Study of the defect modes of a finite one-dimensional periodic structure of three different waveguides

Abstract

In this paper, we used the transfer matrix method (TMM) and Sylvester's theorem to study the effect of the defect’s presence in a periodic acoustic structure. This structure is formed by three different waveguides. The inserted defect is located in the center of the periodic structure. The effect of the discontinuity between two waveguides is not taken into account. The theoretical analysis concerns a 1D rigid waveguide. The effects of higher-order modes, temperature gradients and viscous effects are ignored. We have considered the linear acoustic model and the fluid considered in the waveguides as air. The first study focuses on the acoustic characteristics of the transmission rate and transmission loss of a perfect periodic structure. The effect of different waveguides parameters, such as length and cross-section were analyzed. The results show that the band gaps are very sensitive to these parameters. In the second study, we have examined the properties and effects of the defect insertion in this structure. The numerical results show that the presence of defects in the periodic structure leads to the appearance of defect modes in the band gap. The position of these modes is well controlled in the band gap through increasing the length of the defect. Finally, the importance of this work is reflected through our examination and well exploitation of the acoustic band gap. In addition to that, this study allows us to detect the presence of defects in a periodic structure.