Modeling and simulation of zero-group-velocity combined harmonic generated by two counter-directional Lamb waves...

The zero-group-velocity (ZGV) mode of Lamb waves exhibits unique characteristics, where acoustic energy is trapped within localized regions of the waveguide. Previous research has established that ZGV combined harmonics - generated through the nonlinear interaction of frequency mixing response (FMR) - serve as highly sensitive tools for probing local material nonlinearity. In this study, we present a modeling and numerical analysis of ZGV combined harmonics produced by the mixing of two counter-directional Lamb waves in an adhesively bonded plate, explicitly considering the influence of interfacial properties on FMR efficiency. Based on theoretical analysis, a specific Lamb wave mode triplet is selected to ensure satisfaction of the internal resonance condition. The generation of ZGV combined harmonics at the sum frequency, arising from the interaction of counter-propagating Lamb waves within the plate, is systematically modeled. The results indicate that the efficiency of combined-harmonic generation for sensitive response correlates with the acoustic energy trapping characteristics of ZGV modes. Critically, the spatial location accuracy of the wave mixing phenomenon depends on the central position of the interaction zone rather than its length. Thus, there is no requirement to optimize the mixing zone length for both spatial resolution and signal clarity simultaneously; this inherent balance enhances the applicability of FMR-based nonlinear methods. Finite element (FE) simulations demonstrated that localized interfacial degradation can be detected and characterized by scanning the wave mixing zone of the two primary Lamb waves. The numerical analysis further validated the method's capability to identify multiple localized degradations with varying severity and length in bonded structures. This work elucidates the physical mechanisms underlying ZGV combined-harmonic generation in adhesively bonded plates and presents a promising approach for non-destructive assessment of interfacial integrity via counter-directional Lamb wave mixing.