Journal ArticleDOI
One-dimensional problem of a fractional order two-temperature generalized thermo-piezoelasticity
Mohsin Islam,Mridula Kanoria +1 more
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In this article, the authors derived the thermoelastic stress, strain and conductive temperature in a piezoelastic half-space body in which the boundary is stress free and subjected to thermal loading in the context of the fractional order generalized thermelasticity theory (2TT).Abstract:
This paper is concerned with the determination of the thermoelastic stress, strain and conductive temperature in a piezoelastic half-space body in which the boundary is stress free and subjected to thermal loading in the context of the fractional order two-temperature generalized thermoelasticity theory (2TT). The two-temperature three-phase-lag (2T3P) model, two-temperature Green–Naghdi model III (2TGNIII) and two-temperature Lord–Shulman (2TLS) model of thermoelasticity are combined into a unified formulation introducing unified parameters. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain that is then solved by the state-space approach. The numerical inversion of the transform is carried out by a method based on Fourier series expansion techniques. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. The effect of the fractional order parameter, two-temperature and electric field on...read more
Citations
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Journal ArticleDOI
An investigation on responses of thermoelastic interactions in a generalized thermoelasticity with memory-dependent derivatives inside a thick plate:
TL;DR: In this article, the authors analyzed the thermoelastic interactions inside an infinitely extended thick plate due to axis-symmetric temperature distribution applied at the lower and upper surfaces of the plate under memory-dependent generalized thermo-elasticity.
Journal ArticleDOI
A modified fractional-order generalized piezoelectric thermoelasticity model with variable thermal conductivity
TL;DR: In this article, a modified fractional-order generalized piezoelectric thermoelasticity model with variable thermal conductivity is established in the context of a new consideration of heat conduction with memory-dependent derivative.
The influence of two-temperature fractional order generalized thermoelastic diffusion inside a spherical shell
TL;DR: In this article, the two-temperature thermo-elasto-diffusion interaction inside a spherical shell in the context of fractional order generalized thermoelasticity is considered.
Journal ArticleDOI
Application of Fractional Order Theory of Thermoelasticity to 3D Time-Dependent Thermal Shock Problem for a Half-Space
TL;DR: In this article, a three-dimensional model of thermoelasticity with fractional order heat transfer is established, and the resulting coupled equations together with the Laplace and double Fourier transforms techniques are applied to a half space, which is assumed to be traction free and subjected to a thermal shock that is a function of time.
References
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Book
Applications Of Fractional Calculus In Physics
TL;DR: An introduction to fractional calculus can be found in this paper, where Butzer et al. present a discussion of fractional fractional derivatives, derivatives and fractal time series.
Journal ArticleDOI
Linear Models of Dissipation whose Q is almost Frequency Independent-II
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.
Journal ArticleDOI
A generalized dynamical theory of thermoelasticity
TL;DR: In this article, a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of heat flow.
Journal ArticleDOI
Thermoelasticity without energy dissipation
Albert Edward Green,P. M. Naghdi +1 more
TL;DR: In this article, a general uniqueness theorem for linear thermoelasticity without energy dissipation is proved and a constitutive equation for an entropy flux vector is determined by the same potential function which also determines the stress.
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