Merging Bragg and Local Resonance Bandgaps in Perforated Elastic Metamaterials with Embedded Spiral Holes

Abstract

Perforated elastic metamaterials (EMMs) comprising periodic distribution of holes have recently attracted growing attention due to relatively simple fabrication process and unusual physical properties. Rational design of perforation configuration for practical applications in low-frequency vibration mitigation is challenging and important. In this study, a novel type of perforated EMMs with two bandgap formation mechanisms (i.e., Bragg scattering and local resonance) is proposed for low-frequency and broadband wave attenuation. Four concentric spiral holes are introduced into each matrix material of the conventional EMMs plate with mutually orthogonal rectangular holes. The analysis of bandgap formation mechanism indicates that the coiled waveguide introduced by the spiral holes enhances the wave scattering in the matrix material, and that the wave scattering in the divided matrix material by the orthogonal rectangular holes couples the local resonance modes formed by the spiral holes, where the coupling modes lead to the generation of the coupling bandgap and the improvement of wave attenuation. Both experiments and numerical analyses demonstrate that the proposed metamaterials can create multiple bandgaps in the sub-wavelength frequency domain compared to the metamaterials with single-type holes, which include two Bragg bandgaps with a reduced frequency of 76%, two overlapping bandgaps with local resonance dominating, and two deaf bands.