Non-simple magnetothermoelastic solid cylinder with variable thermal conductivity due to harmonically varying heat

- Journal title : Earthquakes and Structures
- Volume 10, Issue 3, 2016, pp.681-697
- Publisher : Techno-Press
- DOI : 10.12989/eas.2016.10.3.681

Title & Authors

Non-simple magnetothermoelastic solid cylinder with variable thermal conductivity due to harmonically varying heat

Zenkour, Ashraf M.; Abouelregal, Ahmed E.;

Zenkour, Ashraf M.; Abouelregal, Ahmed E.;

Abstract

The model of two-temperature magneto-thermoelasticity for a non-simple variable-thermal-conductivity infinitely-long solid cylinder is established. The present cylinder is made of an isotropic homogeneous thermoelastic material and its bounding plane is traction-free and subjected to a time-dependent temperature. An exact solution is firstly obtained in Laplace transform space to obtain the displacement, incremental temperature, and thermal stresses. The inversion of Laplace transforms has been carried out numerically since the response is of more interest in the transient state. A detailed analysis of the effects of phase-lags, an angular frequency of thermal vibration and the variability of thermal conductivity parameter on the field quantities is presented.

Keywords

thermoelasticity;phase-lags;non-simple;solid cylinder;variable thermal conductivity;

Language

English

Cited by

References

1.

Abbas, I.A. and Zenkour, A.M. (2013), "LS model on electro-magneto-thermo-elastic response of an infinite functionally graded cylinder", Compos. Struct., 96, 89-96.

2.

Biot, M. (1956), "Thermoelasticity and irreversible thermo-dynamics", J. Appl. Phys., 27(3), 240-253.

3.

Carroll, M.M. (1969), "Plane waves in non-simple elastic solids", Int. J. Solid. Struct., 5(2), 109-116.

4.

Chen, P.J., Gurtin, M.E. and Willams, W.O. (1969), "On the thermodynamics of non-simple Elastic material with two temperatures", Zeitschrift fur Angew Mathematik und Physik, 20(1), 107-112.

5.

Chen, P.J. and Gurtin, M.E. (1968), "On a theory of heat conduction involving two temperatures", Zeitschrift fur Angew Mathematik und Physik, 19(4), 614-627.

6.

Ciarletta, M. (1996), "Thermoelasticity of nonsimple materials with thermal relaxation", J. Therm. Stress., 19(8), 731-748.

7.

Das, P. and Kanoria, M. (2012), "Two-temperature magneto-thermo-elasticity response in a perfectly conducting medium based on GN III model", Int. J. Pure Appl. Math., 81(2), 199-229.

8.

Dhar, A.K. (1985), "Mechanical shock problem of coupled thermoelasticity in a non-simple elastic material", Indian J. pure appl. Math., 16(2), 174-178.

10.

Green, A.E. and Rivlin, R.S. (1964), "Simple force and stress multipoles", Arch Ration. Mech. Anal., 16(5), 325-353.

11.

Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of Laplace transform", J. Comp. Appl. Math., 10(1), 113-132.

12.

13.

Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solid., 15(5), 299-309.

14.

Lotfy, Kh. (2014), "Two temperature generalized magneto-thermoelastic interactions in an elastic medium under three theories", Appl. Math. Comput., 227, 871-888.

15.

Nowinski, J.L. (1978), Theory of Thermoelasticity with Applications, Sijthoff & Noordhoff Int., Publishing Comp., Netherlands.

16.

Prasad, R., Kumar, R. and Mukhopadhyay, S. (2010), "Propagation of harmonic plane waves under thermoelasticity with dual-phase-lags", Int. J. Eng. Sci., 48(12), 2028-2043.

17.

Quintanilla, R. (2004), "On existence, structural stability, convergence and spatial behavior in thermoelastic with two temperature", Acta Mech., 168(1-2), 161-173.

18.

Tzou, D. (1995), "A unified field approach for heat conduction from macro-to micro-scales", J. Heat Transfer, 117(1), 8-16.

19.

Warren, W.E. and Chen, P.J. (1973), "Wave propagation in the two temperature theory of thermoelasticity", Acta Mech., 16(1-2), 21-23.

20.

Wozniak, C. (1967), "Thermoelasticity of non-simple orinted materials", Int. J. Eng. Sci., 5(8), 605-612.

21.

Quintanilla, R. (2003), "Thermoelasticity without energy dissipation of nonsimple materials", ZAMM-J. Appl. Math. Mech./Zeitschrift fur Angewandte Mathematik und Mechanik, 83(3), 172-180.

22.

Zenkour, A.M. and Abbas, I.A. (2014), "Magneto-thermoelastic response of an infinite functionally graded cylinder using the finite element method", J. Vib. Control, 20, 1907-1919.

23.

Zenkour, A.M. and Abbas I.A. (2015), "Electro-magneto-thermo-elastic response of infinite functionally graded cylinders without energy dissipation", J. Magnet. Magnet. Mater., 395, 123-129.

24.

Zenkour, A.M. and Abouelregal, A.E. (2014a), "Nonlocal thermoelastic vibrations for variable thermal conductivity nanobeams due to harmonically varying heat", J. Vib., 16(8), 3665-3678.

25.

Zenkour, A.M. and Abouelregal, A.E. (2014b), "The effect of two temperatures on a FG nanobeam induced by a sinusoidal pulse heating", Struct. Eng. Mech., 51(2), 199-214.