G. Douglas Meegan
Mark F. Hamilton
E. A. Zabolotskaya
Dept. of Mech. Eng., Univ. of Texas at Austin, Austin, TX 78712-1063
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.]