S. R. Mahmoud

A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets:

In this paper, a new higher-order shear and normal deformation theory for the bending and free vibration analysis of sandwich plates with functionally graded isotropic face sheets is developed. The number of unknown functions involved in the present theory is only five, as against six or more in case of other shear and normal deformation theories. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. The boundary conditions for the plate are assumed to be simply supported in all edges and in the static analysis, the plate is assumed to be subjected to a sinusoidally distributed load. Both symmetric and non-symmetric sandwich plates are considered. The equations of motion are obtained using Hamilton’s principle. Numerical results of present theory are compared with three-dimensional elasticity solutions and other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and efficient in predicting the bending and free vibration responses of sandwich plates with functionally graded isotropic face sheets.

On Generalized Magneto-thermoelastic Rayleigh Waves in a Granular Medium Under the Influence of a Gravity Field and Initial Stress

In this paper, the influence of magnetic field, gravity field and initial stress on Rayleigh waves propagation in a granular medium under incremental thermal stresses and relaxation times is studied. The frequency equation of Rayleigh waves is obtained in the form of a determinant containing a term involving the coefficient of friction of a granular medium. Some special cases are obtained from this study. Analytically, from the results obtained, one may illustrate that the effect of relaxation times, gravity field, initial stress and magnetic field on Rayleigh wave velocity are very pronounced. It is found that the frequency equation of Rayleigh waves changes with respect to this friction. When the medium is an orthotropic and the magnetic field and friction coefficient vanish, the derived frequency equation reduces to that obtained by Abd-Alla and Ahmed. Relevant results from previous investigations are deduced as special cases of this study.

A simple shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations

This paper deals with the thermo-mechanical deformation behaviour of shear deformable functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The presented theory is variationally consistent, does not require shear correction factor and gives rise to transverse shear stress variation such that the transverse shear stresses vary in hyperbolic manner across the thickness satisfying shear stress-free surface conditions. A power-law distribution for the mechanical characteristics is adopted to model the continuous variation of properties from those of one component to those of the other. The sandwich plate faces are made of isotropic, two-constituent (ceramic–metal) material distribution through the thickness. The core layer is still homogeneous and made of an isotropic metal material. Several kinds of non-symmetric sandwich plates are presented. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical results of the present simple shear deformation theory are presented to show the effect of material distribution and foundation parameters on the deflections and stresses. A wide variety of results is presented for the static response of sandwich plates under thermo-mechanical loads.

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.

EFFECT OF THE ROTATION ON WAVE MOTION THROUGH CYLINDRICAL BORE IN A MICROPOLAR POROUS MEDIUM

In the present paper, we have studied the propagation of axial symmetric cylindrical surface waves through rotating cylindrical bore in a micropolar porous medium of infinite extent possessing cubic symmetry. The frequency equation for surface wave propagation in the micropolar porous medium has been derived and liquid filled bore are derived. The effect of the rotation on phase velocity of surface wave has been studied in detail. Radius of bore and other material parameters for empty and liquid filled bore are derived. A particular case of interest has been deduced. Numerical results have been obtained and illustrated graphically to understand the behavior of phase velocity versus wave number of a wave. The results have indicated that the effect of rotation on phase velocity is highly pronounced. Comparisons are made in the absence of rotation.

Modeling a Microstretch Thermoelastic Body with Two Temperatures

We consider a theory of thermoelasticity constructed by taking into account the heat conduction in deformable bodies which depends on two temperatures. The first one is the conductive temperature, the second is the thermodynamic temperature, and the difference between them is proportional to the heat supply.

Nonsimple material problems addressed by the Lagrange’s identity

Our paper is concerned with some basic theorems for nonsimple thermoelastic materials. By using the Lagrange identity, we prove the uniqueness theorem and some continuous dependence theorems without recourse to any energy conservation law, or to any boundedness assumptions on the thermoelastic coefficients. Moreover, we avoid the use of positive definiteness assumptions on the thermoelastic coefficients.

Effect of Rotation and Magnetic Field through Porous Medium on Peristaltic Transport of a Jeffrey Fluid in Tube

This paper is concerned with the analysis of peristaltic motion of a Jeffrey fluid in a tube with sinusoidal wave travelling down its wall. The effect of rotation, porous medium, and magnetic field on peristaltic transport of a Jeffrey fluid in tube is studied. The fluid is electrically conducting in the presence of rotation and a uniform magnetic field. An analytic solution is carried out for long wavelength, axial pressure gradient, and low Reynolds number considerations. The results for pressure rise and frictional force per wavelength were obtained, evaluated numerically, and discussed briefly.

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.