Abstract
In this paper, the authors proposed a class of hierarchical square honeycomb metamaterials (HSHMs) with low-frequency broad bandgaps (BGs) and flat energy band characteristics. The mechanical model of the square honeycomb structure and the in-plane mode lattice dynamics model of the HSHMs are presented. The formation mechanism of BGs and flat energy band characteristics are obtained by combining the band structure with transmission spectra, which was calculated using the finite-element method. The numerical results show that the HSHM structure has multiple BGs below 100 Hz, and the transmission spectra are in accordance with the band structure calculations. Additionally, the effects of the scatterer shape and the honeycomb parameters of the elastic element on the BGs are further analyzed and discussed. Based on the analysis, it was concluded that the BGs can be modulated in a wider and lower frequency range by changing the scale factor, the length-to-width ratio of the honeycomb side beam, and layer dislocation. These research results provide a novel structure for the design and application of acoustic metamaterials.
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