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

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.

A Modified Two-Relaxation Thermoelastic Model for a Thermal Shock of Rotating Infinite Medium

“…where ∇ 2 = ∂ 2 ∂x 2 + ∂ 2 ∂z 2 ; θ = T − T 0 , wherein T is the temperature over the reference temperature T 0 ; = ρ is the medium density; c e is the certain heat at constant strain, K is the parameter of thermal conductivity; e = e kk = u k,k is the volumetric strain where u i is the components of displacement; γ = α t (3λ + 2µ) is the parameter of thermoelastic coupling in which λ, µ are Lame's constants and α t is the coefficient of thermal expansion; and D 1 , D m 1 are the operators of time-derivative, which can be written as [33][34][35][36][37][38][39][40],…”