Hierarchical design and vibration suppression of the hexachiral hybrid acoustic metamaterial

This paper introduces a novel locally resonant hierarchical hexachiral acoustic metamaterial (HAM) with doublenegative characteristics, aimed at achieving broad low -frequency bands. The dispersion relation of HAM is investigated integrating the wave equation and Bloch theory. HAM opens three new bandgaps within 0-2200 Hz, with the widest bandgap measuring 291 Hz. Comparing to the classical hexachiral structure, HAM has the 47.7% increase in bandgap width and a reduction in centre frequency. Subsequent the dynamic effective parameters and the modes analysis are calculated numerically to explain the physical mechanism of wave propagation. The different modes, equivalent to the spring -mass model through the equivalent modelling method, show significant local translational and rotational resonances and the double -negative properties. It explains the generation of the low frequency bandgaps and the pass band with negative group velocities. Validation of transmission spectrums are achieved through vertical frequency sweep tests. Additionally, the tunability of the structure is verified by manipulating the number and position of oscillators, realizing a bandgap optimization. When compared to the metamaterial without an oscillator, the total bandwidth increases 154%. This study contributes a novel scheme and comprehensive insights for the engineering application of low -frequency vibration resistance.