“…The distribution of sound or elastic waves will then be limited to the propagation of the defect at the point or along the line (Roundy and Trolier-McKinstry, 2018; Wu et al, 2017b; Yoon et al, 2016). Due to the existence of BGs and defect states, PCs have many potential applications, which can be widely used in acoustic waveguides, portable devices, wireless sensors, and other devices (Jin et al, 2015; Li and Assouar, 2016; Sun et al, 2022; Taleb and Darbari, 2019). PCs waveguides can transmit sound energy or signals within a specific frequency range, which will be limited to a specified path (Ash et al, 2017; Han and Zhang, 2020; Liu et al, 2020; Piliposyan, 2018).…”