scholarly journals Effect of Initial Stress and Magnetic Field on Propagation of Shear Wave in Non Homogeneous Anisotropic Medium Under Gravity Field~!2009-03-27~!2009-06-14~!2009-12-23~!

2010 ◽  
Vol 3 (1) ◽  
pp. 58-65 ◽  
Author(s):  
A.M. Abd-Alla ◽  
S.R. Mahmoud ◽  
M.I.R. Helmi
Keyword(s):  
Magnetic Field ◽  
Gravity Field ◽  
Initial Stress ◽  
Shear Wave ◽  
Anisotropic Medium ◽  
Homogeneous Anisotropic Medium

Two-temperature generalized magneto-thermoelastic medium for dual-phase-lag model under the effect of gravity field and hydrostatic initial stress

2016 ◽  
Vol 12 (2) ◽  
pp. 362-383 ◽  
Author(s):  
Samia M Said
Keyword(s):  
Magnetic Field ◽  
Gravity Field ◽  
Initial Stress ◽  
Mode Analysis ◽  
Phase Lag ◽  
Temperature Dependent ◽  
Content Type ◽  
Temperature Dependent Properties ◽  
Hydrostatic Initial Stress ◽  
Two Temperature

Purpose – The dual-phase-lag (DPL) model and Lord-Shulman theory with one relaxation time are applied to study the effect of the gravity field, the magnetic field, and the hydrostatic initial stress on the wave propagation in a two-temperature generalized thermoelastic problem for a medium with an internal heat source that is moving with a constant speed. The paper aims to discuss this issue. Design/methodology/approach – The exact expressions of the considered variables are obtained by using normal mode analysis. Findings – Numerical results for the field quantities are given in the physical domain and illustrated graphically in the absence and presence of the gravity field as well as the magnetic field. Comparisons are made between the results of the two different models with and without temperature dependent properties and for two different values of the hydrostatic initial stress. A comparison is also made between the results of the two different models for two different values of the time. Originality/value – In the present work, the author shall formulate a two-temperature generalized magneto-thermoelastic problem for a medium with temperature dependent properties and with an internal heat source that is moving with a constant speed under the influence of a gravity field and a hydrostatic initial stress. Normal mode analysis is used to obtain the exact expressions for the displacement components, thermodynamic temperature, conductive temperature, and stress components. A comparison is carried out between the considered variables as calculated from the generalized thermoelasticity based on the DPL model and the L-S theory in the absence and presence of a magnetic field as well as a gravity field. Comparisons are also made between the results of the two theories with and without temperature dependent properties and for two different values of hydrostatic initial stress. A comparison is also made between the results of the two different models for two different values of the time.

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.

Effect of Rotation, Gravity, Primary Stress and Magnetic Field on Shear Waves Spreading in an Anisotropic Incompressible Sandy Elastic Medium

2019 ◽  
Vol 16 (11) ◽  
pp. 4443-4454
Author(s):  
S. H. Elhag ◽  
F. S. Bayones
Keyword(s):  
Magnetic Field ◽  
Elastic Medium ◽  
Gravity Field ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Incompressible Medium ◽  
Primary Stress ◽  
Dry Sand ◽  
Inhomogeneous Elastic Medium

In this paper, we investigated the spreading of shear wave in an anisotropic non-homogeneous elastic medium under effect of dry sand, rotation, gravity, primary stress, and magnetic field. We have reached equation of variation of shear wave velocity c1 in an anisotropic incompressible medium according to sand, rotation, gravity, primary stress, and magnetic field, then we used graphs to illustrate to show the effect of direction of spreading of shear wave. The results indicate that the effect of dry sand, rotation, gravity, primary stress, and magnetic field on the spreading of shear wave in an anisotropic inhomogeneous elastic medium are very pronounced. The results have been obtained are discussed and presented visually, the results demonstrate that the effect of sand, gravity field, primary stress, magnetic field, anisotropy and rotation are noticeable.

