Non‐Bragg Bands in Acoustic Quasi‐Periodic Fibonacci Waveguides

Abstract

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.