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

Yu. A. Il'inskii

E. A. Zabolotskaya

Dept. of Mech. Eng., Univ. of Texas, Austin, TX 78712-1063

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.]