32. Two-dimensional generalized thermo-elastic problem for anisotropic half-space

Debkumar Ghosh1, Abhijit Lahiri2, Ibrahim A. Abbas3

1, 2Department of Mathematics, Jadavpur University, Kolkata, 700032, India

3Department of Mathematics, Sohag University, Sohag, Egypt

1Corresponding author

E-mail: 1debkumarghosh2020@gmail.com, 2lahiriabhijit2000@yahoo.com, 3ibrabbas7@yahoo.com

Received 8 February 2017; accepted 12 March 2017

DOI https://doi.org/10.21595/mme.2017.18236


Abstract. This paper concerns with the study of wave propagation in fibre reinforced anisotropic half space under the influence of temperature and hydrostatic initial stress. Lord-Shulman theory is applied to the heat conduction equation. The resulting equations are written in the form of vector matrix differential equation by using Normal Mode technique, finally which is solved by Eigen value approach.

Keywords: eigenvalue, generalized thermoelasticity, normal mode, vector-matrix differential equation.


[1]        Green W. A. Bending waves in strongly anisotropic plates. Quarterly Journal of Mechanics and Applied Mathematics, Vol. 35, 1982, p. 485‑507.

[2]        Abbas I. A., Othman M. I. A. Generalized thermoelastic interaction in a fiber-reinforced anisotropic half-space under hydrostatic initial stress. Journal of Vibration Control, Vol. 18, Issue 2, 2011, p. 175‑182.

[3]        Baylis E. R., Green W. A. Flexural waves in fiber reinforced laminated plates. Journal of Sound and Vibration, Vol. 110, 1986, p. 1‑26.

[4]        Rogerson G. A. Penetration of impact waves in a six-ply fiber composite laminate. Journal of Sound and Vibration, Vol. 158, 1992, p. 105‑120.

[5]        Dhaliwal R. S., Sherief H. H. Generalized thermoelasticity for anisotropic media. Quarterly of Applied Mathematics, Vol. 33, 1980, p. 1‑8.

[6]        Sherief H. H., El-Sayed A., El-Latief A. Fractional order theory of thermoelasticity. International Journal of Solids and Structures, Vol. 47, 2010, p. 269‑275.

[7]        Santra S., Das N. C., Kumar R., Lahir A. Three dimensional fractional order generalized thermoelastic problem under effect of rotation in a half space. Journal of Thermal Stresses, Vol. 38, 2015, p. 309‑324.

[8]        Bachher M., Sarkar N., Lahiri A. Generalized thermoelastic infinite medium with voids subjected to a instantaneous heat sources with fractional derivative heat transfer. International Journal of Mechanical Sciences, Vol. 89, 2014, p. 84‑91.

[9]        Lord H. W., Shulman Y. A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, Vol. 15, 1967, p. 299‑309.

[10]     Green A. E., Lindsay K. A. Thermoelasticity. Journal of Elasticity, Vol. 2, 1972, p. 1‑7.

[11]     Green A. E., Naghdi P. M. A re-examination of the basic results of thermomechanics. Proceedings of the Royal Society of London A, Vol. 432, 1991, p. 171‑194.

[12]     Green A. E., Naghdi P. M. On undamped heat waves in an elastic solid. Thermal Stresses, Vol. 15, 1992, p. 252‑264.

[13]     Green A. E., Naghdi P. M. Thermoelasticity without energy dissipation. Elasticity, Vol. 31, 1993, p. 189‑208.

[14]     Ibrahim A. Abbas Generalized magnetothermoelasticity in a fiber-reinforced anisotropic half‑space. International Journal of Thermophysics, 2011, https://doi.org/10.1007/s10765-011-0957-3.

Cite this article

Ghosh Debkumar, Lahiri Abhijit, A. Abbas Ibrahim Two‑dimensional generalized thermo‑elastic problem for anisotropic half‑space. Mathematical Models in Engineering, Vol. 3, Issue 1, 2017, p. 27‑40.


Mathematical Models in Engineering. June 2017, Volume 3, Issue 1

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