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

## 4pPAa13. Theoretical model for nonlinear Stoneley and Scholte waves.

**G. Douglas Meegan
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Mark F. Hamilton
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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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The Hamiltonian formalism used previously to derive model equations for
nonlinear Rayleigh waves [Zabolotskaya, J. Acoust. Soc. Am. 91, 2569 (1992)] is
used here to obtain a mathematical model for nonlinear Stoneley and Scholte
waves. Planar interfaces formed by contact between two isotropic materials are
assumed. The resulting coupled spectral equations are expressed in the same
form as those for Rayleigh waves. In particular, the nonlinearity coefficient
matrix can be written as R[sub ml][sup S]=R[sub ml][sup (1)]+KR[sub ml][sup
(2)], where K is a constant and R[sub ml][sup (i)] (corresponding to medium
i=1,2) are matrices having the same mathematical form as the matrix obtained
for Rayleigh waves. Since R[sub ml][sup S] exhibits the same symmetries as the
nonlinearity matrix for Rayleigh waves, the model equations for Stoneley and
Scholte waves can be analyzed with the same mathematical techniques that have
been employed in recent investigations of nonlinear Rayleigh waves (see, e.g.,
other papers in this session). The coupled spectral equations were solved
numerically for Stoneley and Scholte waves at interfaces formed by a variety of
media pairs, including some geological materials. Comparisons of harmonic
generation and shock formation are made with the corresponding processes in
Rayleigh waves. [Work supported by AASERT and ONR.]