On the Initial Stress, Magnetic Field, Voids and Rotation Effects on Plane Waves in Generalized Thermoelasticity

El-Naggar, A. M.; Kishka, Z.; Abd-Alla, A. M.; Abbas, Ibrahim A.; Abo‐Dahab, S. M.; Elsagheer, M.

doi:10.1166/jctn.2013.2862

Cited by 54 publications

(26 citation statements)

References 24 publications

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“…The comparison between the approximate solutions which obtained, by using HPM (32) and VIM (38) is shown in Table 1. Now we make the comparison between the approximate solutions obtained by the variation iteration method and the approximate solution obtained by the homotopy perturbation method as shown in Figures 1, 2, 3, 4, and 5.…”

Section: The Vim For the Time-space Fractional Nonlinear Bbm Equationmentioning

confidence: 99%

“…Olszewski [31] studied the uncertainty relation between intervals of energy and time derived for the electromagnetic radiation of a harmonic oscillator. El-Naggar et al [32] investigated the initial stress, magnetic field, voids, and rotation effects on plane waves in generalized thermoelasticity. Khrennikov [33] discussed "Einstein's Dream" Quantum Mechanics as Theory of Classical Random Fields.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations

Gepreel

Nofal

Alotaibi

2013

Journal of Applied Mathematics

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We implement relatively analytical techniques, the homotopy perturbation method, and variational iteration method to find the approximate solutions for time and space fractional Benjamin-Bona Mahony equation. The fractional derivatives are described in the Caputo sense. These methods are used in applied mathematics to obtain the analytic approximate solutions for the nonlinear Bejamin-Bona Mahoney (BBM) partial fractional differential equation. We compare between the approximate solutions obtained by these methods. Also, we present the figures to compare between the approximate solutions. Also, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. We use the improved ( / )-expansion function method to find exact solutions of nonlinear fractional BBM equation.

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Section: The Vim For the Time-space Fractional Nonlinear Bbm Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations

Gepreel

Nofal

Alotaibi

2013

Journal of Applied Mathematics

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“…Some authors used Laurant's theorem [1]- [8] to express each complex potential as a power series, and others [9]- [16] used complex variable method of Cauchy integral. The extensive literature on the isotropic is now available and we can only mention a few recent interesting investigations in refs [17]- [26].…”

Section: Introductionmentioning

confidence: 99%

Presence of Heat on an Infinite Plate with a Curvilinear Hole Having Two Poles

Bayones¹

2015

JMP

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In the present paper Cauchy integral methods have been applied to derive exact and expressions for Goursat's function for the first and second fundamental problems of isotropic homogeneous perforated infinite elastic media in the presence of uniform flow of heat. For this, we considered the problem of a thin infinite plate of specific thickness with a curvilinear hole where the origins lie in the hole is conformally mapped outside a unit circle by means of a specific rational mapping. Moreover, the three stress components xx σ , yy σ and xy σ of the boundary value problem in the thermoelasticity plane are obtained. Many special cases of the conformal mapping and four applications for different cases are discussed and many main results are derived from the work.

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“…Sadeq et al 21 investigated the steady state thermoelasticity of hollow nanospheres. El-Naggar et al 22 discussed the initial stress, magnetic field, voids and rotation effects on plane waves in generalized thermoelasticity.…”

Section: Introductionmentioning

confidence: 99%

On Rayleigh Waves in a Homogeneous Orthotropic Electromagnetic Gravitational Half-Space Material with Rotation and Initial Stress Under Four Thermo-Elastic Models

Allam¹,

Rida²,

Mohamed³

et al. 2014

jnl of comp & theo nano

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In this paper, the effect of rotation with a uniform angular velocity, initial stress and gravity on Rayleigh waves in electro-magnetoelastic homogeneous orthotropic material half-space under four models of generalized thermoelasticity: Classical and Dynamical coupled model (CD), LordShulman model (LS), Green-Lindsay model (GL), Green-Naghdi model (GN type II) is devoted to study the problem. The Lame's potentials are used to obtain the frequency equation which determines the velocity of Rayleigh waves which obtained as a real part and the attenuation coefficient as imaginary part under the rotation, magnetic field, electric field, initial stress and gravity field. Numerical results have been obtained and illustrated graphically for each case. Comparison is made with the results predicted by the theories of thermo elasticity in the absence of electric field and heat flux.

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On the Initial Stress, Magnetic Field, Voids and Rotation Effects on Plane Waves in Generalized Thermoelasticity

Cited by 54 publications

References 24 publications

Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations

Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations

Presence of Heat on an Infinite Plate with a Curvilinear Hole Having Two Poles

On Rayleigh Waves in a Homogeneous Orthotropic Electromagnetic Gravitational Half-Space Material with Rotation and Initial Stress Under Four Thermo-Elastic Models

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