This paper derives the resonance conditions for one-way resonant mixing of nonlinear Lamb waves. Two mode triplets are identified that satisfy such resonance conditions. It is also found that, when the primary waves are pulses of finite duration, the signal envelope of the corresponding resonant mixed wave is either a diamond or an elongated hexagon. The dimensions of these shapes are obtained explicitly in terms of the pulse lengths and group velocities of the Lamb modes in the mode triplet. These analytical results are verified by numerical simulations using the finite element method. Finally, a nondestructive evaluation method based on one-way mixing of Lamb waves is proposed for the inspection of a large area of a plate for damage distribution via a single access point. Numerical simulations of this nondestructive evaluation technique are conducted. It is found that using shorter pulses gives better spatial resolution, thus better suited for locating and sizing the damage zone, while using longer pulses gives a higher signal to noise ratio, thus better suited for quantifying the degree of damage in the damage zone. Results of this paper clarify some of the confusion in the existing literature regarding the resonance conditions for one-way mixing of nonlinear Lamb waves. They also provide a better understanding of the physical characteristics of the resonant mixed wave. Such understanding enables the design of optimal measurement systems for one-way mixing of Lamb waves for the purpose of conducting large area nondestructive evaluation of plate-like structures from a single access point. This proposed one-way mixing nondestructive evaluation technique can be extended to pipes.

中文翻译：

---

薄板中兰姆波单向混合的解析与数值研究

本文推导出非线性兰姆波单向谐振混合的谐振条件。确定了满足这种共振条件的两个模式三元组。还发现，当主波是有限持续时间的脉冲时，相应的谐振混合波的信号包络是菱形或细长的六边形。这些形状的尺寸是根据模式三重态中兰姆模式的脉冲长度和群速度明确获得的。这些分析结果通过使用有限元方法的数值模拟得到验证。最后，提出了一种基于兰姆波单向混合的无损评估方法，用于通过单个接入点检查大面积板的损伤分布。对这种无损评估技术进行了数值模拟。发现使用较短的脉冲提供更好的空间分辨率，因此更适合定位和确定损伤区域的大小，而使用更长的脉冲提供更高的信噪比，因此更适合量化损伤区域中的损伤程度。本文的结果澄清了现有文献中关于非线性兰姆波单向混合的共振条件的一些混淆。它们还可以更好地了解谐振混合波的物理特性。这种理解使得能够设计用于单向混合兰姆波的最佳测量系统，以便从单个接入点对板状结构进行大面积无损评估。