26. Plane wave propagation in a 3D anisotropic half‑space under Green-Naghdi theory II

S. Chakraborty1, S. C. Mandal2, A. K. Das3, N. Sarkar4, A. Lahiri5

1, 2, 5Department of Mathematics, Jadavpur University, Kolkata, 700032, India

3Department of Geology, Asutosh College, 92, S. P. Mukherjee Road, Kolkata, 700026, India

4Department of Applied Mathematics, University of Calcutta, Kolkata, 700009, India

4Corresponding author

E-mail: 1csanjukjta1977@gmail.com, 2scmandal@math.jdvu.ac.in, 3akdas.geology@gmail.com, 4nsarkarindian@gmail.com, 5lahiriabhijit2000@yahoo.com

Received 26 August 2016; accepted 27 October 2016

DOI https://doi.org/10.21595/mme.2016.17621

Abstract. In this paper, the theory of coupled thermoelasticity in three dimension is employed for triclinic half-space, subjected to time dependent heat source on the boundary of the space which is traction free and is considered in the context of Green-Naghdi model of type II (thermoelasticity without energy dissipation) of generalized thermoelasticity. Normal mode analysis is used to the non-dimensional coupled equations. Finally, the resulting equations are written in the form of a vector-matrix differential equation which is then solved by eigenvalue approach. Numerical results for the temperature, thermal stresses, and displacements are presented graphically and analyzed. Mathematical results shown in thermoelastic curves were supplemented by tectonic movements of elastic lithospheric plates.

Keywords: anisotropic solid, Green-Naghdi model II, normal mode analysis, eigenvalue approach, lithostatic pressure and lithospheric plates.


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Cite this article

Chakraborty S., Mandal S. C., Das A. K., Sarkar N., Lahiri A. Plane wave propagation in a 3D anisotropic half‑space under Green‑Naghdi theory II. Mathematical Models in Engineering, Vol. 2, Issue 2, 2016, p. 114‑134.


Mathematical Models in Engineering. December 2016, Volume 2, Issue 2

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