Focusing higher-order Lamb waves based on the Luneburg lens

Abstract

In order to improve the spatial resolution and the signal-to-noise ratio of Lamb waves in structural health monitoring systems or non-destructive testing techniques, this study presents the construction of Luneburg lenses for focusing higher-order Lamb waves based on the thickness variation. The dispersion curves of Lamb waves are calculated firstly, from which the relation between the phase velocity of a specific mode and the plate thickness is quantified. After that, the plate thickness is determined via the refractive index variation. To demonstrate the generality of this design scheme, two lenses, i.e., the A1-wave-based Luneburg lens and the S2-wave-based Luneburg lens are constructed, and their focusing abilities are examined via numerical simulations in both the time domain and frequency domain. It is revealed that the A1 wave and S2 wave can be focused with a focusing size smaller than one wavelength. The design methodology is easy to realize and can be used to control higher-order Lamb waves efficiently, which also provides potential application values in wave detections and energy collections.