Harmonic interactions in plane and cylindrical nonlinear Rayleigh waves

In a recent article [E. A. Zabolotskaya, J. Acoust. Soc. Am. 91, 2569–2575 (1992)], a new theoretical model for nonlinear Rayleigh waves in isotropic solids was derived and used to generate numerical results that demonstrate the distortion of time waveforms. In the present paper, attention is focused on the predicted behavior of the spectral components. Quasilinear solutions are obtained for second harmonic generation in both plane and cylindrical Rayleigh waves. Following Merklinger’s analysis of finite amplitude sound in fluids [J. Acoust. Soc. Am. 54, 1760–1761 (1973)], the quasilinear solutions are used to develop taper functions that account for the finite amplitude loss of energy from the source frequency component. Numerical results are presented in the form of propagation and saturation curves for the first several harmonics, and ‘‘extra attenuation’’ (EXDB) curves for the source frequency. The analytical solutions for the taper functions are found to be in reasonable agreement with the numerical results. Time waveforms are also presented. [Work supported by the David and Lucile Packard Foundation and by ONR.]