scholarly journals A Study on Fractional Order Thermoelastic Half Space

2020 ◽  
Vol 25 (4) ◽  
pp. 191-202
Author(s):  
Sourov Roy ◽  
Abhijit Lahiri
Keyword(s):  
Half Space ◽  
Fractional Order ◽  
Equations Of Motion ◽  
Generalized Thermoelasticity ◽  
Dimensional Problem ◽  
Governing Equations ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Eigen Value ◽  
The Laplace Transform

AbstractIn this paper, we consider a one dimensional problem on a fractional order generalized thermoelasticity in half space subjected to an instantaneous heat source. The Laplace transform as well as eigen value approach techniques are applied to solve the governing equations of motion and heat conduction. Closed form solutions for displacement, temperature and stress are obtained and presented graphically.

scholarly journals Interactions due to Moving Heat Sources in Generalized Thermoelastic Half-Space using L-S Model

2013 ◽  
Vol 18 (3) ◽  
pp. 815-831 ◽  
Author(s):  
N. Sarkar ◽  
A. Lahiri
Keyword(s):  
Half Space ◽  
Heat Sources ◽  
Dimensional Problem ◽  
Eigenvalue Approach ◽  
One Dimensional ◽  
Coupled Equations ◽  
The Laplace Transform ◽  
Moving Plane ◽  
Generalized Thermoelastic ◽  
S Model

Abstract A one-dimensional problem for a homogeneous, isotropic and thermoelastic half-space subjected to a moving plane of heat source on the boundary of the space, which is traction free, is considered in the context of Lord- Shulaman model (L-S model) of thermoelasticity. The Laplace transform and eigenvalue approach techniques are used to solve the resulting non-dimensional coupled equations. Numerical results for the temperature, thermal stress, and displacement distributions are represented graphically and discussed

scholarly journals The Effect of Magnetic Field and Initial Stress on Fractional Order Generalized Thermoelastic Half-Space

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sunita Deswal ◽  
Sandeep Singh Sheoran ◽  
Kapil Kumar Kalkal
Keyword(s):  
Magnetic Field ◽  
Initial Stress ◽  
Half Space ◽  
Fractional Order ◽  
Generalized Thermoelasticity ◽  
Order Theory ◽  
Homogeneous Half Space ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Space Formulation

The aim of this paper is to study magneto-thermoelastic interactions in an initially stressed isotropic homogeneous half-space in the context of fractional order theory of generalized thermoelasticity. State space formulation with the Laplace transform technique is used to obtain the general solution, and the resulting formulation is applied to the ramp type increase in thermal load and zero stress. Solutions of the problem in the physical domain are obtained by using a numerical method of the Laplace inverse transform based on the Fourier expansion technique, and the expressions for the displacement, temperature, and stress inside the half-space are obtained. Numerical computations are carried out for a particular material for illustrating the results. Results obtained for the field variables are displayed graphically. Some comparisons have been shown in figures to present the effect of fractional parameter, ramp parameter, magnetic field, and initial stress on the field variables. Some particular cases of special interest have been deduced from the present investigation.

scholarly journals A One-Dimensional Thermoelastic Problem due to a Moving Heat Source under Fractional Order Theory of Thermoelasticity

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Tianhu He ◽  
Ying Guo
Keyword(s):  
Heat Source ◽  
Laplace Transform ◽  
Fractional Order ◽  
Order Parameter ◽  
Order Theory ◽  
Numerical Inversion ◽  
Moving Heat Source ◽  
Dimensional Problem ◽  
Governing Equations ◽  
One Dimensional

The dynamic response of a one-dimensional problem for a thermoelastic rod with finite length is investigated in the context of the fractional order theory of thermoelasticity in the present work. The rod is fixed at both ends and subjected to a moving heat source. The fractional order thermoelastic coupled governing equations for the rod are formulated. Laplace transform as well as its numerical inversion is applied to solving the governing equations. The variations of the considered temperature, displacement, and stress in the rod are obtained and demonstrated graphically. The effects of time, velocity of the moving heat source, and fractional order parameter on the distributions of the considered variables are of concern and discussed in detail.

