scholarly journals Influence of Initial Stress and Gravity Field on Propagation of Rayleigh and Stoneley Waves in a Thermoelastic Orthotropic Granular Medium

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
S. M. Ahmed ◽  
S. M. Abo-Dahab
Keyword(s):  
Gravity Field ◽  
Initial Stress ◽  
Physical Meaning ◽  
Rayleigh Waves ◽  
Granular Medium ◽  
Frequency Equation ◽  
Eighth Order ◽  
Stoneley Waves ◽  
Complex Roots ◽  
Determinantal Expression

The propagation of Rayleigh and Stoneley waves in a thermoelastic orthotropic granular half-space supporting a different layer under the influence of initial stress and gravity field is studied. The frequency equation of Rayleigh waves in the form of twelfth-order determinantal expression and the frequency equation of Stoneley waves in the form of eighth-order determinantal expression are obtained. The standard equation of dispersion is discussed to obtain Rayleigh and Stoneley waves that have complex roots; the real part gives the velocity of Rayleigh or Stoneley waves but the imaginary part gives the attenuation coefficient. Finally, the numerical results have been given and illustrated graphically, and their physical meaning has been explained.

scholarly journals Stoneley waves in a non-homogeneous orthotropic granular medium under the influence of gravity

2005 ◽  
Vol 2005 (19) ◽  
pp. 3145-3155 ◽  
Author(s):  
S. M. Ahmed
Keyword(s):  
Gravity Field ◽  
Granular Medium ◽  
Frequency Equation ◽  
Sixth Order ◽  
Stoneley Waves ◽  
Determinantal Expression

The aim of this paper is to investigate the Stoneley waves in a non-homogeneous orthotropic granular medium under the influence of a gravity field. The frequency equation obtained, in the form of a sixth-order determinantal expression, is in agreement with the corresponding result when both media are elastic. The frequency equation when the gravity field is neglected has been deduced as a particular case.

scholarly journals Rayleigh waves in a thermoelastic granular medium under initial stress

2000 ◽  
Vol 23 (9) ◽  
pp. 627-637 ◽  
Author(s):  
S. M. Ahmed
Keyword(s):  
Initial Stress ◽  
Rayleigh Waves ◽  
Granular Medium ◽  
Thermal Stresses ◽  
Frequency Equation ◽  
Determinantal Expression

We study the effect of initial stress on the propagation of Rayleigh waves in a granular medium under incremental thermal stresses. We also obtain the frequency equation, in the form of a twelfth-order determinantal expression, which is in agreement with the corresponding classical results.

scholarly journals Rayleigh Waves in Generalized Magneto-Thermo-Viscoelastic Granular Medium under the Influence of Rotation, Gravity Field, and Initial Stress

2011 ◽  
Vol 2011 ◽  
pp. 1-47 ◽  
Author(s):  
A. M. Abd-Alla ◽  
S. M. Abo-Dahab ◽  
F. S. Bayones
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Surface Waves ◽  
Gravity Field ◽  
Initial Stress ◽  
Attenuation Coefficient ◽  
Rayleigh Waves ◽  
Granular Medium ◽  
Granular Media ◽  
Special Cases

The surface waves propagation in generalized magneto-thermo-viscoelastic granular medium subjected to continuous boundary conditions has been investigated. In addition, it is also subjected to thermal boundary conditions. The solution of the more general equations are obtained for thermoelastic coupling. 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 media which determines Rayleigh waves velocity as a real part and the attenuation coefficient as an imaginary part, and the effects of rotation, magnetic field, initial stress, viscosity, and gravity field on Rayleigh waves velocity and attenuation coefficient of surface waves have been studied in detail. Dispersion curves are computed numerically for a specific model and presented graphically. Some special cases have also been deduced. The results indicate that the effect of rotation, magnetic field, initial stress, and gravity field is very pronounced.

scholarly journals On Rayleigh waves in a thinly layered laminated thermoelastic medium with stress couples under initial stresses

1988 ◽  
Vol 1 (3) ◽  
pp. 161-176
Author(s):  
Pijush Pal Roy ◽  
Lokenath Debnath
Keyword(s):  
Phase Velocity ◽  
Initial Stress ◽  
Rayleigh Waves ◽  
Couple Stress ◽  
Frequency Equation ◽  
Initial Stresses ◽  
Displacement Fields ◽  
Thermoelastic Medium ◽  
Couple Stresses

A study is made of the propagation of Rayleigh waves in a thinly layered laminated thermoelastic medium under deviatoric, hydrostatic, and couple stresses. The frequency equation of the Rayleigh waves is obtained. The phase velocity of the Rayleigh waves depends on the initial stress, deviatoric stress, and the couple stress. The laminated medium is first replaced by an equivalent anisotropic thermoelastic continuum. The corresponding thermoelastic coefficients (after deformation) are derived in terms of initially isotropic thermoelastic coefficients (before deformation) of individual layers. Several particular cases are discussed for the determination of the displacement fields with or without the effect of the couple stress.

Stoneley and Rayleigh waves in thermoelastic materials with voids

2019 ◽  
Vol 25 (14) ◽  
pp. 2053-2062 ◽  
Author(s):  
SS Singh ◽  
Lalawmpuia Tochhawng
Keyword(s):  
Phase Velocity ◽  
Rayleigh Wave ◽  
Surface Waves ◽  
Rayleigh Waves ◽  
Frequency Equation ◽  
Attenuation Coefficients ◽  
Stoneley Waves ◽  
Materials With Voids ◽  
Modes Of Vibration ◽  
Phase Velocity And Attenuation

The present paper deals with the propagation of surface waves (Stoneley and Rayleigh waves) in thermoelastic materials with voids. The frequency equations of the Stoneley waves at the bonded and unbonded interfaces between two dissimilar half-spaces of thermoelastic materials with voids are obtained. The numerical values of the determinant for bonded and unbonded interface are calculated for a particular model. We also derived the frequency equation of the Rayleigh wave in thermoelastic materials with voids. The phase velocity and attenuation coefficients have shown that there are two modes of vibration. These two modes are computed and they are depicted graphically. The effect of thermal parameters in these surface waves is discussed.

Propagation of Rayleigh waves at the boundary of an orthotropic elastic solid: Influence of initial stress and gravity

2020 ◽  
Vol 26 (21-22) ◽  
pp. 2070-2080 ◽  
Author(s):  
Mohan D Sharma
Keyword(s):  
Initial Stress ◽  
Algebraic Equation ◽  
Rayleigh Waves ◽  
Plane Waves ◽  
Symmetry Plane ◽  
Elastic Solid ◽  
Quadratic Equation ◽  
Frequency Equation ◽  
Complex Frequency ◽  
Orthotropic Elastic Medium

Propagation of harmonic plane waves is considered in an orthotropic elastic medium in the presence of initial stress and gravity. Roots of a quadratic equation define the propagation of one quasi-longitudinal wave and one quasi-transverse wave in a symmetry plane in this medium. These two waves are coupled in the identical phase to define the propagation of Rayleigh waves at the boundary of the medium. Two conditions at the stress-free boundary translate into a complex frequency equation, which explains the dispersive behavior of this Rayleigh wave. For the presence of radical terms, this complex equation is rationalized into a real algebraic equation. Only one root of this algebraic equation satisfies the mother frequency equation and hence represents the propagation of dispersive Rayleigh waves at the boundary of the orthotropic solid. The influence of initial stress and gravity on velocity and polarization of Rayleigh waves is observed through a numerical example.

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