Magnetoelastic longitudinal wave propagation in a transversely isotropic circular cylinder

Abd-alla, Abo-el-nour N.; Abbas, Ibrahim A.

doi:10.1016/s0096-3003(01)00012-1

Cited by 7 publications

(5 citation statements)

References 15 publications

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“…For numerical calculations, we consider the following transformation

\begin{matrix} left Ω^{*} = \frac{ω}{ω^{*}}, ω^{*} = \frac{c_{2}}{b}, Ω_{1} = β_{1} Ω, \\ left β_{1} = \frac{c_{2}}{c_{1}}, β_{2} = \frac{c_{2}}{c}, h = \frac{a}{b} . \end{matrix}

The calculations of the roots of the frequency equation , represent a major task and requires extensive effort of numerical computations. The computations have been carried out on an electronic computer for the case of Zinc Oxide which has the following physical constants , where 1 Gauss/Oersted

= 4 (π) 10^{- 7}

Tm/A.

\begin{matrix} true \\ right \begin{matrix} ρ = 5676 kg / m^{3} & c_{13} = 10.51 (10^{10}) normalN / m^{2} & c_{66} = 4.25 (10^{10}) normalN / m^{2} \\ c_{11} = 20.97 (10^{10}) normalN / m^{2} & c_{33} = 21.09 (10^{10}) normalN / m^{2} & c = 3 (10^{8}) normalm / \sec \\ c_{12} = 12.11 (10^{10}) normalN / m^{2} & c_{44} = 4.25 (10^{10}) normalN / m^{2} & μ_{o} \end{matrix} \end{matrix}

…”

Section: The Numerical Resultsmentioning

confidence: 99%

“…Consider decomposition of the displacement vector of the form

u = \nabla Φ + \nabla \times Ψ

to separate the dilatational and rotational components of strain. There for the displacement components become and :

u_{r} (r, θ, t) = Φ_{, r} + (1 / r) Ψ,_{θ}, u_{θ} (r, θ, t) = (1 / r) Φ_{, θ} - Ψ,_{r}

where

Ψ (r, θ, t) = (0, 0, Ψ)

.…”

Section: Formulation Of the Problem And Basic Equationsmentioning

confidence: 99%

“…Abd‐alla et al. considered magnetoelastic longitudinal wave propagation in a transversely isotropic circular cylinder. Das and Bhattacharya , Andreou and Dassios investigated the problems of elastic wave in the presence of a steady magnetic field.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The influence of hydrostatic stress on the frequency equation of flexural waves in a magnetoelastic transversly isotropic circular cylinder

Abd-alla

Raizah

Placidi

2015

Z. Angew. Math. Mech.

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In this paper, we investigated the influence of initial stress on the frequency equation of flexural waves in a transversely isotropic circular cylinder permeated by a magnetic field. The problem is represented by the equations of elasticity taking into account the effect of the magnetic field as given by Maxwell's equations in the quasi‐static approximation. The free stress conditions on the inner and outer surfaces of the hollow circular cylinder were used to form a frequency equation in terms of the wavelength, the cylinder radii, the initial stress and the material constants. The frequency equations have been derived in the form of a determinant involving Bessel functions and its roots given the values of the characteristic circular frequency parameters of the first three modes for various geometries. These roots, which correspond to various modes, have been verified numerically and represented graphically in different values for the initial stress. It is recognized that the flexural elastic waves in a solid body propagated under the influence of initial stress can be differentiated in a clear manner from those propagated in the absence of an initial stress. We also observed the initial stress has a great effect on the propagation of magnetoelastic flexural waves. Therefore this research is theoretically useful to convey information on electromagnetic properties of the material: for example through a precise measurement of the surface current induced by the presence of the magnetic field.

