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

In this paper is investigating the theory of generalized thermoelasticity under two temperature is used to solve boundary value problems of 2-D half-space its bound?ary with different types of heating under gravity effect. The governing equations are solved using new mathematical methods under the context of Lord-Shulman, Green-Naghdi theory of type III (G-N III) and the three-phase-lag model to inves?tigate the surface waves in an isotropic elastic medium subjected to gravity field, magnetic field, and initial stress. The general solution obtained is applied to a spe?cific problem of a half-space and the interaction with each other under the influence of gravity. The physical domain by using the harmonic vibrations is used to obtain the exact expressions for the Waves velocity and attenuation coefficients for Stoneley waves, Love waves, and Rayleigh waves. Comparisons are made with the results between the three theories. Numerical work is also performed for a suitable material with the aim of illustrating the results. The results obtained are calculated numerical?ly and presented graphically with some comparisons in the absence and the presence the influence of gravity, initial stress and magnetic field. It clears that the results ob?tained agree with the physical practical results and agree with the previous results if the gravity, two temperature, and initial stress neglect as special case from this study.

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Magnetic field on surface waves propagation in gravitational thermoelastic media with two temperature and initial stress in the context of three theories

Thermal Science ◽

10.2298/tsci20285b ◽

2020 ◽

Vol 24 (Suppl. 1) ◽

pp. 285-299

Author(s):

Jamel Bouslimi ◽

Sayed Abo-Dahab ◽

Khaled Lotfy ◽

Sayed Abdel-Khalek ◽

Eied Khalil ◽

...

Keyword(s):

Magnetic Field ◽

Surface Waves ◽

Initial Stress ◽

Half Space ◽

Generalized Thermoelasticity ◽

Phase Lag ◽

Mathematical Methods ◽

Numerical Work ◽

Suitable Material ◽

Two Temperature

In this paper is investigating the theory of generalized thermoelasticity under two temperature is used to solve boundary value problems of 2-D half-space its bound?ary with different types of heating under gravity effect. The governing equations are solved using new mathematical methods under the context of Lord-Shulman, Green-Naghdi theory of type III (G-N III) and the three-phase-lag model to inves?tigate the surface waves in an isotropic elastic medium subjected to gravity field, magnetic field, and initial stress. The general solution obtained is applied to a spe?cific problem of a half-space and the interaction with each other under the influence of gravity. The physical domain by using the harmonic vibrations is used to obtain the exact expressions for the Waves velocity and attenuation coefficients for Stoneley waves, Love waves, and Rayleigh waves. Comparisons are made with the results between the three theories. Numerical work is also performed for a suitable material with the aim of illustrating the results. The results obtained are calculated numerical?ly and presented graphically with some comparisons in the absence and the presence the influence of gravity, initial stress and magnetic field. It clears that the results ob?tained agree with the physical practical results and agree with the previous results if the gravity, two temperature, and initial stress neglect as special case from this study.

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2D PROBLEM FOR A SPHERE IN THE FRACTIONAL ORDER THEORY THERMOELASTICITY TO AXISYMMETRIC TEMPERATURE DISTRIBUTION

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.11.1.1 ◽

2022 ◽

Vol 11 (1) ◽

pp. 1-15

Author(s):

S.G. Khavale ◽

K.R. Gaikwad

Keyword(s):

Temperature Distribution ◽

Fractional Order ◽

Direct Method ◽

Order Theory ◽

Laplace Transform Technique ◽

The Laplace Transform ◽

Copper Material ◽

Mathcad Software ◽

Axisymmetric Temperature ◽

A Direct Method

In the present article, we implement the fractional thermoelasticity theory to a 2D issue for a sphere whose surface is free from traction, subject to a provided axisymmetric temperature distribution of heat. The medium is supposed to be quiescent initially. A direct method is used to get a solution and the Laplace transform technique is used. Mathematical models for copper material are designed as a particular instance. Numerical results are computed with help of Mathcad software and graphically represented and the fractional-order parameter effect has been explained.

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A Study on Fractional Order Thermoelastic Half Space

International Journal of Applied Mechanics and Engineering ◽

10.2478/ijame-2020-0058 ◽

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.

