Resonance-induced band gaps in a periodic waveguide

The band gaps in periodic structures are usually regarded as being induced by the Bragg resonances. Until the recent years, the non-Bragg nature resonances were not taken into account in analysing and computing the band gaps, though it can exist in all kinds of waveguides with periodic structures. Here, the resonance-induced band gaps in a periodic acoustic duct are investigated extensively and a graphical method is introduced to analyse the dependence of these resonances on the duct geometry. With this method, it becomes quite easy to estimate the frequency band gaps of the waveguide and shape the band structures by choosing the proper geometric parameters. Our analysis show that the location and the width of the band gap are closely related to the wavenumber and the amplitude of the wall corrugations, and the non-Bragg resonance can result in the obvious band gap when the wall wavenumber is close to the cut-off frequency of the first mode.