Effect of Initial Stress and Impedance Boundary in Transversely Isotropic Materials

This paper aimed at studying the effect of initial stress and impedance boundary surface on the elastic waves propagation in transversely isotropic materials. The governing equations of transversely isotropic materials with initial stress are treated in the xy-plane to obtain the phase velocities of two waves, quasi-longitudinal (qP) and quasi-transverse (qS) waves. The normal mode operation is employed to obtain the expression of the displacement components and stress components. The problem of reflection of incident waves at the impedance boundary of transversely isotropic material is also investigated in the presence of initial stress to obtain the amplitude ratios of reflected waves. The variations of displacement and force stress are illustrated with respect to the axis of propagation by employing amplitude ratio expression. The effect of initial stress and impedance parameters on the expression of displacement and force stress as well as amplitude ratios of transversely isotropic materials are illustrated graphically for a particular model.

Automated summary

This paper investigates the influence of initial stress and impedance boundary surface on the propagation of elastic waves in transversely isotropic materials. The phase velocities of quasi-longitudinal (qP) and quasi-transverse (qS) waves are obtained by treating the governing equations of transversely isotropic materials with initial stress in the xy-plane. The displacement components and stress components are expressed using the normal mode operation. The reflection of incident waves at the impedance boundary is analyzed under the presence of initial stress to determine the amplitude ratios of reflected waves. The variations in displacement and force stress are graphically illustrated with respect to the propagation axis, showing the impact of initial stress and impedance parameters on transversely isotropic materials.