Generalized Brewster angle for wave reflection from a fluid-transversely isotropic solid interface

Abstract

The definition of Brewster angle for ultrasonic wave reflection is generalized to include wave incidence from an inviscid compressible fluid, such as water, in order to show its possible applications in the area of nondestructive evaluation. The interface considered is a plane boundary separating two semi-infinite linear elastic media. Our medium is the fluid and the other is a transversely isotropic solid. The generalized Brewster angle is defined as the angle of incidence of longitudinal waves for which there is no reflection. This definition guarantees that it is the only angle of incidence for which the amplitude of the reflected wave is independent of the amplitude of the incident longitudinal wave. The Brewster angle, in the sense of Snell's law, is independent of the medium containing the incident wave(s) and, because it can be determined experimentally, it offers a unified approach to the study of ultrasonic reflection from fluid-solid interfaces. For plane elastic waves propagating in the plane of symmetry of the transversely isotropic solid an explicit formula is obtained which yields the Brewster angle (or angles). Analysis of this formula reveals several features of the Brewster angles with practical applications in the area of ultrasonic nondestructive evaluation.