Nonlinear Stoneley and Scholte waves

Spectral evolution equations are derived for plane, progressive, finite-amplitude Stoneley and Scholte waves that propagate along plane interfaces formed by two semi-infinite, isotropic media in contact. The evolution equations have mathematical forms identical to those obtained previously for Rayleigh waves [E. A. Zabolotskaya, J. Acoust. Soc. Am. 91, 2569–2575 (1992)], and they are expressed explicitly in terms of the second- and third-order elastic constants of the media. Calculations were performed to simulate nonlinear surface wave propagation in several pairs of real media. Harmonic generation and shock formation associated with the Stoneley and Scholte modes are compared with the corresponding processes in Rayleigh waves. Waveform distortion is shown to be very similar for the three types of surface waves when the propagation distance is normalized by an appropriate shock formation distance.