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

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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Electromagnetic Field and Three-Phase-Lag in a Compressed Rotating Isotropic Homogeneous Micropolar Thermo-Viscoelastic Half-Space

10.22541/au.160579082.27209018/v1 ◽

2020 ◽

Author(s):

S.M. Abo-Dahab ◽

A. Abd-Alla ◽

araby kilany

Keyword(s):

Magnetic Field ◽

Electromagnetic Field ◽

Initial Stress ◽

Half Space ◽

Viscoelastic Medium ◽

Normal Mode Analysis ◽

Mode Analysis ◽

Phase Lag ◽

Three Phase ◽

The Impact

A unified mathematical model of three-phase-lag in a compressed rotating isotropic homogeneous micropolar thermo-viscoelastic medium based on a ramp type thermal shock is developed. An application of this model is carried out to resolve the problem of a perfectly conducting half-space subjected to certain boundary conditions in the presence of an electromagnetic field. Lame’s potentials and normal mode analysis techniques are employed to get the general analytical solutions. Specific attention is paid to explore the impact of the rotation, magnetic field, ramp time, as well as initial stress on the distributions of temperature, displacement, stress, and induced electric and magnetic distribution. The findings show that the impact of the rotation, magnetic field, viscous, ramp parameter, initial stress, and phase-lag on the micropolar thermo-viscoelastic medium is noticeable.

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Two Temperature Magneto-Thermoelasticity with Initial Stress: State Space Formulation

Journal of Thermodynamics ◽

10.1155/2013/754798 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 7

Author(s):

Sunita Deswal ◽

Kapil Kumar Kalkal

Keyword(s):

State Space ◽

Generalized Thermoelasticity ◽

Elastic Half Space ◽

Mathematical Methods ◽

Initial Stress State ◽

Numerical Work ◽

Displacement Potential ◽

Suitable Material ◽

Space Formulation ◽

Propagation Of Waves

Magneto-thermoelastic interactions in an initially stressed isotropic homogeneous elastic half-space with two temperatures are studied using mathematical methods under the purview of the L-S model of linear theory of generalized thermoelasticity. The formalism deals with the state space approach with the purpose of counteracting the difficulties of handling the displacement potential functions. Of specific concern here is the propagation of waves owing to ramp type increase in temperature and load. The medium is considered to be permeated by a uniform magnetic field. The expressions for different field parameters such as displacement, temperature, strain, and stress in the physical domain are obtained by applying a numerical inversion technique. Results of some earlier workers have been deduced from the present formulation. Numerical work is also performed for a suitable material with the aim of illustrating the results.

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Two-temperature generalized magneto-thermoelastic medium for dual-phase-lag model under the effect of gravity field and hydrostatic initial stress

Multidiscipline Modeling in Materials and Structures ◽

10.1108/mmms-09-2015-0049 ◽

2016 ◽

Vol 12 (2) ◽

pp. 362-383 ◽

Cited By ~ 7

Author(s):

Samia M Said

Keyword(s):

Magnetic Field ◽

Gravity Field ◽

Initial Stress ◽

Mode Analysis ◽

Phase Lag ◽

Temperature Dependent ◽

Content Type ◽

Temperature Dependent Properties ◽

Hydrostatic Initial Stress ◽

Two Temperature

Purpose – The dual-phase-lag (DPL) model and Lord-Shulman theory with one relaxation time are applied to study the effect of the gravity field, the magnetic field, and the hydrostatic initial stress on the wave propagation in a two-temperature generalized thermoelastic problem for a medium with an internal heat source that is moving with a constant speed. The paper aims to discuss this issue. Design/methodology/approach – The exact expressions of the considered variables are obtained by using normal mode analysis. Findings – Numerical results for the field quantities are given in the physical domain and illustrated graphically in the absence and presence of the gravity field as well as the magnetic field. Comparisons are made between the results of the two different models with and without temperature dependent properties and for two different values of the hydrostatic initial stress. A comparison is also made between the results of the two different models for two different values of the time. Originality/value – In the present work, the author shall formulate a two-temperature generalized magneto-thermoelastic problem for a medium with temperature dependent properties and with an internal heat source that is moving with a constant speed under the influence of a gravity field and a hydrostatic initial stress. Normal mode analysis is used to obtain the exact expressions for the displacement components, thermodynamic temperature, conductive temperature, and stress components. A comparison is carried out between the considered variables as calculated from the generalized thermoelasticity based on the DPL model and the L-S theory in the absence and presence of a magnetic field as well as a gravity field. Comparisons are also made between the results of the two theories with and without temperature dependent properties and for two different values of hydrostatic initial stress. A comparison is also made between the results of the two different models for two different values of the time.

