Bandgap variation of a locally resonant metamaterial induced by temperature variation and pre-tension in the shape memory alloy resonators

Abstract

Elastic/acoustic metamaterials with local resonance (LR) arrays have bandgaps that can forbid or suppress the propagation of elastic waves. In this paper, the shape memory alloy (SMA) is utilized in the metamaterial structure to yield variable bandgaps. The relationship between LR bandgap and temperature during heating and cooling is obtained using a metamaterial beam with a periodic array of SMA resonators, and the effect of pre-tension of SMA on the bandgap of this SMA-based metamaterial structure is explored. The experimental results show that the bandgap of this structure varies along with temperature variation. However, as the elastic modulus of SMA varies differently between situations of heating and cooling, such bandgap variation phenomenon differs as well. Additionally, it is concluded that introducing pre-tension in the SMA resonators broadens the variable range of the bandgap during heating although such deformation gradually vanishes due to shape memory effect. It is also verified by simulation that, apart from pre-tension, pre-bending and pre-torsion in the SMA resonators also have significant impact on the bandgap of this structure. Moreover, higher-order bandgaps are observed varying in a similar way as the first-order bandgap, but the entire variation range is more remarkable. By carefully choosing and adjusting the pre-deformation types and parameters, it is possible to manipulate simultaneously both the starting frequency and the width of the bandgap.