In this Letter, an algebraic topology analysis on the bandgaps in phononic Fibonacci waveguides consisting of wide and narrow stainless steel pipes is presented. It has been found that the non‐Bragg forbidden gaps can also exist in quasi‐periodic waveguide structures based on the constructed relations between the quasi‐periodic and periodic waveguides. The so‐called non‐Bragg gaps are caused by the resonances between different transverse modes while the same modes with matching longitudinal wavenumbers always result in the traditional Bragg gaps. In the experiments in this study, the observed non‐Bragg gap appears earlier than the Bragg one in the previous generations of Fibonacci sequences, and the sound attenuation is much more intense, because the lower generations with shorter lengths can only provide enough interaction effects in the transverse dimension. The algebraic topology methods and the observations of non‐Bragg gaps in quasi‐periodic waveguides can not only enrich the knowledge on wave structure interactions but also benefit various applications in wave control engineering.

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ARTICLES YOU MAY BE INTERESTED INFast surface acoustic wave solution method based on the generalized Green's function AIP Advances 8, 085210 (2018) We demonstrate the localization of water surface waves and its evolution by introducing a defect into a trough with periodic sidewalls. Taking the advantage of water wave visualization, we observed a defect mode arising in the forbidden band and its formation process, that the water waves gradually accumulate at the defect, and accordingly, the energy gets smaller in the incidence part but larger in the exit part. After a certain time, when the accumulated energy gets large enough to produce a defect mode, we can obtain a steady state and an extraordinary transmission. It was also found that the transmission frequency linearly depends on the defect length with the negative slope and the localizations in different defects were also observed and analyzed. Due to the ubiquity of wave phenomena, the observation of water wave localization not only present a visual picture for the fundamental resonance concept, but also find applications in various fields, such as underwater acoustics, ultrasonics, electromagnetic waves, and optics. © 2018 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

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