International Journal of Applied Science and Engineering
Published by Chaoyang University of Technology

Baljeet Singh*

Department of Mathematics, Post Graduate Government College, Sector-11, Chandigarh - 160 011, India


 

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ABSTRACT


Sinha and Sinha (J. Phys. Earth, 22, 237-244, 1974) studied a problem on the reflection of thermoelastic waves at a stress free thermally insulated solid half-space in context of the Lord and Shulman theory of generalized thermoelastcity. He showed the existence of three plane waves (two longitudinal waves and a shear wave) in a homogeneous, linear and isotropic thermoelastic medium. He also obtained the reflection coefficients of reflected waves theoretically and numerically for the incident plane waves. Due to the engineering applications, a problem on the reflection of thermoelastic waves at a non-free boundary surface is considered in this paper. The reflection coefficients of various reflected waves are obtained by considering the new boundary conditions at non-free surface. For a particular material representing the half-space, the reflection coefficients are also computed numerically and are shown graphically against the angle of incidence for different values of boundary parameters.


Keywords: Generalized thermoelasticity; Non-free surface; Reflection coefficients; Thermal relaxation.


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REFERENCES


  1. [1] Lord H. and Shulman,Y. 1967. A generalised dynamical theory of thermoelasticity, Journal of Mechanics and Physics of Solids, 15 : 299-309.

  2. [2] Green A.E. and Lindsay, K.A. 1972. Thermoelasticity, Journal of Elasticity, 2 : 1-7.

  3. [3] Biot, M.A. 1956. Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics, 2 : 240-253.

  4. [4] Green A. E. and Naghdi, P. M. 1993. Thermoelasticity without energy dissipation, Journal of Elasticity, 31 : 189-208.

  5. [5] Chandrasekharaiah, D.S. 1998. Hyperbolic Thermoelasticity: a review of recent literature, Applied Mechanics Review, 51 : 705-729.

  6. [6] Hetnarski R.B. and Ignaczak, J. 1999. Generalized thermoelasticity, Journal of Thermal Stresses, 22 : 451-476.

  7. [7] Ignaczak J. and Ostoja-Starzewski, M. 2009. "Thermoelasticity with Finite Wave Speeds", Oxford University Press.

  8. [8] Sinha A. N. and Sinha, S. B. 1974. Reflection of thermoelastic waves at a solid half-space with thermal relaxation, Journal of Physics of the Earth, 22 : 237-244.

  9. [9] Sinha S.B. and Elsibai, K. A. 1996. Reflection of thermoelastic waves at a solid half-space with two thermal relaxation times, Journal of Thermal Stresses, 19 : 763-777.

  10. [10] Sinha S.B. and Elsibai, K. A. 1997. Reflection and refraction of thermoelastic waves at an interface of two semi-infinite media with two thermal relaxation times, Journal of Thermal Stresses, 20 : 129-146.

  11. [11] Singh, B. 2000. Wave propagation in heat-flux dependent generalized thermoelasticity, Bulletin of Calcutta Mathematical Society, 92 : 257-272.

  12. [12] Singh, B. 2002. Reflection of thermo-viscoelastic waves from free surface in the presence of magnetic field. Proceedings of National Academy of Sciences, India, 72A : 109-120.

  13. [13] Sharma, J.N., Kumar V. and Chand, D. 2003. Reflection of generalized thermoelastic waves from the boundary of a half-space, Journal of Thermal Stresses, 26 : 925-942.

  14. [14] Song, Y.-Q., Zhang, Y.-C., Xu, H.-Y. and Lu, B.-H. 2004. Reflection of magneto-thermoviscoelastic waves under generalized thermoviscoelasticity, International Journal of Thermophysics, 25 : 909-929.

  15. [15] Singh, B. 2005. Reflection of P and SV waves from free surface of an elastic solid with generalized thermodiffusion, Journal of Earth System and Sciences, 114 : 159-168.

  16. [16] Othman, M. I. A. and Song, Y. 2006. The effect of rotation on the reflection of magneto-thermoelastic waves under thermoelasticity without energy dissipation, Acta Mechanica, 184 : 189-204.

