14. State-space approach to 3D generalized thermoviscoelasticity under Green and Naghdi theory II

M. Bachher1, N. Sarkar2, A. Lahiri3

1, 3Department of Mathematics, Jadavpur University, Kolkata-700 032, India

2Department of Applied Mathematics, University of Calcutta, Kolkata-700 009, India

2Corresponding author

E-mail: 1mitali.ju08@gmail.com, 2nsarkarindian@gmail.com, 3lahiriabhijit2000@yahoo.com

(Received 23 November 2015; accepted 27 December 2015)

Abstract. The present paper is aimed at studying the effects of viscosity on thermoelastic interactions in a three-dimensional homogeneous isotropic half-space solid medium whose surface is subjected to a thermal shock and is assumed to be stress free. The formulation is applied to the generalized thermoelasticity based on the GN model without energy dissipation (GN II model). The normal mode analysis together with state-space approach is used to obtain the exact analytical expressions for the field variables considered. Numerical computations are performed for a specific material and the results obtained are represented graphically. Comparisons are made within the theory in the presence and absence of viscosity effects.

Keywords: generalized thermoviscoelasticity, GN model, energy dissipation, normal mode analysis, state-space approach.

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Cite this article

Bachher M., Sarkar N., Lahiri A. State‑space approach to 3D generalized thermoviscoelasticity under Green and Naghdi theory II. Mathematical Models in Engineering, Vol. 1, Issue 2, 2015, p. 111‑124.

 

Mathematical Models in Engineering. December 2015, Volume 1, Issue 2

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