Some special solutions of Rayleigh's equation and the reflections of body waves at a free surface

Abstract

A new representation of all roots of Rayleigh's equation for all values of Poisson's ratio v is proposed. A new analytical expression for the double root is derived. It is found to be simply related to special Brewster angles, which occur for incident longitudinal or transversal waves at a stress-free surface. Some peculiarities of the reflection coefficients R(PS) and R(SP) are discussed.