Normal Mode Analysis of Generalized Magneto-Thermoelastic Medium with Initial Stress Under Green-Naghdi Theory

• Alzaerah. Ramadhan Mohammed Aldeeb

  Department of MatheDepartment of Mathematics, faculty of education Alzawia University, Libya matics, faculty of education Alzawia University, Libya

  Author

The normal mode analysis method was used to study the effect of both the initial stress and the magnetic field on a thermally elastic body. This method is used to obtain the exact expressions for the considered variables. Some particular cases are also discussed in the context of the problem. The generalized thermal elasticity equations were reviewed under the influence of the basic initial stress and the magnetic field using the theory (Green-Naghdi) of the second and third types (the second type with no energy dispersion and the third type with energy dispersion). The different physical quantities were illustrated in the presence and absence of both the initial stress and the magnetic field. The results of this research show the extent of difference between the second and third types of Green and Naghdi's theory. All results and figures were obtained using (MATLAB R2013a) program.

Abd-Alla, A., El-Naggar, A., & Fahmy, M. (2003). Magneto-thermoelastic problem in non-homogeneous isotropic cylinder. Heat and Mass transfer, 39(7), 625-629.

Abd-Elaziz, E. M., Marin, M., & Othman, M. I. (2019). On the effect of Thomson and initial stress in a thermo-porous elastic solid under GN electromagnetic theory. Symmetry, 11(3), 413.

Abo-Dahab, S., Abd-Alla, A., & Alqarni, A. (2017). A two-dimensional problem with rotation and magnetic field in the context of four thermoelastic theories. Results in physics, 7, 2742-2751.

Ailawalia, P., Khurana, G., & Kumar, S. (2009). Effect of rotation in a generalized thermoelastic medium with two temperature under the influence of gravity. International Journal of Applied Mathematics and Mechanics, 5(5), 99-116.

Ailawalia, P., & Narah, N. S. (2009). Effect of rotation in a generalized thermoelastic medium with hydrostatic initial stress subjected to ramp-type heating and loading. International Journal of Thermophysics, 30(6), 2078-2097.

Atwa, S. Y. (2014). Generalized magneto-thermoelasticity with two temperature and initial stress under Green–Naghdi theory. Applied Mathematical Modelling, 38(21-22), 5217-5230.

Bargmann, S., & Steinmann, P. (2006). Theoretical and computational aspects of non-classical thermoelasticity. Computer Methods in Applied Mechanics and Engineering, 196(1-3), 516-527.

Chandrasekharaiah, D. (1998). Hyperbolic thermoelasticity: a review of recent literature.

Choudhuri, S. R., & Debnath, L. (1985). Magneto-thermo-elastic plane waves in generalized thermoelasticity. J. Elasticity, 15(1), 59-68.

Green, A., & Naghdi, P. (1993). Thermoelasticity without energy dissipation. Journal of elasticity, 31(3), 189-208.

Green, A. E., & Lindsay, K. A. (1972). Thermoelasticity. Journal of elasticity, 2(1), 1-7.

Hetnarski, R. B., & Ignaczak, J. (1999). Generalized thermoelasticity. Journal of Thermal Stresses, 22(4-5), 451-476.

Lord, H. W., & Shulman, Y. (1967). A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, 15(5), 299-309.

Montanaro, A. (1999). On singular surfaces in isotropic linear thermoelasticity with initial stress. The Journal of the Acoustical Society of America, 106(3), 1586-1588.

Othman, M., & Edeeb, E. (2016). Effect of initial stress on generalized magneto-thermoelasticity medium with voids: a comparison of different theories. Int J Eng Math Comput Sci, 4(5), 15-26.

Othman, M., & Song, Y. (2006). The effect of rotation on the reflection of magneto-thermoelastic waves under thermoelasticity without energy dissipation. Acta Mechanica, 184(1), 189-204.

Othman, M. A., & Atwa, S. Y. (2011). The effect of magnetic field on 2-D problem of generalized thermoelasticity with energy dissipation. International Journal of Industrial Mathematics, 3(3), 213-226.

Othman, M. I., & Atwa, S. Y. (2012). Thermoelastic plane waves for an elastic solid half-space under hydrostatic initial stress of type III. Meccanica, 47(6), 1337-1347.

Othman, M. I., Atwa, S. Y., Jahangir, A., & Khan, A. (2013a). Effect of magnetic field and rotation on generalized thermo-microstretch. Elastic solid with mode-I crack under the Green Naghdi theory. Computational Mathematics and Modeling, 24(4), 566-591.

Othman, M. I., Atwa, S. Y., Jahangir, A., & Khan, A. (2013b). Generalized magneto‐thermo‐microstretch elastic solid under gravitational effect with energy dissipation. Multidiscipline Modeling in Materials and Structures.

Othman, M. I., & Kumar, R. (2009). Reflection of magneto-thermoelasticity waves with temperature dependent properties in generalized thermoelasticity. International Communications in Heat and Mass Transfer, 36(5), 513-520.

Othman, M. I., & Song, Y. (2007). Reflection of plane waves from an elastic solid half-space under hydrostatic initial stress without energy dissipation. International Journal of Solids and Structures, 44(17), 5651-5664.

Paria, G. (1966). Magneto-elasticity and magneto-thermo-elasticity. In Advances in Applied Mechanics (Vol. 10, pp. 73-112). Elsevier.

Sherief, H. H., & Helmy, K. A. (2002). A two-dimensional problem for a half-space in magneto-thermoelasticity with thermal relaxation. International Journal of Engineering Science, 40(5), 587-604.

Singh, B. (2008). Effect of hydrostatic initial stresses on waves in a thermoelastic solid half-space. Applied Mathematics and Computation, 198(2), 494-505.

Singh, B., Kumar, A., & Singh, J. (2006). Reflection of generalized thermoelastic waves from a solid half-space under hydrostatic initial stress. Applied Mathematics and Computation, 177(1), 170-177.

Tzou, D. Y. (1995). A unified field approach for heat conduction from macro-to micro-scales.

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