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

Journal of Mathematics ◽

10.1155/2013/489863 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 5

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.

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Surface Waves in a Viscoelastic Liquid Half-Space Under Initial Stress in Presence of Thermal and Magnetic Field

International Journal of Applied and Computational Mathematics ◽

10.1007/s40819-016-0191-6 ◽

2016 ◽

Vol 3 (2) ◽

pp. 1449-1467

Author(s):

Rajeev Ghatuary ◽

Nilratan Chakraborty

Keyword(s):

Magnetic Field ◽

Surface Waves ◽

Initial Stress ◽

Half Space ◽

Viscoelastic Liquid

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RAYLEIGH WAVE PROPAGATION WITH THE EFFECT OF INITIAL STRESS, MAGNETIC FIELD AND TWO TEMPERATURE IN THE DUAL PHASE LAG THERMOELASTICITY

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.9.100 ◽

2020 ◽

Vol 9 (9) ◽

pp. 7535-7545

Author(s):

A. Kumar ◽

Sangeeta ◽

H. Sharma

Keyword(s):

Magnetic Field ◽

Wave Propagation ◽

Rayleigh Wave ◽

Initial Stress ◽

Phase Lag ◽

Dual Phase ◽

Two Temperature

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Mathematical Model on Gravitational Electro-Magneto-Thermoelasticity with Two Temperature and Initial Stress in the Context of Three Theories

Mathematics ◽

10.3390/math8050735 ◽

2020 ◽

Vol 8 (5) ◽

pp. 735

Author(s):

Sayed M. Abo-Dahab ◽

Alaa A. El-Bary ◽

Yas Al-Hadeethi ◽

Mohamed Alkashif

Keyword(s):

Magnetic Field ◽

Initial Stress ◽

Two Dimensions ◽

Phase Lag ◽

Space Problem ◽

Type Iii ◽

Three Phase ◽

Stress Components ◽

Fundamental Equations ◽

Two Temperature

The main aim of this paper is to study two temperature thermoelasticity in a generalization form to solve the half-space problem of two dimensions under gravity, perturbed magnetic field, and initial stress. The fundamental equations are solved considering a new mathematical technique under Lord-Şhulman (LS), Green-Naghdi (GN type III) and three-phase-lag (3PHL) theories to investigate displacement, stress components, and temperature distribution. The results obtained by the three theories, i.e., (LS), (GN type III), and (3PHL), considering the absence and the presence of gravity, initial stress, and magnetic field have been compared. The results were numerically calculated and graphically displayed to exhibit the physical meaning of the phenomenon and the external parameters’ effect. A comparison has been presented between the results obtained in the absence and the presence of the external considered parameters and with the previously obtained results by other researchers.

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Rotation and Magnetic Field Effect on Surface Waves Propagation in an Elastic Layer Lying over a Generalized Thermoelastic Diffusive Half-Space with Imperfect Boundary

Mathematical Problems in Engineering ◽

10.1155/2015/671783 ◽

2015 ◽

Vol 2015 ◽

pp. 1-15 ◽

Cited By ~ 16

Author(s):

S. M. Abo-Dahab ◽

Kh. Lotfy ◽

A. Gohaly

Keyword(s):

Magnetic Field ◽

Surface Waves ◽

Half Space ◽

Attenuation Coefficient ◽

Elastic Layer ◽

Finite Thickness ◽

Relaxation Times ◽

Magnetic Field Effect ◽

Plane Boundary ◽

Special Cases

The aim of the present investigation is to study the effects of magnetic field, relaxation times, and rotation on the propagation of surface waves with imperfect boundary. The propagation between an isotropic elastic layer of finite thickness and a homogenous isotropic thermodiffusive elastic half-space with rotation in the context of Green-Lindsay (GL) model is studied. The secular equation for surface waves in compact form is derived after developing the mathematical model. The phase velocity and attenuation coefficient are obtained for stiffness, and then deduced for normal stiffness, tangential stiffness and welded contact. The amplitudes of displacements, temperature, and concentration are computed analytically at the free plane boundary. Some special cases are illustrated and compared with previous results obtained by other authors. The effects of rotation, magnetic field, and relaxation times on the speed, attenuation coefficient, and the amplitudes of displacements, temperature, and concentration are displayed graphically.

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