Geomechanics and Engineering

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Fractional order thermoelastic wave assessment in a two-dimension medium with voids

  • Hobiny, Aatef D. (Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University) ;
  • Abbas, Ibrahim A. (Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University)
  • Received : 2019.11.10
  • Accepted : 2020.03.12
  • Published : 2020.04.10
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Abstract

In this article, the generalized thermoelastic theory with fractional derivative is presented to estimate the variation of temperature, the components of stress, the components of displacement and the changes in volume fraction field in two-dimensional porous media. Easily, the exact solutions in the Laplace domain are obtained. By using Laplace and Fourier transformations with the eigenvalues method, the physical quantities are obtained analytically. The numerical results for all the physical quantities considered are implemented and presented graphically. The results display that the present model with the fractional derivative is reduced to the Lord and Shulman (LS) and the classical dynamical coupled (CT) theories when the fractional parameter is equivalent to one and the delay time is equal to zero and respectively.

Keywords

Acknowledgement

Supported by : King Abdulaziz University

This work was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No (DF-182-130-1441). The authors, therefore, gratefully acknowledge the DSR technical and financial support.

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