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Title: Wave propagation in a duct with a periodic Helmholtz resonators array
Authors: Wang, X
Mak, CM 
Issue Date: Feb-2012
Source: Journal of the Acoustical Society of America, Feb 2012, v. 131. no. 2, p. 1172–1182
Abstract: Helmholtz resonator is often used to reduce noise in a narrow frequency range. To obtain a broader noiseattenuation band, combing several resonators is a possible way. This paper presents a theoretical study of sound propagation in a one-dimensional duct with identical side-branch resonators mounted periodically. The analysis of each resonator was based on a distributed-parameter model that considered multi-dimensional wave propagation in its neck-cavity interface. This model provided a more accurate prediction of the resonant frequency of the resonator than traditional lumped-parameter model. Bloch wave theory and the transfer matrix method were used to investigate wave propagation in these spatially periodic resonators. The results predicted by the theory fit well with the computer simulation using a three-dimensional finite element method and the experimental results. This study indicates that the wave coupling in this periodic system results in the dispersion of the frequency band into the stop and the pass bands. The long-term significance is that periodic resonators may more effectively control noise in ducts by broadening the bandwidth they attenuate and increasing the magnitude of sound attenuation.
Keywords: Acoustic variables control
Computer simulation
Finite element method
Frequency bands
Natural frequencies
Transfer matrix method
Publisher: Acoustical Society of America
Journal: Journal of the Acoustical Society of America 
ISSN: 0001-4966
EISSN: 1520-8524
DOI: 10.1121/1.3672692
Rights: Copyright 2012 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.
The following article appeared in Wang, X., & Mak, C. M. (2012). Wave propagation in a duct with a periodic helmholtz resonators array. Journal of the Acoustical Society of America, 131(2), 1172-1182 and may be found at
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