Selective filter using Thue–Morse structures by the finite element and transfer matrix methods

This work analyzes the propagation of acoustic waves in quasi-periodic structures for filter applications. The study focuses on a proposed one-dimensional quasi-periodic structure employing generalized Thue–Morse sequences. The suggested configuration consists of two basic building blocks: the block ‘X’ is a parallel configuration of closed resonators grafted on the main duct. The block ‘Y’ has a single open resonator integrated into the same main duct. Using the transfer matrix method and finite element method, the study investigates the acoustic bandgap characteristics of Thue–Morse. The present work leverages both methods, comparing their predictions and emphasizing the impact of multidimensional effects, particularly in the context of Thue–Morse sequences. Besides, the results show that acoustic band gaps can be tuned, and there are localized modes that can help filter waves and suppress high-frequency noise.