Properties of band gaps in phononic crystal pipe consisting of expansion chambers with extended inlet/outlet

Abstract

Noise reduction is an interesting and important subject in the piping systems of many applications, in order to suppress noise in the pipe, many significative researches have been done. In recent years, the acoustic wave propagation in the phononic crystal pipe has received increasing attention. The characteristic band gaps in phononic crystal pipe can forbid wave to propagate within the band-gap frequency range, which provides a new way to control the noise in piping system. In this paper, the acoustic properties of phononic crystal pipe consisting of expansion chambers with the extended inlet/outlet are investigated theoretically and numerically. By combining the two-dimensional mode matching method and the transfer matrix method, the band structure and transmission loss, especially the band-gap properties of the phononic crystal structure are presented. The obtained results exhibit excellent agreement with the results from the finite element method. Then, this theoretical method is compared with the one-dimensional plane wave method, and it is found that the results from the proposed method are more accurate within the studied frequency range. Further, the effect of modal order in the band-gap frequency range is analyzed, which shows that the mode matching method has a good convergence.The wave scattering and resonance of the chamber will induce the Bragg and locally-resonant band gaps in the periodic pipe, respectively. Further analysis on the transmission coefficient in a band gap is conducted. It shows that the transmission coefficient decays exponentially with the periodic number increasing, which demonstrates that the suppression of the wave propagation in phononic crystal pipe is caused by the band-gap rather than the impedance mismatch. Then the effects of variable parameters including the lattice constant and the length of the insertion on the location and width of the band gaps are investigated. The results show that the lattice constant mainly controls the Bragg band gaps and the length of the insertion exerts a significant influence on the locally-resonant band gaps. Finally, the coupling behaviors of band gaps are studied to expand their widths. It is found that the Bragg band gaps can be coupled with the locally-resonant band gaps via changing the lattice constant and the length of the insertion, which can give rise to wider band gaps. Furthermore, the coupling between two locally-resonant band gaps is proposed by changing the length of the insertion, which also produces wider band gaps.This study can provide new ideas for designing the phononic crystal pipe to suppress the noise in piping system.