Reflection in a highly anisotropic medium for three-dimensional plane waves under initial stresses

Abstract

The present paper is concerned with the reflection of three-dimensional plane waves at a traction free boundary of a half-space composed of triclinic crystalline material under initial stresses. The analytical expressions of all the three phase velocities of quasi-compressional (qP) and quasi-shear waves qS1 and qS2 (or may be denoted by qSV and qSH) in three dimensions under initial stresses have been found by a simple procedure. We have obtained closed form expressions in three dimensions for the amplitude ratios of reflection coefficients of the three quasi waves in terms of the phase velocity, propagation vector, initial stresses and the stiffness coefficients of the medium. The variation of reflected coefficients with the angle of incidence is investigated numerically and discussed. We have drawn graphs for different polar angle and azimuth. The study clearly indicates that anisotropy and initial stresses have substantial effect on the reflection of three-dimensional plane waves in triclinic crystalline medium.