A simple method for comparing waveform distortion of nonlinear surface waves in different cubic crystals

Abstract

Simulations of monofrequency, nonlinear surface acoustic waves propagating in cubic crystals were performed using the theory of Hamilton, Il’inskii, and Zabolotskaya [J. Acoust. Soc. Am. 105, 639–651 (1999)]. Nonlinearity matrix elements, which describe the coupling strength of harmonic interactions, provide a useful tool for characterizing the nature of the waveform distortion and can be computed without integrating large systems of equations. In cases where the surface is a plane of mirror symmetry, the nonlinearity matrix elements are real valued, and the longitudinal components of the waveforms typically form either compression or rarefaction shocks. However, in cases where the surface has lower symmetry, the nonlinearity matrix elements are complex valued, and the resulting waveform distortion is typically asymmetric, sometimes with low-frequency oscillations forming near peaks and shocks. A simple transformation based on the phase of the dominant nonlinearity matrix element was shown to provide a reasonable approximation of the asymmetric distortion in many cases. Comparisons will be presented between approximate and exact solutions in the (111) plane for several real crystals. These results are consistent with measured surface wave pulses reported previously [R. E. Kumon et al., J. Acoust. Soc. Am. 103, 2926(A) (1998)]. [Work supported by ONR.]