Fractional-Order Thermoelastic Wave Assessment in a Two-Dimensional Fiber-Reinforced Anisotropic Material

Samah Horrigue and Ibrahim A. Abbas
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Samah Horrigue: Faculty of Sciences, University of Jeddah, Jeddah 21589, Saudi Arabia
Ibrahim A. Abbas: Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt

Mathematics, 2020, vol. 8, issue 9, 1-14

Abstract: The present work is aimed at studying the effect of fractional order and thermal relaxation time on an unbounded fiber-reinforced medium. In the context of generalized thermoelasticity theory, the fractional time derivative and the thermal relaxation times are employed to study the thermophysical quantities. The techniques of Fourier and Laplace transformations are used to present the problem exact solutions in the transformed domain by the eigenvalue approach. The inversions of the Fourier-Laplace transforms hold analytical and numerically. The numerical outcomes for the fiber-reinforced material are presented and graphically depicted. A comparison of the results for different theories under the fractional time derivative is presented. The properties of the fiber-reinforced material with the fractional derivative act to reduce the magnitudes of the variables considered, which can be significant in some practical applications and can be easily considered and accurately evaluated.

Keywords: Laplace transforms; thermal relaxation time; spherical cavity; fiber-reinforced medium; eigenvalues method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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