Investigation of energy trapping effect for nonlinear guided waves in a topographical structure

Abstract

Cumulative second harmonic generation (SHG), where the amplitude of the generated second harmonic increases with propagation distance, is commonly utilized to enhance the measurability of nonlinear guided waves by providing a sufficient signal-to-noise ratio. Investigating and confirming the cumulative SHG of feature guided waves (FGWs) in topographical waveguides is crucial for accurately assessing material nonlinearity in such structures. This study examines the cumulative SHG of FGWs propagating in a typical topographic structure of a welded joint through both numerical simulations and experimental investigations. A theoretical model is developed using the semi-analytical finite-element (SAFE) method and perfectly matched layer (PML) to analyze the propagation characteristics of FGWs in a welded joint. The numerical and experimental results provide verification of the “trapping effect” of FGWs within the welded joint. Furthermore, the “cumulative effect” of SHG of FGWs is observed. Remarkably, both the experimental and numerical findings demonstrate that cumulative SHG of FGWs can be achieved by employing suitable mode selection and frequency tuning in the topographic structure, which aligns well with the theoretical predictions. This investigation contributes to advancing our understanding of cumulative SHG in FGWs propagated within topographical structures. These findings have practical implications for accurately characterizing material nonlinearity in topographic waveguides.