Kumar, R., Kaur, M., Rajvanshi, S. (2016). Response of Two Temperatures on Wave Propagation in Micropolar Thermoelastic Materials with One Relaxation Time Bordered with Layers or Half Spaces of Inviscid Liquid. Journal of Solid Mechanics, 8(3), 495-510.

R Kumar; M Kaur; S.C Rajvanshi. "Response of Two Temperatures on Wave Propagation in Micropolar Thermoelastic Materials with One Relaxation Time Bordered with Layers or Half Spaces of Inviscid Liquid". Journal of Solid Mechanics, 8, 3, 2016, 495-510.

Kumar, R., Kaur, M., Rajvanshi, S. (2016). 'Response of Two Temperatures on Wave Propagation in Micropolar Thermoelastic Materials with One Relaxation Time Bordered with Layers or Half Spaces of Inviscid Liquid', Journal of Solid Mechanics, 8(3), pp. 495-510.

Kumar, R., Kaur, M., Rajvanshi, S. Response of Two Temperatures on Wave Propagation in Micropolar Thermoelastic Materials with One Relaxation Time Bordered with Layers or Half Spaces of Inviscid Liquid. Journal of Solid Mechanics, 2016; 8(3): 495-510.

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

^{1}Department of Mathematics, Kurukshetra University, Kurukshetra 136119, India

^{2}Department of Mathematics, Sri Guru Teg Bahadur Khalsa College, Anandpur Sahib, Punjab 140124, India

^{3}Department of Applied Sciences, Gurukul Vidyapeeth, Institute of Engineering and Technology, Banur, Sector #7, District Patiala, Punjab 140601, India

Abstract

The present study is concerned with the propagation of Lamb waves in a homogeneous isotropic thermoelastic micropolar solid with two temperatures bordered with layers or half spaces of inviscid liquid subjected to stress free boundary conditions. The generalized theory of thermoelasticity developed by Lord and Shulman has been used to investigate the problem. The secular equations for symmetric and skew- symmetric leaky and nonleaky Lamb wave modes of propagation are derived. The phase velocity and attenuation coefficient are computed numerically and depicted graphically. The amplitudes of stress, microrotation vector and temperature distribution for the symmetric and skew-symmetric wave modes are computed analytically and presented graphically. Results of some earlier workers have been deduced as particular cases.

[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.