Abstract
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.
Highlights
The propagation of thermoelastic waves in a granular medium under initial stress and gravity field has applications in soil mechanics, earthquake science, geophysics, mining engineering, and so forth
We take a set of orthogonal Cartesian axes Ox1x2x3 such that the interface and the free surface of the granular layer resting on the granular half-space of different material are the planes x3 H and x3 0, respectively, with the origin O being any point on the interface surface; x3-axis is positive in the direction towards the exterior of the half-space, and x1-axis is positive along the direction of Rayleigh waves and Stoneley waves propagation
To investigate the possibility Stoneley waves in thermoelastic granular medium under the influence of initial stress and gravity field, we replace the layer by a half-space H → ∞, in the preceding problem, in this case eiλjH → 0, and the coefficients of e−iλjH j 3, 4, 5, 6 must vanish
Summary
The propagation of thermoelastic waves in a granular medium under initial stress and gravity field has applications in soil mechanics, earthquake science, geophysics, mining engineering, and so forth. The problem of Stoneley waves plays an important role in the earthquake science, optics, geophysics, and plasma physics Many authors such as Abd-Alla and Ahmed 9, , El-Naggar et al , Das et al , and others investigated the effect of gravity of the propagation of surface waves Stoneley waves and Rayleigh waves in an elastic solid medium. Goda illustrated the effect of inhomogeneity and anisotropy on Stoneley waves; Abd-Alla et al discussed Rayleigh waves in a magnetoelastic half-space of orthotropic material under influence of initial stress and gravity field. Vinh and Seriani discussed the explicit secular equations of Stoneley waves in a nonhomogeneous orthotropic elastic medium under the influence of gravity. Abd-Alla et al investigated Rayleigh waves in generalized magneto-thermo-viscoelastic granular medium under the influence of rotation, gravity field. The results obtained are displayed graphically and their physical meaning has been explained
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