### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 4pPA5. Nonlinear elastic wave propagation along free surfaces of a thick
plate.

**M. F. Hamilton
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Yu. A. Il'inskii
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E. A. Zabolotskaya
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*Dept. of Mech. Eng., Univ. of Texas, Austin, TX 78712-1063
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Nonlinear elastic wave propagation along free surfaces of a thick
isotropic plate is investigated theoretically. The finite thickness of the
plate introduces dispersion. In the linear approximation the solution is a
superposition of symmetric and antisymmetric modes, and the wave field
undulates along the surfaces of the plate. Nonlinearity is taken into account
with the Hamiltonian formalism used to model Rayleigh waves of finite amplitude
[Zabolotskaya, 2569--2575 (1992)]. The resulting coupled spectral
equations were integrated numerically to investigate harmonic generation and
waveform distortion in an initially monochromatic wave generated on one side of
the plate. Two different plate thicknesses were considered, 20 and 100 shear
wavelengths. For the thicker plate, and with a shock formation distance much
smaller than the dispersion length, the solutions resemble those for nonlinear
Rayleigh waves in a half-space. For the thinner plate, and with the two length
scales of the same order, propagation curves for the second harmonic component
exhibit the ``growth-decay cycles'' that have been measured in experiments and
discussed in a previous article [Shull et al., 418--427 (1993)]. [Work
supported by NSF, Schlumberger, and the Office of Naval Research.]