Numerical investigation of bandgap characteristics in integrated metallic metafilters for nonlinear guided wave applications

Guided waves propagating in nonlinear media, featuring second harmonic generation, represent a promising avenue for early-stage damage detection due to their high sensitivity and long-range propagation capabilities. However, nonlinear ultrasonic measurements are hindered by nonlinearities induced by the experimental system, necessitating careful calibrations that have restricted their application to laboratory settings. While several phononic crystal and metamaterial designs have been devised to enhance nonlinear-based ultrasonic testing, most are tailored for suppressing second harmonics within a frequency range of 100-300 kHz, primarily utilizing low-frequency excitation. In this paper, we propose a metallic ring-shaped metafilter designed to explore high-order bandgaps. To fully understand the bandgap characteristics, we begin by analyzing mode shapes, providing insights into the underlying wave mechanics. The efficacy of the designed filter is subsequently assessed through 3D time step elastodynamic simulations. In addition, this study underscores the significance of parameters such as the number of rings employed in the filter, signal duration, and bandgap width in optimizing its performance. Furthermore, the observed mode conversion phenomena from S₀ to A₀ guided wave modes underscore the filter’s capacity to influence guided wave propagation. The defect localization technique, based on the time difference of arrival of second-order wave modes, accurately predicts the defect location with an error margin of less than 0.2%. The present investigation showcases advancements in the sensitivity of nonlinear-based guided wave testing for characterizing microstructural changes, promising substantial potential for detecting incipient damage in practical structural health monitoring applications.