Theory of Fractional Order Generalized Thermoelasticity

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Hamdy M. Youssef
Keyword(s):  
Heat Conduction ◽  
Laplace Transform ◽  
State Space ◽  
Uniqueness Theorem ◽  
Half Space ◽  
Fractional Order ◽  
Elastic Material ◽  
Generalized Thermoelasticity ◽  
New Model ◽  
One Dimensional

In this work, a new model of thermoelasticity theory has been constructed in the context of a new consideration of heat conduction with fractional order, and its uniqueness theorem has been approved also. One-dimensional application for a half-space of elastic material, which is thermally shocked, has been solved by using Laplace transform and state-space techniques. According to the numerical results and its graphs, conclusion about the new theory of thermoelasticity has been constructed.

scholarly journals Thermoelastic Diffusion Multicomponent Half-Space under the Effect of Surface and Bulk Unsteady Perturbations

2019 ◽  
Vol 24 (1) ◽  
pp. 26 ◽  
Author(s):  
Sergey Davydov ◽  
Andrei Zemskov ◽  
Elena Akhmetova
Keyword(s):  
Half Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Local Equilibrium ◽  
Linear Equations ◽  
Integral Form ◽  
External Effects ◽  
Thermoelastic Diffusion ◽  
One Dimensional ◽  
The Laplace Transform

This article presents an algorithm for solving the unsteady problem of one-dimensional coupled thermoelastic diffusion perturbations propagation in a multicomponent isotropic half-space, as a result of surface and bulk external effects. One-dimensional physico-mechanical processes, in a continuum, have been described by a local-equilibrium model, which included the coupled linear equations of an elastic medium motion, heat transfer, and mass transfer. The unknown functions of displacement, temperature, and concentration increments were sought in the integral form, which was a convolution of the surface and bulk Green’s functions and external effects functions. The Laplace transform on time and the Fourier sine and cosine transforms on the coordinate were used to find the Green’s functions. The obtained Green’s functions was analyzed. Test calculations were performed on the examples of some technological processes.

scholarly journals Eigen Value Approach to Generalized Thermoelastic Interactions in an Unbounded Body with Circular Cylindrical Cavity without Energy Dissipation

2017 ◽  
Vol 22 (4) ◽  
pp. 811-825 ◽  
Author(s):  
S. Chakraborty
Keyword(s):  
Energy Dissipation ◽  
Cylindrical Cavity ◽  
Generalized Thermoelasticity ◽  
Displacement Component ◽  
Eigen Value ◽  
The Laplace Transform ◽  
Circular Cylindrical Cavity ◽  
Matrix Differential ◽  
Vector Matrix ◽  
Without Energy Dissipation

Abstract The theory of generalized thermoelasticity in the context of the Green-Naghdi model -II (thermoelasticity without energy dissipation) is studied for an infinite circular cylindrical cavity subjected to two different cases of thermoelastic interactions when the radial stress is zero for (a) maintaining constant temperature and (b) temperature is varying exponentially with time. The Laplace transform from time variable is used to the governing equations to formulate a vector matrix differential equation which is then solved by the eigen value approach. Numerical computations for the displacement component, temperature distribution and components of thermal stress have been made and presented graphically.

scholarly journals Characterization of the Vibration and Strain Energy Density of a Nanobeam under Two-Temperature Generalized Thermoelasticity with Fractional-Order Strain Theory

2021 ◽  
Vol 26 (4) ◽  
pp. 78
Author(s):  
Hamzah Abdulrahman Alharthi
Keyword(s):  
Fractional Order ◽  
Numerical Solutions ◽  
Generalized Thermoelasticity ◽  
Strain Theory ◽  
Aspect Ratios ◽  
The Laplace Transform ◽  
Beam Thickness ◽  
Novel Model ◽  
Two Temperature

In this work, fractional-order strain theory was applied to construct a novel model that introduces a thermal analysis of a thermoelastic, isotropic, and homogeneous nanobeam. Under supported conditions of fixed aspect ratios, a two-temperature generalized thermoelasticity theory based on one relaxation time was used. The governing differential equations were solved using the Laplace transform, and their inversions were found by applying the Tzou technique. The numerical solutions and results for a thermoelastic rectangular silicon nitride nanobeam were validated and supported in the case of ramp-type heating. Graphs were used to present the numerical results. The two-temperature model parameter, beam size, ramp-type heat, and beam thickness all have a substantial influence on all of the investigated functions. Moreover, the parameter of the ramp-type heat might be beneficial for controlling the damping of nanobeam energy.

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