M. F. Hamilton
Yu. A. Il'inskii
E. A. Zabolotskaya
Dept. of Mech. Eng., Univ. of Texas, Austin, TX 78712-1063
Nonlinear effects in surface waves, like those in bulk elastic waves, are enhanced dramatically by microinhomogeneous features such as cracks and grains that are common in rocks. Since surface waves experience less geometrical spreading loss than bulk waves, nonlinearity can be even more pronounced than in bulk waves. A brief review of theoretical models for studying nonlinear surface wave propagation will be presented. The models are based on the theory developed by Zabolotskaya [J. Acoust. Soc. Am. 91, 2569--2575 (1992)] for nonlinear Rayleigh waves in isotropic solids. In subsequent articles published in the Journal the theory was used to study harmonic generation, waveform distortion, and shock formation in plane waves, cylindrical waves, and diffracting surface wave beams. Radiation from both time harmonic and pulsed sources was investigated. Reported values for second- and third-order elastic moduli were used to calculate coefficients of nonlinearity for a number of rocklike materials. The theoretical model was recently extended to encompass nonlinear Stoneley, Scholte, and Lamb waves, and to include effects of anisotropy and piezoelectricity. Most experiments reported on nonlinear surface waves are associated with the development of nonlinear SAW devices in the 1970s. Several of these experiments will be revisited, and new interpretations of the measurements will be offered. [Work supported by NSF, the Office of Naval Research, and the Schlumberger Foundation.]