Effect of Hydrostatic Initial Stress on a Rotating Half-Space in the Context of a Two-Relaxation Power-Law Model

Maryam H. Aljadani () and Ashraf M. Zenkour
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Maryam H. Aljadani: Department of Mathematics, Jamoum University College, Umm Al-Qura University, Makkah 21421, Saudi Arabia
Ashraf M. Zenkour: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2022, vol. 10, issue 24, 1-22

Abstract: The simple and refined Lord–Shulman theories, the simple and refined Green–Lindsay theories as well as the coupled thermoelasticity theory were all employed to investigate the deformation of a rotating thermoelastic half-space. The present medium is subjected to initial pressure, bounded by hydrostatic initial stress and rotation. A unified heat conduction equation is presented. The normal mode strategy is applied to get all analytical expressions of temperature, stresses, and displacements. Some outcomes are tabulated to validate the present refined theories with the simple and classical thermoelasticity theories. The effect of hydrostatic initial stress was investigated on all field quantities of the rotating thermoelastic half-space with and without initial pressure. Two- and three-dimensional plots are illustrated in the context of refined theories to discuss the behaviors of all variables through the coordinate axes. Some particular cases of special interest have been deduced from the present investigation.

Keywords: unified conduction equation; Lord–Shulman theory; Green–Lindsay theory; hydrostatic stress; rotating half-space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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