Zero Group Velocity (ZGV) modes are peculiar guided waves that can exist in elastic plates or cylinders, and have proved to be very sensitive tools in characterizing materials or thickness variations with sub-percent accuracy at space resolutions of about the plate thickness. In this article we show theoretically and experimentally how such a mode can be generated as the sum-frequency interaction of two high amplitude primary waves, and then serve as a local probe of material non-linearity. The solutions to the phase matching condition, i.e. condition for a constructive non-linear effect, are obtained numerically in the mark of classical, quadratic non-linearity. The coupling coefficients that measure the transfer rate of energy as a function of time from primary to secondary modes are derived. Experiments are conducted on an aluminum plate using piezo-electric transducers and a laser interferometer, and explore the interaction for incident symmetric and anti-symmetric fundamental Lamb modes. In an experiment operated without voltage amplifier we demonstrate that the resonant nature of these ZGV modes can be leveraged to accumulate energy from long excitations and produce detectable effects at extraordinarily low input power even in such weakly non-linear material.

零群速度 (ZGV) 模式是一种特殊的导波，可以存在于弹性板或圆柱体中，并且已被证明是表征材料或厚度变化的非常敏感的工具，在大约板厚的空间分辨率下具有亚百分比的精度。在本文中，我们从理论上和实验上展示了如何通过两个高振幅主波的和频相互作用产生这种模式，然后作为材料非线性的局部探测。相位匹配条件的解，即构造非线性效应的条件，在经典的二次非线性标记中以数值方式获得。导出测量作为时间函数的能量从初级到次级模式的传递速率的耦合系数。使用压电换能器和激光干涉仪在铝板上进行实验，并探索入射对称和反对称基本兰姆模式的相互作用。在一个没有电压放大器的实验中，我们证明了这些 ZGV 模式的谐振特性可以用来从长激发中积累能量，并在极低的输入功率下产生可检测的效果，即使在这种弱非线性材料中也是如此。