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In this paper we have discussed the propagation of torsional wave in a composite layer overlying an anisotropic heterogeneous half space with initial stress. The method of separation of variables is applied to find the dispersion equation. Numerical results analyzing the dispersion equation are discussed and presented by means of graphs. The effect of reinforcement, inhomogeneity parameter and the initial stress on the propagation of torsional surface wave is the main objective in our study. It has been observed that the directional rigidities of the half space have a favoring effect on the phase velocity, whereas the density and initial stress parameter in the half-space have the adverse effect on the velocity of torsional surface wave. It is remarkable to quote that reinforcement prevails in the medium, the phase velocity increases significantly.

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The present paper is concerned with the propagation of plane waves in self–reinforced media. The velocities of quasi-P and quasi-S waves in an unbounded self–reinforced medium under initial stresses and under gravity field have been derived. Also the reflection coefficients and the partition of energy of reflected quasi-P and quasi-SV waves due to incident quasi-P and quasi-SV waves have been obtained under the influence of initial stress and gravity field. It has been noticed that the velocities, reflection coefficients and energy coefficients not only depend on the initial stress and gravity but also on the direction of propagation. The results are in agreement with the classical case in the absence of initial stresses and gravity. In presence of initial stresses and gravity field, the velocities, reflection coefficients and energy coefficients of quasi-P and quasi-S waves are calculated numerically and are presented by means of graphs.