Arvind Kumar This email address is being protected from spambots. You need JavaScript enabled to view it.1 , Rajneesh Kumar2 and S. M. Abo-Dahab3,4

1Department of Mathematics, Punjab Technical University, Jalandhar, India
2Department of Mathematics, Kurukshetra University Kurukshetra, Haryana, India
3Department of Mathematics, Faculty of Science, Taif University, Saudi Arabia
4Department of Mathematics, Faculty of Science, SVU, Qena, Egypt


Received: September 20, 2016
Accepted: October 28, 2016
Publication Date: June 1, 2017

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This paper is concerned with the study of propagation of Rayleigh waves in a homogeneous isotropic microstretch-thermoelastic solid half-space with microtemperatures in the context of theory of thermoelasticity. The medium is subjected to stress free, isothermal boundary. After developing a mathematical model, the dispersion curve in the form of polynomial equation is obtained. Phase velocity and attenuation coefficient of Rayleigh wave are computed numerically. The numerically simulated results are depicted graphically. Some special cases are also deduced from the present investigation.

Keywords: Rayleigh Wave, Microstretch-thermoelastic, Phase Velocity, Attenuation Coefficient, Microtemperature


  1. [1] Eringen, A. C., “Linear Theory of Micropolar Elasticity,” Journal of Mathematics and Mechanics, Vol. 15, pp. 909923 (1966).
  2. [2] Marin, M., “Some Basic Theorems in Elastostatics of Micropolar Materials with Voids,” J. Comp. Appl. Math., Vol. 70, No. 1, pp. 115126 (1996). doi: 10. 1016/0377-0427(95)00137-9
  3. [3] Marin, M. and Marinescu, C., “Thermoelasticity of Initially Stressed Bodies, Asymptotic Equipartition of Energies,” Int. J. Engg. Sci., Vol. 36, No. 1, pp. 7386 (1998). doi: 10.1016/S0020-7225(97)00019-0
  4. [4] Kumar, R. and Ailawalia, P., “Interactions due to Mechanical/Thermal Sources in Micropolar Thermoelastic Medium Possessing Cubic Symmetry,” International Journal of Solids and Structures, Vol. 43, No. 9, pp. 27612798 2006. doi: 10.1016/j.ijsolstr.2005.11.002
  5. [5] Kumar, R. and Gupta, R. R., Deformation due to Inclined Loads in an Orthotropic Micropolar Thermoelastic Medium with Two Temperatures,” Applied Mathematics and Information Sciences, Vol. 4, No. 3, pp. 413428 (2010).
  6. [6] Marin, M., “A Domain of Influence Theorem for Microstretch Elastic Materials,” Nonlinear Analysis: Real World Applications, Vol. 11, pp. 34463452 (2010). doi: 10.1016/j.nonrwa.2009.12.005
  7. [7] Marin, M., “On Existence and Uniqueness in Thermoelasticity of Micropolar Bodies,” Comptes Rendus, Acad. Sci. Paris, Series II, Vol. 32, pp. 475480 (1995).
  8. [8] Kumar, R. and Kumar, A., “Elastodynamic Response of Thermal Laser Pulse in Micropolar Thermoelastic Mass Diffusion Medium,” Journal of Thermodynamics, Article ID 6163090 (2016). doi: 10.1155/2016/6163090
  9. [9] Eringen, A. C., Micropolar Elastic Solids with stretch, Ari Kitabevi Matbassi, Vol. 24, pp. 118 (1971).
  10. [10] Eringen, A. C., “Theory of Thermomicrostretch Elastic Solids,” International Journal of Engineering Science, Vol. 28, No. 12, pp. 12911301 (1990). doi: 10.1016/0020-7225(90)90076-U
  11. [11] Kumar, R. and Kumar, A., “Elastodynamic Response due to Mechanical Forces in a Microstretch Thermoelastic Medium with Mass Diffusion,” Material Physics and Mechanics, Vol. 22, pp. 4452 (2015).
  12. [12] Kumar, R., Kumar, A. and Singh, D., “Thermomechanical Interactions of Laser Pulse with Microstretch Thermoelastic Medium,” Archives of Mechanics, Vol. 67, No. 6, pp. 439456 (2015).
  13. [13] Grot, R. A., “Thermodynamics of a Continuum with Microstructure,” Int. J. Engg. Sci., Vol. 7, pp. 801814 (1969). doi: 10.1016/0020-7225(69)90062-7
  14. [14] Riha, P., “On the Microcontinuum Model of Heat Conduction in Materials with Inner Structure,” Int. J. Engg. Sci., Vol. 14, pp. 529535 (1976). doi: 10.1016/ 0020-7225(76)90017-3
  15. [15] Iesan, D. and Quintanilla, R., On Thermoelastic Bodies with Inner Structure and Microtemperatures,” J. Math. Anal. Appl., Vol. 354, pp. 1223 (2009). doi: 10.1016/ j.jmaa.2008.12.017
  16. [16] Iesan, D. and Quintanilla, R., “On a Theory of Thermoelasticity with Microtemperatures,” J. Therm. Stress., Vol. 23, pp. 199215 (2000).
  17. [17] Iesan, D., “On a Theory of Micromorphic Elastic Solids with Microtemperatures,” J. Therm. Stress., Vol. 24, pp. 737752 (2007). doi: 10.1080/014957301300 324882
  18. [18] Iesan, D., “Thermoelasticity of Bodies with Microstructure and Microtemperatures,” Int. J. Solids Structures., Vol. 44, pp. 86488662 (2007). doi: 10.1016/ j.ijsolstr.2007.06.027
  19. [19] Scalia, A., Svandze, M. and Tracinà, R., “Basic Theorems in the Equilibrium Theory of Thermoelasticity with Microtemperatures,” J. Therm. Stress, Vol. 33, No. 8, pp. 721753 (2010). doi: 10.1080/01495739.2010. 482348
  20. [20] Scalia, A. and Svandze, M., “On the Representation of Solutions of the Theory of Thermoelasticity with Microtemperatures,” J. Therm. Stress., Vol. 29, pp. 849 863 (2006).
  21. [21] Kumar, R. and Kansal T., “Propagation of Rayleigh Waves on the Free Surface of Transversely Isotropic Generalized Thermoelastic Diffusion,” Applied Mathematics and Mechanics, Vol. 29, No. 11, pp. 1451 1462 (2008). doi: 10.1007/s10483-008-1106-6
  22. [22] Kumar, R. and Gupta, V., “Problem of Rayleigh Waves in Generalized Thermoelastic with Mass Diffusion,” Canadian Journal of Physics, Vol. 93, No. 10, pp. 10091014 (2015). doi: 10.1007/s10483-008-1106-6
  23. [23] Singh, B., “Propagation of Rayleigh Wave in a Thermoelastic Solid Half-space with Microtemperatures,” International Journal of Geophysics, Vol. 2014, Article ID 474502. doi: 10.1155/2014/474502
  24. [24] Kumar, R. and Ahuja, Garg, S. K., “Rayleigh Waves in Isotropic Microstretch Thermoelastic Diffusion Half Space,” Latin American Journal of Solids and Structures, Vol. 11, pp. 299319 (2014). doi: 10.1590/ S1679-78252014000200009
  25. [25] Eringen, A. C., “Plane Waves in Nonlocal Micropolar Elasticity,” Int. J. Engg. Sci., Vol. 22, pp. 11131121 (1984). doi: 10.1016/0020-7225(84)90112-5
  26. [26] Dhaliwal, R. S. and Singh, A., Dynamic Coupled Thermoelasticity. Hindustan Publication Corporation, New Delhi (1980).