Free Vibrations in a Spherical Non-Homogeneous Elastic Region

Abd-Alla, A. M.

doi:10.1166/jctn.2013.3148

Cited by 5 publications

(3 citation statements)

References 9 publications

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“…(10) and (33), Substituting from Eqs. (24), (28), (29), (36) and (37) in the above equation, we get,…”

Section: Boundary Conditionsmentioning

confidence: 99%

On Magnetic Field and Two Thermal Relaxation Times for p-Waves Propagation at Interface Between Two Solid Liquid Media Under Initial Stress and Heat Sources

Abo‐Dahab¹

2015

Jnl of Comp & Theo Nano

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In this paper an investigation is made to study the effects of two thermal relaxation times, heat sources, initial stress, and magnetic field on propagation of p-waves propagation. The GreenLindsay theory is devoted to solve the problem. The boundary conditions at the interface are applied. The appropriate expressions to find the amplitudes ratios for the incident p-waves have been obtained. The amplitudes ratios of reflection and transmitted coefficients for the incident waves are computed numerically, considering the heat sources, initial stress, and magnetic field effects and the results obtained have been presented graphically.

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“…(10) and (33), Substituting from Eqs. (24), (28), (29), (36) and (37) in the above equation, we get,…”

Section: Boundary Conditionsmentioning

confidence: 99%

On Magnetic Field and Two Thermal Relaxation Times for p-Waves Propagation at Interface Between Two Solid Liquid Media Under Initial Stress and Heat Sources

Abo‐Dahab¹

2015

Jnl of Comp & Theo Nano

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“…[45][46][47][48][49][50][51][52][53][54][55][56][57][58]. Recently Lotfy and Abo-Dahab 59 investigated a two-dimensional problem of two temperature generalized thermoelasticity with normal mode analysis under thermal shock problem.…”

Section: Abo-dahab and Lotfymentioning

confidence: 99%

Generalized Magneto-Thermoelasticity with Fractional Derivative Heat Transfer for a Rotation of a Fibre-Reinforced Thermoelastic

Abo‐Dahab¹,

Lotfy²

2015

j comput theor nanosci

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An electro-magneto thermoelastic coupled problem for a homogeneous, isotropic, thermally and electrically conducting half-space solid whose surface is subjected to a thermal shock is considered in two-dimensional space. We introduced the coupled theory (CD), Lord-Schulman (LS) theory and Green-Lindsay (GL) theory to study the influence of fractional derivative heat transfer allowing the second sound effects of magnetic field and rotation on 2-D problem of a fibre-reinforced thermoelastic. The methodology applied here is use of the normal mode analysis is used to solve the problem of a thermal shock problem. Some particular cases are also discussed in the context of the problem. Deformation of a body depends on the nature of force applied as well as the type of boundary conditions. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons have been shown in figures to estimate the effect of the fractional order on all the studied fields.

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“…The extensive literature on the topic is now available and we can only mention a few recent interesting investigations in Refs. [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Problem of Two Temperature Generalized Thermoelasticity with Normal Mode Analysis Under Thermal Shock Problem

Lotfy¹,

Abo‐Dahab²

2015

j comput theor nanosci

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The theory of two-temperature generalized thermoelasticity based on the theory of Youssef is used to solve boundary value problems of two dimensional half-space with heating its boundary with different types of heating. The governing equations are solved using new mathematical methods under the purview of the Lord-Şhulman (LS) and the classical dynamical coupled theory (CD). The general solution obtained is applied to a specific problem of a half-space subjected to one types of heating the thermal shock type. The normal mode method is used to obtain the exact expressions for the displacement components, force stresses and temperature distribution. The variations of the considered variables through the horizontal distance are illustrated graphically. Comparisons are made with the results between the two theories. Numerical work is also performed for a suitable material with the aim of illustrating the results. The conductive temperature, the dynamical temperature, the stress and the strain distributions are shown graphically with some comparisons.

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Free Vibrations in a Spherical Non-Homogeneous Elastic Region

Cited by 5 publications

References 9 publications

On Magnetic Field and Two Thermal Relaxation Times for p-Waves Propagation at Interface Between Two Solid Liquid Media Under Initial Stress and Heat Sources

On Magnetic Field and Two Thermal Relaxation Times for p-Waves Propagation at Interface Between Two Solid Liquid Media Under Initial Stress and Heat Sources

Generalized Magneto-Thermoelasticity with Fractional Derivative Heat Transfer for a Rotation of a Fibre-Reinforced Thermoelastic

Two-Dimensional Problem of Two Temperature Generalized Thermoelasticity with Normal Mode Analysis Under Thermal Shock Problem

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