Bulk wave reflection formulas are extended to the surface-wave case, considering Rayleigh and Stoneley waves in terms of refracted inhomogeneous longitudinal and transversal waves, linked by the surface coupling. In this manner, a physical mechanism of second-harmonic generation process is clearly shown. The analytical expressions and physical pictures of Rayleigh- and Stoneley-wave harmonic generation have been derived in a second-order approximation. The solution shows that the second-harmonic surface waves have a field structure different from the fundamental ones and varying with the propagation distance. Some parameters were defined to characterize the elastic surface-wave second-harmonic generation efficiency. Numerical data for some isotropic materials are present. The steady-state form of finite amplitude surface wave is described and explained by a clear physical model.
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Shui et al. (1988) studied this question.
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