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Thermoelastic fractional derivative model for exciting viscoelastic microbeam resting on Winkler foundation

Journal of Vibration and Control ◽

10.1177/1077546320956528 ◽

2020 ◽

pp. 107754632095652 ◽

Cited By ~ 1

Author(s):

Ahmed E Abouelregal

Keyword(s):

Fractional Derivative ◽

Fractional Order ◽

Governing Equation ◽

Axial Load ◽

Generalized Thermoelasticity ◽

Beam Theory ◽

Order Theory ◽

Winkler Foundation ◽

Laplace Transform Technique ◽

Viscoelastic Microbeam

In the current investigation, the thermoelastic vibration of a viscoelastic microbeam resting on the Winkler foundation is studied using the fractional-order theory. To describe the damping of the viscoelastic material according to experimental results, the Kelvin–Voigt model is replaced by a new form with a fractional-order derivative. The generalized thermoelasticity model and Euler–Bernoulli beam theory are used to construct the governing equation. The microbeam is subjected to axial load, ultrafast laser heating, and varying sinusoidal heat. The governing equation is then solved using the Laplace transform technique to determine the deflection and thermoelastic interaction responses of microbeams. The effects of many parameters such as the coefficient of viscosity, axial load, fractional derivative order, laser pulse duration, and foundation parameter on the microbeam response are explained and discussed in detail.

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Effect of variable thermal conductivity on a half-space under the fractional order theory of thermoelasticity

International Journal of Mechanical Sciences ◽

10.1016/j.ijmecsci.2013.05.016 ◽

2013 ◽

Vol 74 ◽

pp. 185-189 ◽

Cited By ~ 77

Author(s):

H. Sherief ◽

A.M. Abd El-Latief

Keyword(s):

Thermal Conductivity ◽

Half Space ◽

Fractional Order ◽

Order Theory ◽

Variable Thermal Conductivity

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Fractional order generalized thermoelastic response in a half space due to a periodically varying heat source

Multidiscipline Modeling in Materials and Structures ◽

10.1108/mmms-04-2017-0022 ◽

2018 ◽

Vol 14 (1) ◽

pp. 2-15 ◽

Cited By ~ 2

Author(s):

Jitesh Tripathi ◽

Shrikant Warbhe ◽

K.C. Deshmukh ◽

Jyoti Verma

Keyword(s):

Mathematical Model ◽

Heat Source ◽

Laplace Transform ◽

Half Space ◽

Fractional Order ◽

Order Parameter ◽

Order Theory ◽

Numerical Inversion ◽

Content Type ◽

Copper Material

Purpose The present work is concerned with the solution of a fractional-order thermoelastic problem of a two-dimensional infinite half space under axisymmetric distributions in which lower surface is traction free and subjected to a periodically varying heat source. The thermoelastic displacement, stresses and temperature are determined within the context of fractional-order thermoelastic theory. To observe the variations of displacement, temperature and stress inside the half space, the authors compute the numerical values of the field variables for copper material by utilizing Gaver-Stehfast algorithm for numerical inversion of Laplace transform. The effects of fractional-order parameter on the variations of field variables inside the medium are analyzed graphically. The paper aims to discuss these issues. Design/methodology/approach Integral transform technique and Gaver-Stehfast algorithm are applied to prepare the mathematical model by considering the periodically varying heat source in cylindrical co-ordinates. Findings This paper studies a problem on thermoelastic interactions in an isotropic and homogeneous elastic medium under fractional-order theory of thermoelasticity proposed by Sherief (Ezzat and El-Karamany, 2011b). The analytic solutions are found in Laplace transform domain. Gaver-Stehfast algorithm (Ezzat and El-Karamany, 2011d; Ezzat, 2012; Ezzat, El Karamany, Ezzat, 2012) is used for numerical inversion of the Laplace transform. All the integrals were evaluated using Romberg’s integration technique (El-Karamany et al., 2011) with variable step size. A mathematical model is prepared for copper material and the results are presented graphically with the discussion on the effects of fractional-order parameter. Research limitations/implications Constructed purely on theoretical mathematical model by considering different parameters and the functions. Practical implications The system of equations in this paper may prove to be useful in studying the thermal characteristics of various bodies in real-life engineering problems by considering the time fractional derivative in the field equations. Originality/value In this problem, the authors have used the time fractional-order theory of thermoelasticity to solve the problem for a half space with a periodically varying heat source to control the speed of wave propagation in terms of heat and elastic waves for different conductivity like weak conductivity, moderate conductivity and super conductivity which is a new and novel contribution.

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