Multilayer-split-tube resonators with low-frequency band gaps in phononic crystals

Abstract

In this paper, low-frequency band gaps in two-dimensional Helmholtz resonant phononic crystals (PCs) composed of multilayer-split-tube resonators are investigated. The band structures, transmission spectra, and pressure field of the acoustic modes of these PCs are calculated by using a finite element method (FEM). The numerical results show that the first band gap of the structure is from 88 to 140 Hz. The transmission spectra are in accordance with those of the dispersion relation calculations. The acoustic modes of the bands are analyzed to reveal the nature of this phenomenon. It is found that the interaction between the local resonance and the traveling wave modes in proposed structure is responsible for the formation of the first band gap. The influences of the structural parameters on the band gaps are investigated by using FEM and the electrical circuit analogy. Numerical results show that the band gaps can be modulated in an even wider frequency range by changing the structural parameters, such as the rotation angle, the number of tubes, and the radius of the outer tube. The structural design results provide an effective way for phononic crystals to obtain the low-frequency band gaps, which have potential application in the low-frequency noise reduction.