Low-frequency band gap design of acoustic metamaterial based on cochlear structure

In this paper, a new chiral spiral structure based on the cochlear structure is proposed. The chiral spiral structure consists of four orthogonally oriented cochlear structures with the same geometric parameters connected at the inner endpoints of the four cochlear structures. Based on the Bloch’s theory and finite element method, the band gap characteristics of the proposed chiral spiral structure are studied. The effects of ligament bending angle (θ), the ratio of arc radius of cochlear contour (α), the ligament thickness (t_c ), and the level of the chiral spiral structure (n) on the chiral spiral structure are discussed. The results show that the two-level chiral spiral structure (n= 2) has the best band gap characteristics when θ = 180° and α = 0.45. With the decrease of t_c and the increase of n, the opening frequency of the first band gap gradually decreases. When n = 22, the chiral spiral structure has the lowest opening frequency, 1.91 Hz. The existence of the band gap is verified through the low amplitude elastic wave transmission tests. The distribution of the iso-frequency lines indicates that with the increase n, the propagation of elastic waves of the chiral spiral structure shows more distinct directivity, which provides a basis for the propagation control of elastic waves. These findings can provide new design ideas and directions for low-frequency vibration and noise control.