### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 4pPAa12. Evolution equations for nonlinear Rayleigh wave propagation.

**M. F. Hamilton
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Yu. A. Il
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E. A. Zabolotskaya
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*Dept. of Mech. Eng., Univ. of Texas at Austin, Austin, TX 78712-1063
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Time domain evolution equations are derived for nonlinear Rayleigh wave
propagation along the free surface of an isotropic solid. The evolution
equations are expressed in different forms: one for the horizontal displacement
component, and one for a complex displacement variable. Both equations are
derived from spectral equations published earlier [Zabolotskaya, J. Acoust.
Soc. Am. 91, 2569 (1992)]. To simplify the derivation of equations for the
displacement variables, not all components of the nonlinearity coefficient
matrix are retained. However, the terms which are retained possess the same
mathematical properties (symmetries in the frequency domain, singularities in
the time domain, and others) as the terms that are not taken into account.
Moreover, with appropriate definition of the shock formation distance, it is
shown that numerical solutions based on the simplified equations yield close
agreement with numerical solutions based on the complete nonlinearity matrix.
The nonlinear terms in the new evolution equations are expressed as time
derivatives and Hilbert transforms of the displacement variables. Waveforms
calculated with the time domain evolution equations are shown to agree with
results based on the original frequency domain equations. [Work supported by
the Packard Foundation, ONR, and NSF.]