The SH0 wave manipulation in graded stubbed plates and its application to wave focusing and frequency separation

Abstract

In this study, a methodology to artificially control the propagation of fundamental shear horizontal (SH0) waves in elastic plates is proposed using stubs with spatially graded height, and two novel phenomena, wave focusing and low-pass wave filtering, are realized. As a basis for this, the band structure analysis is carried out for an aluminum plate with hexagonally arranged stubs, and the relationships between the wave velocity, the band gap and the stub height are established. Based on these results, omni-directional SH0 wave-based Luneburg and Maxwell fish-eye lenses, as well as low-pass wave filter, are designed artificially using multiple stubs with spatially graded heights. It is demonstrated that both of the lenses exhibit good focusing ability, with the focusing size smaller than the wavelength. Additionally, they can work with a finite bandwidth around the design frequency. It has also been revealed both in time and frequency domain simulations that the SH0 wave with a lower frequency can travel over a longer distance when it enters the low-pass wave filter, which demonstrates its frequency separation capability.