.
• 30. A.M. Zenkour, D.S. Mashat, A.E. Abouelregal, The effect of dual-phase-lag model on reflection of thermoelastic waves in a solid half space with variable material properties, Acta Mechanica Solida Sinica, 26, 659–670, 2013.
• 31. I.A. Abbas, A.M. Zenkour, Dual-phase-lag model on thermoelastic interactions in a semi-infinite medium subjected to a ramp-type heating, Journal of Computational and Theoretical Nanoscience, 11, 642–645, 2014.
• 32. A.E. Abouelregal, A.M. Zenkour, Effect of phase lags on thermoelastic functionally graded microbeams subjected to ramp-type heating, IJST, Transactions of Mechanical Engineering, 38, 321–335, 2014.
• 33. A.C. Eringen, Mechanics of Continua, Wiley, New York, 1967.
• 34. N. Noda, Thermal stresses in materials with temperature-dependent properties, Thermal Stresses I, R.B. Hetnarski (Editor), North-Holland, Amsterdam, 1986.
• 35. G. Honig, U. Hirdes, A method for the numerical inversion of Laplace transform, Journal of Computational and Applied Mathematics, 10, 113–132, 1984.
• 36. J.C. Misra, N.C. Chattopadhyay, S.C. Samanta, Study of the thermoelastic interactions in an elastic half space subjected to a ramp-type heating—a state-space approach, International Journal of Engineering Sciences, 34, 579–596, 1996.