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“…For numerical calculations, we consider the following transformation

\begin{matrix} left Ω^{*} = \frac{ω}{ω^{*}}, ω^{*} = \frac{c_{2}}{b}, Ω_{1} = β_{1} Ω, \\ left β_{1} = \frac{c_{2}}{c_{1}}, β_{2} = \frac{c_{2}}{c}, h = \frac{a}{b} . \end{matrix}

= 4 (π) 10^{- 7}

Tm/A.

\begin{matrix} true \\ right \begin{matrix} ρ = 5676 kg / m^{3} & c_{13} = 10.51 (10^{10}) normalN / m^{2} & c_{66} = 4.25 (10^{10}) normalN / m^{2} \\ c_{11} = 20.97 (10^{10}) normalN / m^{2} & c_{33} = 21.09 (10^{10}) normalN / m^{2} & c = 3 (10^{8}) normalm / \sec \\ c_{12} = 12.11 (10^{10}) normalN / m^{2} & c_{44} = 4.25 (10^{10}) normalN / m^{2} & μ_{o} \end{matrix} \end{matrix}

…”

Section: The Numerical Resultsmentioning

confidence: 99%

“…Consider decomposition of the displacement vector of the form

u = \nabla Φ + \nabla \times Ψ

to separate the dilatational and rotational components of strain. There for the displacement components become and :

u_{r} (r, θ, t) = Φ_{, r} + (1 / r) Ψ,_{θ}, u_{θ} (r, θ, t) = (1 / r) Φ_{, θ} - Ψ,_{r}

where

Ψ (r, θ, t) = (0, 0, Ψ)

.…”

Section: Formulation Of the Problem And Basic Equationsmentioning

confidence: 99%

See 1 more Smart Citation

The influence of hydrostatic stress on the frequency equation of flexural waves in a magnetoelastic transversly isotropic circular cylinder

Abd-alla

Raizah

Placidi

2015

Z. Angew. Math. Mech.

Self Cite

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“…21 Abd-alla and Abbas investigated the magnetoelastic longitudinal wave propagation in a transversely isotropic circular cylinder. 22 Mykityuk studied the thermoelastic vibrations of a thick-walled cylinder of time-varying thickness. 23 Zhitnyaya analyzed an uncoupled problem of the thermoelastic vibrations of a cylinder.…”

Section: Introductionmentioning

confidence: 99%

Exact Solution for a Free Vibration of Thermoelastic Hollow Cylinder Under GNIII Model

Abbas¹

2016

IJAV

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The exact analytic solutions are obtained with the use of the eigenvalue approach for a free vibration problem of a thermoelastic hollow cylinder in the context of Green and Naghdi theory (GNIII). The dispersion relations for the existence of various types of possible modes of vibrations in the considered hollow cylinder are derived in a compact form and the validation of the roots for the dispersion relation is presented. To illustrate the analytic results, the numerical solution of various relations and equations has been carried out to compute the frequency, thermoelastic damping and frequency shift of vibrations in a hollow cylinder of copper material with MATHEMATICA and MATLAB software.

show abstract

“…Abd-alla and Abbas [21] studied the longitudinal wave propagation in a transversely isotropic circular cylinder under primary magnetic field. Mykityuk [22] studied the thermoelastic vibrations of a thick-walled cylinder of time-varying thickness.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of a thermoelastic hollow cylinder with one relaxation time

Abbas

Hobiny

2015

Can. J. Phys.

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The aim of this paper is to study the free vibration problem of a thermoelastic hollow cylinder in the context of the Lord and Shulman theory with one relaxation time. The eigenvalue approach is used to get the analytical solutions. The dispersion relations for the existence of various types of possible modes of vibrations are obtained. The validation of the roots for the dispersion relation is presented. The numerical results of frequency shift, natural frequency, and thermoelastic damping of vibrations have been presented graphically. PACS No.: 62.20.Dc. Résumé : Nous étudions ici les vibrations libres d'un cylindre creux fait d'un matériau thermoélastique, en utilisant la théorie de Lord et Shulman avec un seul temps de relaxation. Nous utilisons une approche aux valeurs propres afin de trouver des solutions analytiques et obtenons les relations de dispersion pour les différents modes possibles de vibration. Nous validons les racines de ces relations de dispersion. Nous présentons graphiquement le déplacement en fréquence, la fréquence naturelle et l'amortissement thermoélastique des vibrations. [Traduit par la Rédaction]

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Magnetoelastic longitudinal wave propagation in a transversely isotropic circular cylinder

Cited by 7 publications

References 15 publications

The influence of hydrostatic stress on the frequency equation of flexural waves in a magnetoelastic transversly isotropic circular cylinder

The influence of hydrostatic stress on the frequency equation of flexural waves in a magnetoelastic transversly isotropic circular cylinder

Exact Solution for a Free Vibration of Thermoelastic Hollow Cylinder Under GNIII Model

Free vibration of a thermoelastic hollow cylinder with one relaxation time

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