On supercritical incidence of a finite‐amplitude plane dilatational wave in an elastic solid

Abstract

An earlier analysis [K. T. Shu and J. H. Ginsberg, J. Acoust. Soc. Am. Suppl. 1 85, S139 (1989)] described nonlinear reflection and refraction phenomena of a finite‐amplitude dilatational wave at subcritical incidence on a plane interface between two bonded solids. The present work extends the earlier description to cases where the angle of incidence exceeds the critical value. The incoming wave is assumed to originate from the slower medium, so two critical angles exist, associated with evanescence of either the transmitted dilatational or shear wave. The finite‐amplitude version of Snell's law indicates that the dependence of the phase speed of the incident wave on its instantaneous amplitude induces, in the case of evanescent waves, fluctuations in the phase velocity parallel to the interface and in the decay rate normal to the boundary. This effect mirrors the fluctuations in the transmission and reflection angles of propagative waves. A numerical algorithm is developed to evaluate reflected or transmitted waveforms at a specified field point. In the special case of incidence close to a linear critical angle, the finite amplitude Snell's law indicates that the corresponding wave fluctuates between propagative and evanescent properties within a single period. [Work supported by NSF.]