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Influence of rotation and generalized magneto-thermoelastic on Rayleigh waves in a granular medium under effect of initial stress and gravity field

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Abstract

Influence of rotation, relaxation times, magnetic field, initial stress and gravity field on attenuation coefficient (Imaginary part of frequency equation root) and Rayleigh waves velocity (the real part of frequency equation root) in an elastic half-space of granular medium is studied. The analytical solution is obtained by using Lame’s potential techniques. The numerical calculations are carried out for the frequency equation of Rayleigh waves velocity. The results are displayed graphically. Some results of previous investigations are deduced as special cases from this study.

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Abbreviations

T :

is temperature difference (θ−T 0)

θ :

is the ratio of the coefficients of heat transfer

t :

is the time

:

is the constant primary magnetic field vector

:

is the electric intensity

s :

is the specific heat per unit mass

ρ :

is the density of the material

P :

is the initial stress

F :

is the coefficient of friction

F j :

are the components of Lorentz’s body forces vector

τ 1,τ 2 :

are the mechanical relaxation times

g :

is the earth gravity

\(\vec{u}\) :

is the component of displacement vector

T o :

is reference temperature solid

:

is the electric current density

ω ij :

is the rotation vector

μ e :

is the magnetic permeability

k :

is the wave number

c :

is speed of Rayleigh waves

λ,μ :

are the Lame’ constants

M :

is the third elastic constant

κ :

is thermal conductivity

K :

is the thickness

:

is the perturbed magnetic field over the constant primary magnetic field

σ ij :

is the stress tensor

ε :

is coupling coefficient

(ξ,η,ζ):

are components of rotation vector of the grain about its center of gravity

References

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  1. S. R. Mahmoud

    Present address: Mathematics Department, Faculty of Science, King Abdul Aziz University, Jeddah, Saudi Arabia

Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Sohag University, 82524, Sohag, Egypt

    S. R. Mahmoud

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Mahmoud, S.R. Influence of rotation and generalized magneto-thermoelastic on Rayleigh waves in a granular medium under effect of initial stress and gravity field. Meccanica 47, 1561–1579 (2012). https://doi.org/10.1007/s11012-011-9535-9

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