A. M. Abd-Alla

Propagation of S-wave in a non-homogeneous anisotropic incompressible and initially stressed medium under influence of gravity field

In this paper, propagation of shear waves in a non-homogeneous anisotropic incompressible, gravity field and initially stressed medium is studied. Analytical analysis reveals that the velocity of propagation of the shear waves depends upon the direction of propagation, the anisotropy, gravity field, non-homogeneity of the medium, and the initial stress. The frequency equation that determines the velocity of the shear wave has been obtained. The dispersion equations have been obtained and investigated for different cases. A comparison is made with the results predicted by Abd-Alla et al. [22] in the absence of initial stress and gravity field. The results obtained are discussed and presented graphically.

Propagation of Rayleigh waves in magneto-thermo-elastic half-space of a homogeneous orthotropic material under the effect of rotation, initial stress and gravity field

The propagation of magneto-thermoelastic plane waves in an initially stressed, homogeneous orthotropic, conducting half-space under a magnetic field, rotation and gravity field have been investigated. The generalized theory of thermoelasticity is employed, by assuming the mechanical behavior as dynamic, to study the problem. The Lame’s potential is used to obtain the frequency equation that determines the velocity of Rayleigh waves that obtained as a real part and the attenuation coefficient as an imaginary part under the rotation, magnetic field, initial stress and gravity field. Numerical results have been given and illustrated graphically for each case considered. Dispersion curves of wave propagation are represented graphically in different theories of thermoelasticity. The results indicate that the effect of rotation, initial stress and gravity field are very pronounced. Comparison is made with the results predicted by the theory of thermoelasticity in the absence of rotation, initial stress and gravity field.

Effect of the rotation on a non-homogeneous infinite cylinder of orthotropic material

The present investigation is concerned with a study effect of non-homogeneous on the elastic stresses in rotating orthotropic infinite circular cylinder subjected to certain boundary conditions. Closed form stress solutions are obtained for rotating orthotropic cylinder with constant thickness for three cases: (1) a solid cylinder; (2) cylinder mounted on a circular rigid shaft; and (3) cylinder with a circular hole at the center. Analytical expressions for the components of the displacement and the stress in different cases are obtained. The effect of the rotation and non-homogeneity on the displacement and stress are studied. Numerical results are given and illustrated graphically for each case is considered. The effects rotating and non-homogeneity are discussed. Comparisons are made with the results predicted in the presence and absence of rotation.

On the problem of radial vibrations in non-homogeneity isotropic cylinder under influence of initial stress and magnetic field

In the present work, the effects of initial stress, magnetic field and non-homogeneity on wave propagation of free harmonic waves in isotropic material are discussed. The one-dimensional equation of elastodynamic is solved in terms of radial displacement and different cases of the boundary conditions for the hollow cylinder are considered. The determination is concerned with the eigenvalues of the natural frequencies of the radial vibrations for different boundary conditions in the case of harmonic vibrations. Numerical results are given and illustrated graphically for each case considered. Comparisons are made with the results in the absence of initial stress, magnetic field and non-homogeneity.

EFFECT OF THE ROTATION ON PLANE VIBRATIONS IN A TRANSVERSELY ISOTROPIC INFINITE HOLLOW CYLINDER

In the present paper, a technique is presented for obtaining estimates for the natural frequencies of axisymmetric vibration for transversely isotropic material. The wave propagation of harmonic waves in hollow cylinder of transversely isotropic materials subjected to certain boundary conditions is studied. The two-dimensional equations of elastodynamic are solved in terms of displacement by using the technique of variables separation. The natural frequency of the plane vibrations in the case of harmonic vibrations has been obtained. The natural frequencies are calculated numerically and the effects of rotation is discussed. The numerical results obtained have been illustrated graphically to understand the behavior of natural frequency versus the ratio h. Comparisons are made with the result in the absence of rotation.

SV-waves incidence at interface between solid-liquid media under magnetic field, initial stress and two thermal relaxation times

In this paper we investigated the propagation of SV-waves under effect of the magnetic field, initial stress and two thermal relaxation times. The problem of reflection and transmission of thermoelastic waves at a solid-liquid interface in presence of initial stress and magnetic field has been investigated subjected to certain boundary conditions. The appropriate expressions to find the amplitudes ratios for the incident wave (SV-waves) have been obtained. The reflection and transmitted coefficients for the incident SV-waves are computed numerically, considering the initial stress, relaxation times, and magnetic field effect and presented graphically. The results indicate that the effects of magnetic field, initial stress and two thermal relaxation times are very pronounced.

Green Lindsay model on reflection and refraction of p- and SV-waves at interface between solid-liquid media presence in magnetic field and initial stress:

In this paper, the reflection and transmission of thermoelastic wave at a solid-liquid interface in presence of initial stress and magnetic field is investigated in context of GL model. After solving the governing equations, we can find the two reflection and refraction coefficients of incident p-(pressure) and SV- (shear vertical) waves in presence of initial stress and magnetic field. The boundary conditions at the interface that: (i) displacement continuity, (ii) vanishing the tangential displacement, (iii) continuity of normal force per unit initial area, (iv) tangential force per unit initial area must vanish, and (v) continuity of temperature is applied. The appropriate expressions to find the amplitude ratios for the two incidence waves (p- and SV-waves) have been obtained. A numerical example is considered for the reflection and transmitted coefficients of the incident waves, in which we study the effect of initial stresses and magnetic field. The results obtained are presented graphically for the effect of magnetic field and initial stress to display the phenomena physical meaning.

The problem of wave propagation in magneto-rotating orthotropic non-homogeneous medium

The present investigation is concerned with a study effect of rotation and magnetic field on the plane deformation and the corresponding stresses in hollow elastic cylinder rotating about its axis with a constant angular velocity. The material of the cylinder is assumed to the non-homogeneous and orthotropic. Results of this paper are presented graphically and then compared with others in the absence of magnetic field, rotation and non-homogeneity. The results indicate that the effect of rotation and non-homogeneity are very pronounced. The variation of stresses and displacements has been shown graphically.