Nonlinear mixing of non-collinear guided waves at a contact interface

Wave mixing offers several practical benefits relative to harmonic generation for detecting both distributed and localised damage. An analytical model is proposed for predicting the frequency, mode and direction of propagation of the mixed modes arising from the nonlinear mixing of two incident guided-wave modes at an interface exhibiting contact acoustic nonlinearity. These predictions are validated by a finite-element (FE) analysis involving a unilateral contact law that models both clapping and frictional sliding at the interface. This analysis also provides quantitative insights regarding the optimal interaction angle between the incident waves in the case of shear-horizontal SH₀ modes, and the dependence of the mixed-wave amplitude on the load ratio (i.e. ratio of contact stress to normal stress across the interface due to both incident waves). The non-collinear mixing of guided waves is also investigated experimentally for various values of contact stress and incident stress amplitude, demonstrating the existence of mixed waves, as well as showing that interface mixing leads to a higher amplitude mixed wave than that due to the background material nonlinearity. This higher amplitude combined with great flexibility in the choice of incident wave parameters (frequency, mode and direction) makes wave mixing an attractive practical approach for detecting contact acoustic nonlinearity at crack-like defects and interfaces. Experimentally, the maximum value of mixed-wave amplitude is obtained at the same value of contact stress for the various incident stress amplitudes, whereas the FE model shows a maximum at a unique value of the load ratio. This difference may be a consequence of surface roughness, which is not included in the FE model.