Defect Modes in One-Dimensional Periodic Closed Resonators

Abstract

In this paper, the study of the presence of defects in an acoustic periodic structure is used in an original way. This structure is composed by closed acoustic resonators. The defect resonator is located in the center of the structure. The Sylvester’s theorem is applied to examine the properties and the effects of these defect modes. We consider 1D geometry and in this case, it’s known that only the plane mode is propagated. The higher-order modes and visco-thermic effects are ignored. We consider the linear acoustic model and the fluid in the waveguides is air. Two kinds of defects state are studied: the first case is corresponding of a waveguide without branched resonator and the second case is corresponding of a closed resonator with a great height. The introduction of a defect in the structure leads to create a resonance peak in the acoustic band gap. To our knowledge this study is original in the field of acoustic wave propagation. We show that the position and the frequency of the defect peak in the band gap are well be controlled by increasing the length of the defect. Finally, it can be said that the interest of this study is reflected in the fact that the band gap is exploited in an original way. Also, this study allows us to detect the presence or not of defects in a periodic structure.