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The resonance conditions of two-way collinear mixing are derived when a longitudinal wave and a transverse wave are propagating in the opposite directions based on cubic nonlinearity. The analytical solutions for mixing waves are obtained. An interesting result is that the resonant longitudinal wave and the resonant transverse wave can be generated, respectively, when considering different resonance conditions. This is different from the case with quadratic nonlinearity that only resonant transverse wave can be generated. For the convenience of applications, the wave mixing of a time-harmonic longitudinal pulse and a time-harmonic transverse pulse is also investigated. A clear mixing process is presented by discussing the parameters introduced in the derivation. Numerical calculation is conducted on material Al, the hexagonal waveforms of the resonant transverse waves are depicted when considering different cases. The results could provide new opportunities for mixing wave applications in nondestructive evaluation.

Two-way collinear mixing of a longitudinal and a transverse plane wave in materials with cubic nonlinearity