Complete bandgap of three-dimensional helical metamaterial tapered rod with power-law radius

Tapered metamaterials have drawn much attention due to the inherent advantage of vibration reduction. However, the bandgap performance in most traditionally periodic structures is only restricted to a single direction. In this paper, aiming at opening up the complete bandgap both in flexural and longitudinal directions, we propose a novel type of three-dimensional helical metamaterial tapered rod with a power-law radius. Complex band analyses and vibration transmission results demonstrate that this metamaterial possesses a broad complete bandgap and several single-directional flexural bandgaps. The formation mechanisms of two bandgap types are also revealed. The complete bandgap is created by the combination effect between the local resonance and Bragg scattering effect. The mode transformation phenomenon immediately takes place before and after this complete bandgap. On the other hand, below the complete bandgap, single-directional bandgaps are generated by the separation effect between the neighboring modes which belong to different dominant directions. It can also be found that the wave attenuation capacity in the complete bandgap is far more significant than that of the single-directional one. Meanwhile, by increasing the initial radius or reducing the residual radius, a stronger local resonance effect can enlarge the complete bandgap and improve the attenuation capacity for evanescent waves. To validate the dynamic characteristics, different tapered rod metamaterials are fabricated and tested. A good agreement can be observed between the numerical predictions and experimental results. Based on these analyses, the three-dimensional helical metamaterial tapered rod paves a promising way for realizing excellent omnidirectional wave attenuation.