Response of GN Type II and Type III Theories on Reflection and Transmission Coefficients at the Boundary Surface of Micropolar Thermoelastic Media with Two Temperatures

Document Type : Research Paper


1 Department of Mathematics, Kurukshetra University, Kurukshetra

2 Department of Applied Sciences, Guru Nanak Dev Engineering College, Ludhiana

3 Department of Applied Sciences, Gurukul Vidyapeeth Institute of Engineering and Technology, Sector-7, Banur, District Patiala


In the present article, the reflection and transmission of plane waves at the boundary of thermally conducting micropolar elastic media with two temperatures is studied. The theory of thermoelasticity with and without energy dissipation is used to investigate the problem. The expressions for amplitudes ratios of reflected and transmitted waves at different angles of incident wave are obtained. Dissipation of energy and two temperature effects on these amplitude ratios with angle of incidence are depicted graphically. Some special and particular cases are also deduced.


[1] Eringen A.C., 1966, Linear theory of micropolar elasticity, Journal of Applied Mathematics and Mechanics 15:909-923.
[2] Eringen A.C., 1970, Foundations of Micropolar Thermoelasticity, International Centre for Mechanical Science, Springer-Verlag, Berlin.
[3] Nowacki W., 1986, Theory of Asymmetric Elasticity, Oxford, Pergamon.
[4] Dost S., Taborrok B., 1978, Generalized micropolar thermoelasticity, International Journal of Engineering Science 16:173-178.
[5] Chandrasekharaiah D.S., 1986, Heat flux dependent micropolar thermoelasticity, International Journal of Engineering Science 24:1389-1395.
[6] Boschi E., Iesan D., 1973, A generalized theory of linear micropolar thermoelasticity, Meccanica 7:154-157.
[7] Boley B. A., Tolins I. S., 1962, Transient coupled thermoelastic boundary value problems in the half-space, Journal of Applied Mechanics 29: 637-646.
[8] Chen P.J., Gurtin M.E., Williams W.O., 1968, A note on non simple heat conduction, Zeitschrift für Angewandte Mathematik und Physik 19:960-970.
[9] Chen P.J., Gurtin M.E., Williams W.O., 1969, On the thermoelastic material with two temperatures, Zeitschrift für Angewandte Mathematik und Physik 20:107-112.
[10] Boley M., 1956, Thermoelastic and irreversible thermodynamics, Journal of Applied Physics 27:240-253.
[11] Warren W.E., Chen P.J., 1973,Wave propagation in the two temperature theory of thermoelasticity, Acta Mechanica 16:21-23.
[12] Youssef H.M., 2006, Theory of two temperature generalized thermoelasticity, Journal of Applied Mathematics 71:383-390.
[13] Kumar R., Mukhopadhyay S., 2010 , Effect of thermal relaxation time on plane wave propagation under two temperature thermoelasticity, International Journal of Engineering Science 48:128-139.
[14] Kaushal S., Sharma N., Kumar R., 2010, Propagation of waves in generalized thermoelastic continua with two temperature, International Journal of Applied Mechanics and Engineering 15:1111-1127.
[15] Ezzat M.A., Awad E.S., 2010, Constitutive relations, uniqueness of solution and thermal shock application in the linear theory of micropolar generalized thermoelasticity involving two temperatures, Journal of Thermal Stresses 33:226-250.
[16] Kaushal S., Kumar R., Miglani A., 2011, Wave propagation in temperature rate dependent thermoelasticity with two temperatures, Mathematical Sciences 5:125-146.
[17] El-Karamany A.S., Ezzat M.A. ,2011, On the two-temperature green–naghdi thermoelasticity theories, Journal of Thermal Stresses 34: 1207-1226.
[18] Banik S., Kanoria. M., 2013, Study of two-temperature generalized thermo-piezoelastic problem, Journal of Thermal Stresses 36: 71-93.
[19] Kumar R., Abbas I. A., 2013, Deformation due to thermal source in micropolar thermoelastic media with thermal and conductive temperatures, Journal of Computational and Theoretical Nanoscience 10: 2241-2247.
