Acoustic multiple transmission peaks in Thue-Morse structures based on lateral resonators

Abstract

This research investigates the acoustic wave propagation in one-dimensional quasi-periodic waveguide structures designed using generalized Thue-Morse sequences. The configuration comprises two distinct resonator blocks: one featuring parallel open/closed resonators and the other containing closed resonators arranged in series within a primary air duct. These structures can be fabricated from materials such as aluminum, brass, or steel. Using the transfer matrix and finite element methods, the study calculates acoustic transmittance under normal incidence, revealing the formation of low-frequency band gaps attributed to the local resonance effects of the quasi-periodic arrangement. The analysis highlights how increasing the cross-section ratio significantly broadens the central band gap in the transmittance spectra, enhancing noise attenuation. Furthermore, the quasi-periodic design generates multiple sharp resonance peaks with high transmittance within the band gaps. The findings show that the number and positioning of these peaks can be controlled by modifying the Thue-Morse sequence order and repetition parameters. Additionally, the study explores how expanding the number of blocks influences the reduction of transmittance in pass bands. These insights hold significant promise for applications in acoustic multiplexing devices. Besides, Thue-Morse sequence of lateral resonators demonstrates a record-high sensitivity of 17.2 Hz·s/m for gas detection, significantly outperforming all recent periodic and quasi-periodic designs.