Tunable bandgaps in a deployable metamaterial

Abstract

In this manuscript, we envision deployable structures (such as solar arrays) and origami-inspired foldable structures as metamaterials capable of tunable wave manipulation. Specifically, we present a metamaterial whose bandgaps can be modulated by changing the fold angle of adjacent panels. The repeating unit cell of the structure consists of a beam (representing a panel) and a torsional spring (representing the folding mechanism). Two important cases are considered. Firstly, the fold angle (angle between adjacent beams), Ψ, is zero and only flexural waves propagate. In the second case, the fold angle is greater than zero (Ψ > 0). This causes longitudinal and transverse vibration to be coupled. FEM models are used to validate both these analyses. Increasing the fold angle was found to inflict profound changes to the wave transmission characteristics of the structure. In general, increasing the fold angles caused the bandwidth of bandgaps to increase significantly. For the lowest four bandgaps we found bandwidth increases of 252 %, 177 %, 230 % and 163 % respectively at Ψ = 90 deg (relative to the bandwidths at Ψ = 0). In addition, significant increase in bandwidth of the odd-numbered bandgaps occurs even at small fold angles- the bandwidth for the first and third bandgaps effectively double in size (increase by 100%) at Ψ = 20 deg relative to those at Ψ = 0. This has important ramifications in the context of tunable wave manipulation and adaptive filtering. In addition, by expanding out the characteristic equation of transfer matrix for the straight structure, we prove that the upper band edge of the nth bandgap will always equal the nth simply supported natural frequency of the constituent beam. Further, we found that the ratio (EI/kt) is an important parameter affecting the bandwidth of bandgaps. For low values of the ratio, effectively, no bandgap exists. For higher values of the ratio (EI/kt), we obtain a relatively large bandgap over which no waves propagate. This can have important ramifications for the design of foldable structures. As an alternative to impedance-based structural health monitoring, these insights can aid in health monitoring of deployable structures by tracking the bandwidth of bandgaps which can provide important clues about the mechanical parameters of the structure.