Tunability of acoustic band gaps using Thue Morse quasiperiodic lateral resonators

In this paper, we have investigated the acoustic transmittance properties of a quasi-periodic waveguide structure based on generalized Thue-Morse sequences (GTMS(m,n)) using the transfer matrix method and finite element method. The structure consists of open and closed lateral resonators arranged non-periodically according to a well-defined recurrence relation. This work aims to examine the effect of the quasi-periodicity of our system on the characteristics of the acoustic band gap. The results show that varying the GTM (m, n) sequences and the parameters of successive repeats m and n control the number, position, and width of the acoustic band gap. Specifically, increasing the order of the GTMS(m,n) widens the central acoustic band gap and increases the number of band gaps between the frequency ranges of 300 Hz and 600 Hz. The creation of these acoustic band gaps is important for selectively filtering frequency intervals where the acoustic wave is completely reflected in order to control and reduce low-frequency noise. On the other hand, we have analyzed the behavior of narrow transmittance peaks localized in the central acoustic band gap. These transmittance peaks are created through the wave interference phenomena resulting from the quasi-periodicity of the GTMS.