ABSTRACT

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.

摘要

基于三次非线性，推导了纵波和横波在相反方向传播时双向共线混频的共振条件。得到了混合波的解析解。一个有趣的结果是，当考虑不同的谐振条件时，可以分别产生谐振纵波和谐振横波。这与只能产生谐振横波的二次非线性情况不同。为方便应用，还研究了时谐波纵向脉冲和时谐波横向脉冲的混波。通过讨论推导中引入的参数，提出了一个清晰的混合过程。对材料Al进行数值计算，在考虑不同情况时，描绘了谐振横波的六边形波形。该结果可为混合波在无损评估中的应用提供新的机会。