State-space Approach to 3D Generalized Thermoviscoelasticity Under Green-Nagdhi Theory

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New Zealand Journal of Mathematics

Vol. 46, (2016), Pages 97-113


N. Sarkar

Department of Applied Mathematics,

University of Calcutta,

92, A.P.C. Road,

Kolkata-700 009,

India.

mailto:nsarkarindian@gmail.com

M. Bachher

Department of Mathematics,

Jadavpur University,

Kolkata-700 032,

India.

A. Lahiri

Department of Mathematics,

Jadavpur University,

Kolkata-700 032,

India.


Abstract The present paper is concerned at investigating the effects of viscosity on generalized thermoelastic interactions in a three-dimensional homogeneous isotropic semi-infinite medium whose surface is subjected to a thermal shock and is assumed to be traction free. The formulation is applied to the generalized thermoelasticity based on the G-N II and III theories. The normal mode analysis together with state-space approach is used to obtain the exact analytical expressions for the studied field variables. Numerical computations are done for a specific material and obtained numerical results are plotted in the form of two- and three-dimensional figures. Comparisons are performed with and without the effects of viscosity. A comparison is also made between G-N II and G-N III models to show the effects of viscosity.

Keywords Thermo-visco-elasticity, G-N model, Energy dissipation, Normal mode analysis, State-space formulation.

Classification (MSC2000) 75F05.

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