D. J. Shull
E. E. Kim
M. F. Hamilton
E. A. Zabolotskaya
Dept. of Mech. Eng., The Univ. of Texas at Austin, Austin, TX 78712-1063
Nonlinear Rayleigh wave beams in isotropic solids 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 [Zabolotskaya, J. Acoust. Soc. Am. 91, 2569--2575 (1992)]. The model equation is expressed in both and time and frequency domains. Quasilinear solutions are presented for second harmonic generation in Gaussian beams, both unfocused and focused. Asymptotic formulas are presented for the second harmonic component in the far field of an arbitrary directive source. Waveform distortion and shock formation are described with numerical solutions for radiation from a source having a uniform amplitude distribution. The numerical results characterize both the near-field and far-field regions of the beam. Numerical results for radiation from uniform sources were presented earlier at 13th ISNA in Bergen, Norway [Shull et al., in Advances in Nonlinear Acoustics, edited by H. Hob(ae ligature)k (World Scientific, Singapore, 1993), pp. 496--501]. We conclude that the main effects of diffraction can be predicted within the existing theoretical framework for nonlinear sound beams in fluids. [Work supported by the David and Lucile Packard Foundation and by ONR.]