Three-Dimensional Fractional Order Generalized Thermoelastic Problem Under the Effect of Rotation in a Half Space

Santra, Sutapa; Das, Narayan Chandra; Kumar, Rajneesh; Lahiri, A.

doi:10.1080/01495739.2014.985551

Cited by 16 publications

(8 citation statements)

References 30 publications

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“…where = − , = − , = − . As in Lahiri et al [7], the general solution of Eq. (27) which is regular as can be written as:…”

Section: Solution Of the Vector-matrix Differential Equationmentioning

confidence: 91%

“…In this method, we obtain a vector-matrix differential equation from the basic equations which reduces finally to an algebraic eigenvalue problem and the solutions for the field variables are obtained by determining the eigenvalues and eigenvectors from the corresponding coefficient matrix. In this theory, body forces and/or heat sources are also accommodated as in Das and Lahiri [7], Bachher et al [8]. Now, two different models of generalized thermoelastisities are extensively used.…”

Section: Introductionmentioning

confidence: 99%

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Two-dimensional generalized thermo-elastic problem for anisotropic half-space

Ghosh¹,

Lahiri²,

Abbas³

2017

Math. models, eng.

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“…where = − , = − , = − . As in Lahiri et al [7], the general solution of Eq. (27) which is regular as can be written as:…”

Section: Solution Of the Vector-matrix Differential Equationmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Two-dimensional generalized thermo-elastic problem for anisotropic half-space

Ghosh¹,

Lahiri²,

Abbas³

2017

Math. models, eng.

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“…For the solution of the vector-matrix differential Eq. 25, we apply the method of eigenvalue approach as in Santra et al [35]. The characteristic equation of matrix is given by:…”

Section: Solution Of the Vector-matrix Differential Equation: Eigenvamentioning

confidence: 99%

Plane wave propagation in a 3D anisotropic half-space under Green-Naghdi theory II

Chakraborty¹,

Mandal²,

Das³

et al. 2016

Math. models, eng.

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In this paper, the theory of coupled thermoelasticity in three dimension is employed for triclinic half-space, subjected to time dependent heat source on the boundary of the space which is traction free and is considered in the context of Green-Naghdi model of type II (thermoelasticity without energy dissipation) of generalized thermoelasticity. Normal mode analysis is used to the non-dimensional coupled equations. Finally, the resulting equations are written in the form of a vector-matrix differential equation which is then solved by eigenvalue approach. Numerical results for the temperature, thermal stresses, and displacements are presented graphically and analyzed. Mathematical results shown in thermoelastic curves were supplemented by tectonic movements of elastic lithospheric plates.

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“…Mathematics 2022, 10, 4727 2 of 22 One of the most important generalized thermoelasticity theories is that of Lord and Shulman (L-S) [14]. Othman and Abbas [15,16] discussed the propagation of plane waves in fiber-reinforced, rotating thermoelastic half-space proposed by L-S under hydrostatic initial stress.…”

Section: Introductionmentioning

confidence: 99%

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

Aljadani

Zenkour

2022

Mathematics

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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.

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Three-Dimensional Fractional Order Generalized Thermoelastic Problem Under the Effect of Rotation in a Half Space

Cited by 16 publications

References 30 publications

Two-dimensional generalized thermo-elastic problem for anisotropic half-space

Two-dimensional generalized thermo-elastic problem for anisotropic half-space

Plane wave propagation in a 3D anisotropic half-space under Green-Naghdi theory II

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

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