Propagation of S-wave in a non-homogeneous anisotropic incompressible and initially stressed medium under influence of gravity field

Keywords: Incompressible Initial stress Anisotropic S-wave Gravity field a b s t r a c t In this paper, propagation of shear waves in a non-homogeneous anisotropic incompress-ible, 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. In recent years, more attention has been given to using the anisotropic material in engineering applications in considerable research activity. The problem of shear waves in an orthotropic elastic medium is very important for the possibility of its extensive application in various branches of science and technology, particularly in optics, earthquake science, acoustics, geophysics and plasma physics. Shear waves propagating over the surface of homogeneous and non-homogeneous elastic half-spaces are a well-known and prominent feature of wave theory. Mahmoud [1] studied the wave propagation in cylindrical poroelastic dry bones and Abd-Alla and Farhan [2] investigated the effect of inhomogeneity on the composite infinite cylinder of orthotropic material. Abd-Alla and Farhan [2] and Abd-Alla and Mahmoud [3] solved the magneto-thermoelastic problem in rotating a non-homogeneous orthotropic hollow cylindrical under the hyperbolic heat conduction model, and investigated the effect of the rotation on propagation of thermoelastic waves in a non-homogeneous infinite cylinder of isotropic material. Abd-Alla et al. [5] presented Rayleigh wave in a magnetoelastic half-space of orthotropic material under influence of initial stress and gravity field. The shear waves in acoustic anisotropic media have been discussed by Grechka et al. [6]. Many authors such as Abd-Alla and Ahmed [7,10] and El-Naggar et al. [11] studied the effect of gravity on the propagation of Rayleigh waves on elastic solid medium. Ahmed [8] studied Rayleigh waves in a thermoelastic granular medium under initial stress. The influence of gravity on the propagation of waves in granular medium is discussed by Ahmed [9]. Das et al. [12] studied the influence of gravity on surface waves in a non-homogeneous isotropic elastic medium. Datta [13] discussed the influence of gravity field on Rayleigh waves propagation in …