Diffraction effects in nonlinear Rayleigh wave beams

Abstract

Nonlinear effects in Rayleigh wave beams are investigated analytically and numerically. Diffraction effects are taken into account within the parabolic approximation, and nonlinearity is taken into account with a theoretical model used previously to investigate plane and cylindrical Rayleigh waves of finite amplitude [E. A. Zabolotskaya, J. Acoust. Soc. Am. 91, 2569–2575 (1992)]. Quasilinear solutions are presented for second-harmonic generation in Gaussian beams, both unfocused and focused. Asymptotic results are derived for the second harmonic in the far field of arbitrary directive sources. Numerical solutions are used to investigate harmonic generation, waveform distortion, and shock formation in Rayleigh wave beams produced by sources with uniform amplitude distributions. Brief consideration is given to effects of source asymmetry on the radiated field.