This paper studies the interactions of two plane waves in elastic solids with quadratic nonlinearity. In particular, the necessary and sufficient conditions for resonant mixing of two plane waves are derived. It is shown that the conventional resonance condition for resonant mixing of plane waves is only a necessary condition, not sufficient. Based on the newly derived necessary and sufficient conditions, resonant mixing of various types of plane waves are investigated and specific conditions for generating a resonant mixed wave are obtained for each case. These results are useful for developing nonlinear ultrasonic nondestructive evaluation techniques using the wave mixing method.

中文翻译：

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具有二次非线性的弹性固体中平面波共振混合的充要条件

本文研究了具有二次非线性的弹性固体中的两个平面波的相互作用。特别地，导出了两个平面波的共振混合的必要和充分条件。已经表明，用于平面波的共振混合的常规共振条件仅是必要条件，还不够。基于新推导的必要条件和充分条件，研究了各种平面波的共振混合，并针对每种情况获得了用于产生共振混合波的特定条件。这些结果对于使用波混合方法开发非线性超声非破坏性评估技术很有用。