State Space Approach to Electro-Magneto-Thermoelasticity with Energy Dissipation

Subject Areas : Engineering

S Biswas ¹ , S. M Abo-Dahab ²

1 - Department of Mathematics, University of North Bengal, Darjeeling-734013, India
2 - Department of Computer Science, Faculty of Computers and Information, Luxor University, Egypt-- Department of Mathematics, Faculty of Science, South Valley University, Egypt

Received: 2020-08-08 Accepted : 2020-10-10 Published : 2020-12-01

Keywords: State space approach, Normal mode analysis, Energy Dissipation, Magnetic effect, Thermal Shock,

Abstract :

In this article a two-dimensional problem of generalized thermoelasticity has been formulated with state space approach. In this formulation, the governing equations are transformed into a matrix differential equation whose solution enables us to write the solution of any two-dimensional problem in terms of the boundary conditions. The resulting formulation is applied to an isotropic half space problem under Green-Naghdi type-III model i.e., with energy dissipation theory of thermoelasticity in the presence of a magnetic field. The bounding surface is traction free and subjected to a time dependent thermal shock. The solution for temperature distribution, displacements and stress components are obtained and presented graphically. The effect of magnetic field, electric field and phase velocity on the considered parameters is observed in the figures.

References:

[1] Biot M., 1956, Thermoelsticity and irreversible thermodynamics, Journal of Applied Physics 27: 240-253.
[2] Lord H., Shulman Y., 1967, A generalized dynamic theory of thermoelasticity, Journal of the Mechanics & Physics of Solids 15: 299-309.
[3] Green A.E., Lindsay K.A., 1972, Thermoelasticity, Journal of Elasticity 2: 1-7.
[4] Green A.E., Naghdi P.M., 1991, A re-examination of the basic properties of thermomechanics, Proceedings of Royal Society London Series A 432: 171-194.
[5] Green A.E., Naghdi P.M., 1992, On damped heat waves in an elastic solid, Journal of Thermal Stresses 15: 252-264.
[6] Green A.E., Naghdi P.M., 1993, Thermoelasticity without energy dissipation, Journal of Elasticity 31: 189-208.
[7] Chandrasekharaih D.S., 1998, Hyperbolic thermoelasticity: A review of recent literature, Applied Mechanics Reviews 51(12): 705-729.
[8] Bahar L.Y., Hetnarski R.B., 1978, State space approach to thermoelasticity, Journal of Thermal Stresses 1: 135-145.
[9] Anwar M., Sherief H., 1988, State space approach to generalized thermoelasticity, Journal of Thermal Stresses 11: 353-365.
[10] Ezzat M.A., Zakaria M., El‐Bary A.A., 2010, Thermo‐electric‐visco‐elastic material, Journal of Applied Polymer Science 117 (4): 1934-1944.
[11] Ezzat M.A., El Bary A.A., El Karamany A.S., 2009, Two-temperature theory in generalized magneto-thermo-viscoelasticity, Canadian Journal of Physics 87(4): 329-336.
[12] Ezzat M.A., El-Karamany A.S., El-Bary A.A., 2015, On thermo-viscoelasticity with variable thermal conductivity and fractional-order heat transfer, International Journal of Thermophysics 36(7): 1684-1697.
[13] Ezzat M.A., El-Bary A.A., 2016, Magneto-thermoelectric viscoelastic materials with memory-dependent derivative involving two-temperature, International Journal of Applied Electromagnetics and Mechanics 50: 549-567.
[14] Ezzat M.A., El-Bary A.A., 2017, Fractional magneto-thermoelastic materials with phase-lag Green-Naghdi theories, Steel and Composite Structures 24(3): 297-307.
[15] Ezzat M.A., El-Bary A.A., 2014, Two-temperature theory of magneto-thermo-viscoelasticity with fractional derivative and integral orders heat transfer, Journal of Electromagnetic Waves and Applications 28(16): 1985-2004.
[16] Ezzat M. A., El-Karamany A.S., El-Bary A.A., 2017, On dual-phase-lag thermoelasticity theory with memory-dependent derivative, Mechanics of Advanced Materials and Structures 24(11): 908-916.
[17] Ezzat M.A. , El-Karamany A.S., El-Bary A.A., 2018, Two-temperature theory in Green–Naghdi thermoelasticity with fractional phase-lag heat transfer, Microsystem Technologies 24(2): 951-961.
[18] El-Karamany A.S., Ezzat M.A., 2004, Thermal shock problem in generalized thermoelasticity under four theories, International Journal of Engineering Science 42: 649-671.
[19] Sherief H.H., El-Maghraby N.M., Allam A.A., 2013, Stochastic thermal shock in generalized thermoelasticity, Applied Mathematical Modelling 37: 762-775.
[20] Ezzat, M. A. and H. M. Youssef. 2010. Three dimensional thermal shock problem of generalized thermoelastic half-space, Applied Mathematical Modelling 34: 3608-3622.
[21] Wang Y.Z., Liu D., Wang Q., Zhou J. Z., 2016, Thermoelastic behavior of elastic media with temperature-dependent properties under thermal shock, Journal of Thermal Stresses 39(4): 460-473.
[22] Baksi A., Bera R.K., Debnath L., 2005, A study of magneto-thermoelastic problems with thermal relaxation and heat sources in a three dimensional infinite rotating elastic medium, International Journal of Engineering Science 43(19-20): 1419-1434.
[23] Said S.M., 2016, Influence of gravity on generalized magneto-thermoelastic medium for three-phase -lag model, Journal of Computational and Applied Mathematics 291: 142-157.
[24] Kalkal K.K., Deswal S., 2014, Effects of phase lags on three dimensional wave propagation with temperature dependent properties, International Journal of Thermophysic 35(5): 952-969.
[25] Youssef H.M., El-Bary A.A., Elsibai K.A., 2014, Vibration of gold nano beam in context of two-temperature generalized thermoelasticity subjected to laser pulse, Latin American Journal of Solids and Structures 11(13): 2460-2482.
[26] Pramanik A.S., Biswas S., 2020, Surface waves in nonlocal thermoelastic medium with state space approach, Journal of Thermal Stresses 43(6): 667-686.