  17. [17] Singh, B. 2006. Reflection of SV waves from the free surface of an elastic solid in generalized thermoelastic diffusion, Journal of Sound and Vibration, 291 : 764-778.

  18. [18] Othman, M. I.A. and Song, Y. 2007. Reflection of plane waves from an elastic solid half-space under hydrostatic initial stress without energy dissipation, International Journal of Solids and Structures, 44 : 5651-5664.

  19. [19] Singh, B. 2007. Wave propagation in a generalized thermoelastic material with voids, Applied Mathematics and Computation, 189 : 698-709.

  20. [20] Das, N.C., Lahiri, A., Sarkar, S. and Basu, S. 2008. Reflection of generalized thermoelastic waves from isothermal and insulated boundaries of a half space, Computer and Mathematics Applications, 56 : 2795-2805.

  21. [21] Singh, B. 2008. Effect of hydrostatic initial stresses on waves in a thermoelastic solid half-space, Applied Mathematics and Computation, 198 : 494-505.

  22. [22] Othman, M. I. A. and Song, Y. 2008. Reflection of magneto-thermo-elastic waves from a rotating elastic half-space, International Journal of Engineering and Science, 46 : 459-474.

  23. [23] Othman, M.I.A. and Kumar, R. 2009. Reflection of magneto-thermoelasticity waves with temperature dependent properties in generalized thermoelasticity, International Communications in Heat and Mass Transfer, 36 : 513-520.

  24. [24] Brock, L. M. 2010. Reflection and Diffraction of Plane Temperature-Step Waves in Orthotropic Thermoelastic Solids, Journal of Thermal and Stresses, 33 : 879-904.

  25. [25] Singh, B. 2010. Reflection of plane waves at the free surface of a monoclinic thermoelastic solid half-space, European Journal of Mechanics - A/Solids, 29 : 911-916.

  26. [26] Brock, L. M. 2011. Plane Waves with Dispersion and Decay: Surface Reflection for Thermoelastic Solids with Thermal Relaxation. Journal of Thermal Stresses, 34 : 687-701.

  27. [27] Singh, B. 2011. On theory of generalized thermoelastic solids with voids and diffusion, European Journal of Mechanics - A/Solids, 30 : 976-982.

  28. [28] Singh, B. and Bala, K. 2012. Reflection of P and SV waves from the free surface of a two-temperature thermoelastic solid half-space, Journal of Mechanics and Material Structures, 7 : 183-193.

  29. [29] Zenkour, A.M., Mashat, D.S. and Abouelregal, A.E. 2013. The effect of dual-phase-lag model on reflection of thermoelastic waves in a solid half space with variable material properties, Acta Mechanica Solida Sinica, 26 : 659-670.

  30. [30] Singh, B. 2013. Wave propagation in dual-phase-lag anisotropic thermoelasticity, Continuum Mechanics and Thermodynamics, 25 : 675-683.

  31. [31] Bijarnia, R. and Singh, B. 2014. Propagation of plane waves in an isotropic two-temperature thermoelastic solid half-space with diffusion, Annals of Solid and Structural Mechanics, 6 : 37-45.

  32. [32] Singh, M. C. and Chakraborty, N. 2015. Reflection of a plane magneto-thermoelastic wave at the boundary of a solid half-space in presence of initial stress, Applied Mathematical Modelling, 39 : 1409-1421.

  33. [33] Singh, B. 2016. Wave propagation in a rotating transversely isotropic two-temperature generalized thermoelastic medium without dissipation, International Journal of Thermophysics, 37: 5, https// doi:10.1007/s10765-015-2015-z.


ARTICLE INFORMATION


Received: 2016-12-07
Revised: 2018-05-17
Accepted: 2018-06-14
Publication Date: 2018-12-01


Cite this article:

Singh, B. 2018. Reflection of thermoelastic waves at a Non-free thermally insulated surface. International Journal of Applied Science and Engineering, 15, 149-161. https://doi.org/10.6703/IJASE.201812_15(3).149


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