Response of Two Temperatures on Wave Propagation in Micropolar Thermoelastic Materials with One Relaxation Time Bordered with Layers or Half Spaces of Inviscid Liquid

Subject Areas : Engineering

R  Kumar ¹ (Department of Mathematics, Kurukshetra University, Kurukshetra 136119, India)
M  Kaur ² (Department of Mathematics, Sri Guru Teg Bahadur Khalsa College, Anandpur Sahib, Punjab 140124, India)
S.C  Rajvanshi ³ (Department of Applied Sciences, Gurukul Vidyapeeth, Institute of Engineering and Technology, Banur, Sector #7, District Patiala, Punjab 140601, India)

Received: 2016-05-29 Accepted : 2016-07-05 Published : 2016-09-20

Keywords:

References:

[1] Eringen A.C., 1966, Linear theory of micropolar elasticity, Journal of Mathematics and Mechanics 15: 909-923.
[2] Lord H.W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity , Journal of the Mechanics and Physics of Solids 15: 299-309.
[3] Eringen A.C., 1970, Foundations of Micropolar Thermoelasticity, International centre for Mechanical Science, Udline Course and Lectures 23, Springen-Verlag, Berlin.
[4] Eringen A.C., 1999, Microcontinuum Field theories I: Foundations and Solids, Springer-Verlag, Berlin.
[5] Nowacki W., 1986, Theory of Asymmetric Elasticity, Oxford, Pergamon.
[6] Touchert T.R, Claus W.D., Ariman T., 1968, The linear theory of micropolar thermoelasticity, International Journal of Engineering Science 6: 37-47.
[7] Dost S., Taborrok B., 1978, Generalized micropolar thermoelasticity, International Journal of Engineering Science 16 : 173-178.
[8] Chandrasekharaiah D.S., 1986, Heat flux dependent micropolar thermoelasticity, International Journal of Engineering Science 24 :1389-1395.
[9] Boschi E., Iesan D., 1973, A generalized theory of linear micropolar thermoelasticity, Meccanica 7: 154-157.
[10] 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.
[11] 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.
[12] Warren W.E., Chen P.J., 1973, Wave propagation in the two temperature theory of thermoelasticity, Acta Mechanica 16: 21-23.
[13] Nayfeh A.H., 1995, Wave Propagation in Layered Anisotropic Media, North Holland, Amsterdam.
[14] Qi Q., 1994, Attenuated leaky rayleigh waves, Journal of Acoustical Society of America 95: 3222-3231.
[15] Wu J., Zhu Z., 1995, An alternative approach for solving attenuated Rayleigh waves, Journal of Acoustical Society of America 97: 3191-3193.
[16] Zhu Z., Wu J., 1995, The propagation of lamb waves in a plate bodered with a viscous fluid, An alternative approach for solving attenuated Rayleigh waves, Journal of Acoustical Society of America 98: 1059-1064.
[17] Nayfeh A. H., Nagy P. B., 1997, Excess attenuation of leaky lamb waves due to viscous fluid loading, Journal of Acoustical Society of America 101: 2649-2658.
[18] Youssef H.M., 2006, Theory of two temperature generalized thermoelastic, IMA Journal of Applied Mathematics 71: 383-390.
[19] Puri P., Jordan P., 2006, On the propagation of harmonic plane waves under the two temperature theory, International Journal of Engineering Science 44: 1113-1126.
[20] Youssef H.M., Al-Lehaibi E.A., 2007, A state approach of two temperature generalized thermoelasticity of one dimensional problem, International Journal of Solid and Structures 44: 1550-1562.
[21] Youssef H.M., Al-Harby H.A., 2007, State space approach of two temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading, Archive Applied Mechanics 77: 675-687.
[22] Magana A., Quintanilla R., 2009, Uniqueness and growth of solution in two temperature generalized thermoelastic theories, Mathematics and Mechanics of Solids 14: 622-634.
[23] Mukhopadhyay S., Kumar R., 2009, Thermoelastic interaction on two temperature generalized thermoelasticity in an infinite medium with a cylindrical cavity, Journal of Thermal Stresses 32: 341-360.
[24] Roushan K., Santwana M., 2010, Effect of thermal relaxation time on plane wave propagation under two temperature thermoelasticity, International Journal of Engineering Science 48: 128-139.
[25] 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.
[26] Kaushal S., Kumar R., Miglani A., 2011, Wave propagation in temperature rate dependent thermoelasticity with two temperatures, Mathematical Sciences 5 : 125-146.
[27] Nowacki W., Nowacki W.K., 1969, Propagation of monochromatic waves in an infinite micropolar elastic plate, Buletin de Academie Polonaise des Sciences, Sere des Sciences Techniques 17: 45-53.
[28] Kumar R., Gogna M. L., 1988, Propagation of waves in micropolar elastic layer with stretch immersed in an infinite liquid, International Journal of Engineering Science 27: 89-99.
[29] Tomar S.K., 2002, Wave propagation in a micropolar elastic layer, Proceedings of National Academy of Sciences, India.
[30] Tomar S.K., 2005, Wave propagation in a micropolar plate with voids, Journal of Vibration and Control 11: 849-863.
[31] Kumar R., Pratap G., 2006, Rayleigh lamb waves in micropolar isotropic elastic plate, Applied Mathematics and Mechanics 27: 1049-1059.
[32] Kumar R., Pratap G., 2007, Propagation of micropolar thermoeastic waves in plate, International Journal of Applied Mechanics and Engineering 12: 655-675.
[33] Kumar R., Pratap G., 2007, Wave propagation in a circular crested micropolar generalized thermoelastic plate, Buletinul Institutului Polithehnic din iasi 3-4: 53-72.
[34] Kumar R., Pratap G., 2008, Propagation of waves in thermoelastic micropolar cubic crystals bordered with layers or half spaces of inviscid fluid, International Journal of Applied Mathematics and Mechanics 4: 19-38.
[35] Kumar R., Pratap G., 2009, Free vibrations in micropolar thermoelastic plate loaded with viscous fluid with two relaxation times, International Journal of Applied Mathematics and Mechanics 5: 39-58.
[36] Kumar R., Pratap G., 2010, Propagation of waves in micropolar thermoelastic cubic crystals, Applied Mathematics and Information Sciences 4: 107-123.
[37] Sharma J.N., Kumar S., Sharma Y.D., 2008, Propagation of rayleigh waves in microstretch thermoelastic continua under inviscid fluid loadings, Journal of Thermal Stresses 31: 18-39.
[38] Sharma J.N., Kumar S.,2009, Lamb waves in micropolar thermoelastic solid plates immersed in liquid with varying temperature, Meccanica 44: 305-319.
[39] 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.
[40] Achenbach J.D., 1976, Wave Propagation in Elastic Solids, 7th edition, North Holland, Amsterdam.