An Interval Parametric Approach for the Solution of One Dimensional Generalized Thermoelastic Problem

Subject Areas : Mechanics of Solids

S Mandal ^{1 *} , S Pal Sarkar ² , T Kumar Roy ³

1 - Department of Mathematics, Sitananda College, Nandigram, Purba Medinipur-721631, India ---Department of Mathematics, IIEST, Shibpur, Howrah-711103, India
2 - Department of Mathematics, IIEST, Shibpur, Howrah-711103, India
3 - Department of Mathematics, IIEST, Shibpur, Howrah-711103, India

Received: 2021-09-10 Accepted : 2021-12-10 Published : 2022-03-30

Keywords: Vector matrix differential equation, Eigen value, Generalized thermoelasticity, Laplace transformation, Interval number,

Abstract :

This paper is presenting the solutions of the one dimension generalized thermo-elastic coupled equations by considering some thermo-elastic constants as interval numbers. As most of the elastic constants are obtained using the experimental methods. Thus there might be some deficiency of exactness to obtain such constants. This kind of deficiency might cause the results on a micro-scale. L-S model has been considered to study the effect of such an interval parametric approach to generalized thermoelasticity. Laplace transform method applied to obtain a system of coupled ordinary differential equations. Then the vector-matrix differential form is used to solve these equations by the eigenvalue approach in Laplace transformed domain. The solution in the space-time domain obtained numerically. The numerical solutions obtained by using some suitable inverse transformation method. The solutions are graphically represented for different values of the parameter of interval parametric form and the significance of obtained results are described along with the behavior of the solutions.

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