### ASA 127th Meeting M.I.T. 1994 June 6-10

## 2pPA10. Diffracting nonlinear Rayleigh wave beams.

**D. J. Shull
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E. E. Kim
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M. F. Hamilton
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E. A. Zabolotskaya
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*Dept. of Mech. Eng., The Univ. of Texas at Austin, Austin, TX 78712-1063
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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.]