Design scheme of an S0 wave-based low-pass wave filter and an A0 wave-based Luneburg lens in a graded stubbed plate

Abstract

Owing to their ability to detect small defects and flaws at very low frequencies, ultrasonic guided waves, as well as their artificial manipulation in structural health monitoring and non-destructive evaluation systems, are generating growing interest both in scientific research and engineering applications. In this paper, a methodology to artificially steer guided waves, i.e. attaching multiple graded cylindrical stubs on the plate surface, is proposed, and two kinds of devices, an S0 wave-based low-pass wave filter and an A0 wave-based Luneburg lens, are designed. Firstly, the band structure of a periodic crystal consisting of a cylindrical stub, hexagonally distributed on the surface of an aluminum plate, is calculated numerically. After validation via the transmission power, band gap evolution with the stub height is achieved, on which basis an S0 wave-based low-pass wave filter is realized and exemplified in both the time and frequency domains. It is revealed that the incident S0 wave with a lower frequency in the range of 110 kHz to 170 kHz can travel over longer distances when it enters the low-pass wave filter, and vice versa. Subsequently, the relationship between the frequency of the A0 branch and the stub height are quantified, which is used to design an omnidirectional A0 wave-based Luneburg lens. This lens exhibits good focusing ability, demonstrated by a focusing size smaller than the working wavelength. Not restricted to a fixed frequency, the Luneburg lens designed is shown to be wideband, and also presents high focusing performance in an effective frequency range centered on the designed frequency. The methodology presented is straightforward, and the two devices fulfilled are easy to manufacture with natural materials, which provides much convenience for experimental verification and final engineering applications.