Combining the deep Earth and lithospheric gravity field to study the density structure of the upper mantle

2021 ◽  
Author(s):  
Bart Root ◽  
Javier Fullea ◽  
Jörg Ebbing ◽  
Zdenek Martinec
Keyword(s):  
Gravity Field ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Field Data ◽  
Wavelength Region ◽  
Density Structure ◽  
Long Wavelength ◽  
Global Gravity ◽  
Deep Earth

<p>Global gravity field data obtained by dedicated satellite missions is used to study the density distribution of the lithosphere. Different multi-data joint inversions are using this dataset together with other geophysical data to determine the physical characteristics of the lithosphere. The gravitational signal from the deep Earth is usually removed by high-pass filtering of the model and data, or by appropriately selecting insensitive gravity components in the inversion. However, this will remove any long-wavelength signal inherent to lithosphere. A clear choice on the best-suited approach to remove the sub-lithospheric gravity signal is missing. </p><p>Another alternative is to forward model the gravitational signal of these deep situated mass anomalies and subtract it from the observed data, before the inversion. Global tomography provides shear-wave velocity distribution of the mantle, which can be transformed into density anomalies. There are difficulties in constructing a density model from this data. Tomography relies on regularisation which smoothens the image of the mantle anomalies. Also, the shear-wave anomalies need to be converted to density anomalies, with uncertain conversion factors related to temperature and composition. Understanding the sensitivity of these effects could help determining the interaction of the deep Earth and the lithosphere.</p><p>In our study the density anomalies of the mantle, as well as the effect of CMB undulations, are forward modelled into their gravitational potential field, such that they can be subtracted from gravity observations. The reduction in magnitude of the density anomalies due to the regularisation of the global tomography models is taken into account. The long-wavelength region of the density estimates is less affected by the regularisation and can be used to fix the mean conversion factor to transform shear wave velocity to density. We present different modelling approaches to add the remaining dynamic topography effect in lithosphere models. This results in new solutions of the density structure of the lithosphere that both explain seismic observations and gravimetric measurements. The introduction of these dynamic forces is a step forward in understanding how to properly use global gravity field data in joint inversions of lithosphere models.</p>

scholarly journals Magnetic field on surface waves propagation in gravitational thermoelastic media with two temperature and initial stress in the context of three theories

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 285-299
Author(s):  
Jamel Bouslimi ◽  
Sayed Abo-Dahab ◽  
Khaled Lotfy ◽  
Sayed Abdel-Khalek ◽  
Eied Khalil ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Initial Stress ◽  
Half Space ◽  
Generalized Thermoelasticity ◽  
Phase Lag ◽  
Mathematical Methods ◽  
Numerical Work ◽  
Suitable Material ◽  
Two Temperature

In this paper is investigating the theory of generalized thermoelasticity under two temperature is used to solve boundary value problems of 2-D half-space its bound?ary with different types of heating under gravity effect. The governing equations are solved using new mathematical methods under the context of Lord-Shulman, Green-Naghdi theory of type III (G-N III) and the three-phase-lag model to inves?tigate the surface waves in an isotropic elastic medium subjected to gravity field, magnetic field, and initial stress. The general solution obtained is applied to a spe?cific problem of a half-space and the interaction with each other under the influence of gravity. The physical domain by using the harmonic vibrations is used to obtain the exact expressions for the Waves velocity and attenuation coefficients for Stoneley waves, Love waves, and Rayleigh waves. Comparisons are made with the results between the three theories. Numerical work is also performed for a suitable material with the aim of illustrating the results. The results obtained are calculated numerical?ly and presented graphically with some comparisons in the absence and the presence the influence of gravity, initial stress and magnetic field. It clears that the results ob?tained agree with the physical practical results and agree with the previous results if the gravity, two temperature, and initial stress neglect as special case from this study.

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