A tunable elastic metamaterial beam with flat-curved shape memory alloy resonators

Abstract

When realizing an elastic metamaterial beam, beam-like resonators are regarded as the simplest forms of distributed resonators and their influences on the 1st flexural wave bandgap have been well studied. In this letter, to study the relation between the curvature of the beam-like resonators and the high-order bandgaps (specifically, the 2nd and 3rd bandgaps) and make the bandgaps tunable, we propose a metamaterial beam with a periodic array of two-way shape memory alloys (SMAs). The considered aging-treated Ni-rich Ti-Ni SMAs remember a curved shape with a central angle of 180° at high temperature (austenite phase, A phase) and a flat shape at low temperature (rhombohedral phase, R phase) without the bias springs required for conventional one-way SMAs. Our analyses show that, while reducing the performance of the 1st bandgap, the central frequency of the 2nd (3rd) bandgap of the metamaterial beam with flat-curved SMAs can be decreased by 30.1% (18.3%) with an increase in the bandgap width by 35.9% (19.7%) compared to that with the flat-flat SMAs. In addition, the first torsional mode-induced flexural bandgap is widened and lowered when using the 180° curved beam resonators. The proposed SMA-based metamaterial utilizing the two-way shape memory effect thus offers a flexible and diverse route for tuning the bandgaps.