Abstract
Ultrasonic wave mixing is a powerful new nondestructive evaluation technique for accessing hidden subtle imperfections in materials. First, this paper derives the resonance conditions of one-way collinear mixing with cubic nonlinearity. The results show that the mixing of two collinear longitudinal waves can generate a resonant longitudinal wave, the mixing of two transverse waves can generate a resonant transverse wave, and the resonant longitudinal wave and transverse wave can be generated, respectively, when two primary longitudinal and transverse waves satisfy different resonance conditions. This is different from the case with quadratic nonlinearity. Furthermore, we obtain the analytical solutions of resonant waves generated by the mixing of harmonic longitudinal and transverse pulses. The waveforms are approximate hexagonal shapes according to the analysis of the envelopes. Finally, the numerical simulation results conducted on material aluminum prove the correctness of the analytical solution. Compared with quadratic nonlinearity, the resonant wave is more sensitive to material constants for some materials when considering one-way collinear mixing of primary longitudinal and transverse pulses based on cubic nonlinearity. The results provide new opportunities on mixing wave applications in nondestructive evaluation.
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