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Reflection of magneto-thermo-elastic waves from a rotating elastic half-space in generalized thermoelasticity under three theories

Othman M. I. A., Song Y.

Mechanics and Mechanical Engineering

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2011

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Vol. 15, nr 1

5-24

EN

The model of the equations of generalized magneto-thermoelasticity based on Lord-Shulman theory (LS) with one relaxation time, Green-Lindsay theory (GL) with two relaxation times, as well as the classical dynamical coupled theory (CD), is used to study the electro-magneto-thermoplastic interactions in a semi-infinite perfectly conducting solid. The entire elastic medium is rotating with a uniform angular velocity. There an initial magnetic field acts parallel to the plane boundary of the half-space. Reflection of magneto-thermoplastic waves under generalized thermoelasticity theory is employed to study the reflection of plane harmonic waves from a semi-infinite rotating elastic solid in a vacuum. The expressions for the reflection coefficients, which are the relations of the amplitudes of the reflected waves to the amplitude of the incident waves, are obtained. Similarly, the reflection coefficients ratios variation with the angle of incident under different conditions are shown graphically. Comparisons are made with the results predicted by the three theories in the presence and absence of rotation.

2

The effect of rotation and thermal shock on a perfect conducting elastic half-space in generalized magneto-thermoelasticity with two relaxation times

Othman M. I. A.

Mechanics and Mechanical Engineering

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2010

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Vol. 14, nr 1

31-55

EN

The propagation of electromagneto-thermoelastic disturbances produced by a thermal shock in a perfectly conducting elastic half-space when the entire elastic medium is rotating with a uniform angular velocity is investigated. The problem is in the context of the Green and Lindsay's generalized thermoelasticity with two relaxation times. There acts an initial magnetic field parallel to the plane boundary of the half-space. The medium deformed because of thermal shock, and due to the application of the magnetic field. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the considered variables are represented graphically. From the distributions, it can be found the wave type heat propagation in the medium. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourier's in essence. In generalized thermoelasticity theory heat propagates as a wave with finite velocity instead of infinite velocity in medium. Comparisons are made wit h the results predicted by the coupled theory in present and absent rotation.

3

Flexural and extensional waves propagation in transversely isotropic plates in generalized thermoelasticity

Verma K. L., Verma S. C., Hasebe N.

International Journal of Applied Mechanics and Engineering

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2004

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Vol. 9, no 3

587-606

EN

In this paper, the boundary value problem concerning the propagation of plane harmonic thermoelastic waves in flat infinite homogeneous transversely isotropic plate of finite thickness in the generalized theory of thermoelasticity with two thermal relaxation times is studied. The frequency equations for a heat conducting thermoelastic plate corresponding to the extensional (symmetric) and flexural (antisymmetric) thermoelastic modes of vibration are obtained and discussed. Special cases of the frequency equations are also discussed. The horizontally polarized SH wave gets decoupled from the rest of motion and propagates without dispersion or damping, and is not affected by thermal variations on the same plate. A numerical solution to the frequency equations for an aluminum plate (isotropic) and zinc plate (transversely isotropic) is given, and the dispersion curves are presented. The three motions namely, longitudinal, transverse and thermal of the medium are found dispersive and coupled with each other due to the thermal and anisotropic effects. The phase velocity of the waves is modified due to the thermal and anisotropic effects and is also influenced by the thermal relaxation time. Relevant results of previous investigations are deduced as special cases.