The present problem deals with the propagation of Love-type surface waves in a bedded structure comprises of an inhomogeneous orthotropic layer and an elastic half-space. The upper boundary and the interface between two media are considered to be corrugated. An analytical method (separation of variables) is adapted to solve the second order PDEs, which governs the equations of motion. Equations for particle motion in the layer and half-space have been formulated and solved separately. Finally, the frequency relation has been established under suitable boundary conditions at the interface of the orthotropic layer and the elastic half-space. Obtained relation is found to be in good agreement with the classical case of Love wave propagation. Remarkable effects of heterogeneity and corrugation parameters on the phase velocity of the considered wave have been represented by the means of graphs. Moreover, the group velocity curves are also plotted to exhibit the profound effect of heterogeneity considered in the layer. Results may be useful in theoretical study of wave propagation through composite layered structure with irregular boundaries. تفاصيل المقالة

A Mathematical model has been considered to study the reflection and refraction phenomenon of plane wave at the interface of an isotropic liquid medium and a triclinic (anisotropic) half-space. The incident plane qP wave generates three types of reflected waves namely quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH) waves in the triclinic medium and one refracted P wave in the isotropic liquid medium. Expression of phase velocities of all the three quasi waves have been calculated. It has been considered that the direction of particle motion is neither parallel nor perpendicular to the direction of propagation in anisotropic medium. Some specific relations have been established between directions of motion and propagation. The expressions for reflection coefficients of qP, qSV, qSH and refracted P waves with respect to incident qP wave are obtained. Numerical computation and graphical representations have been performed for the reflection coefficient of reflected qP, reflected qSV, reflected qSH and refraction coefficient of refracted P wave with incident qP wave. تفاصيل المقالة