[20] Youssef H. M., 2013, State-space approach to two-temperature generalized thermoelasticity without energy dissipation of medium subjected to moving heat source, Applied Mathematics and Mechanics 34: 63-74.
[21] Ailawalia P., Lotfy K.H. , 2014,Two temperature generalized magneto-thermoelastic interactions in an elastic medium under three theories, Applied Mathematics and Computation 227: 871-888.
[22] Green A.E., Naghdi P.M., 1991, A re-examination of the basic postulates of thermomechanics, Proceedings of the Royal Society of London A 357:253-270.
[23] Green A.E., Naghdi P.M., 1992, On undamped heat waves in an elastic solid, Journal of Thermal Stresses 15:253-264.
[24] Green A.E., Naghdi P.M., 1993, Thermoelasticity without energy dissipation, Journal of Elasticity 31:189-209.
[25] Taheri H., Fariborz S., Eslami M.R., 2004, Thermoelasticity solution of a layer using the Green-Naghdi model, Journal of Thermal Stresses 27:795-809.
[26] Mukhopadhyay S., Kumar R., 2008, A problem on thermoelastic interactions in an infinite medium with a cylindrical hole in generalized thermoelasticity III, Journal of Thermal Stresses 31:455-475.
[27] Mohamed N.A., Khaled A.E., Ahmed E.A., 2009, Electromagneto-thermoelastic problem in a thick plate using Green and Naghdi theory, International Journal of Engineering and Science 47:680-690.
[28] Chirita S., Ciarletta M., 2010, On the harmonic vibrations in linear thermoelasticity without energy dissipation, Journal of Thermal Stresses 33:858-878.
[29] Chirita S., Ciarletta M., 2011, Several results in uniqueness and continous dependence in thermoelasticity of type III, Journal of Thermal Stresses 34:873-889.
[30] Passarella F., Zampoli V., 2011, Reciprocal and variational principles in micropolar thermoelasticity of type II, Acta Mechanica 216:29-36.
[31] Abbas I.A. ,2013, A GN model for thermoelastic interaction in an unbounded fiber-reinforced anisotropic medium with a circular hole, Applied Mathematics Letters 26: 232-239.
[32] Ailawalia P., Budhiraja S., Singla A., 2014, Dynamic problem in green-naghdi (Type III) thermoelastic half-space with two temperature, Mechanics of Advanced Materials and Structures 21: 544-552.
[33] Das P., Kar A., Kanoria M., 2013, Analysis of magneto-thermoelastic response in a transversely isotropic hollow cylinder under thermal shock with three-phase-lag effect, Journal of Thermal Stresses 36: 239-258.
[34] Kothari S., Mukhopadhyay S., 2013, Some theorems in linear thermoelasticity with dual phase-lags for an anisotropic medium, Journal of Thermal Stresses 36: 985-1000.
[35] Othman M.I.A., Atwa S.Y., Jahangir A., Khan A. , 2013, Generalized magneto-thermo-microstretch elastic solid under gravitational effect with energy dissipation, Multidiscipline Modeling in Materials and Structures 9:145-176.
[36] Fahmy M.A., 2013, A three-dimensional generalized magneto-thermo-viscoelastic problem of a rotating functionally graded anisotropic solids with and without energy dissipation, International Journal of Computation and Methodology 63: 713-733.
[37] El-Karamany A.S., Ezzat M.A., 2014, On the dual-phase-lag thermoelasticity theory, Meccanica 49: 79-89.
[38] Guo F.L., Song J., Wang G.Q., Zhou Y.F. , 2014, Analysis of thermoelastic dissipation in circular micro-plate resonators using the generalized thermoelasticity theory of dual-phase-lagging model, Journal of Sound and Vibration 333: 2465-2474.
[39] Eringen A.C., 1984, Plane waves in non local micropolar elasticity, International Journal of Engineering Science 22:1113-1121.
[40] Dhaliwal R.S., Singh A., 1980, Dynamic Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi, India.
[41] Gauthier R.D., 1982, Experimental Investigations on Micropolar Media, World Scientific, Singapore.