Localized modes and acoustic band gaps using different quasi-periodic structures based on closed and open resonators

This paper presents an insightful exploration of the effects of quasi-periodic structures on acoustic wave propagation. Because of their exceptional capacity to manipulate wave behavior in ways periodic structures cannot, quasi-periodic structures are essential in studying acoustic wave propagation. Using the transfer matrix method and finite element method, one-dimensional waveguide structures based on quasi-periodic sequences are studied. Three types of sequences are examined in this work, namely the Thue-Morse, Cantor, and Rudin-Shapiro sequences. The aim of this work is to study these different quasi-periodic sequences in an original way and to examine the properties of acoustic transmission. This work adopts a linear acoustic model. Higher-order modes and viscous effects are ignored in the transfer matrix method. The results show that the kinds of sequences studied lead to the creation of wide band gaps with numerous localized states corresponding to the narrow transmission peaks appearing in these acoustic band gaps. A comparison shows that the Thue-Morse sequences give interesting results in terms of acoustic band gap creation and extension compared to the Rudin-Shapiro and Fibonacci sequences. The Thue-Morse, Cantor, and Rudin-Shapiro sequences also show a significant number of transmission peaks in different band gaps compared to the Fibonacci sequence. These results are very interesting for various applications such as low-frequency noise reduction, filtering, and acoustic wave guiding.