南京大学学报(自然科学版) ›› 2015, Vol. 51 ›› Issue (6): 1174–1181.

• • 上一篇    下一篇

随机扰动对周期共鸣器阵列性能影响的研究

王晓楠1,2*   

  • 出版日期:2015-11-14 发布日期:2015-11-14
  • 作者简介:(1.上海市环境科学研究院,上海,200233;2.上海城市环境噪声控制工程技术研究中心,上海,200233)
  • 基金资助:
    基金项目:上海市自然科学基金(14ZR1435200)
    收稿日期:2015-06-30
    *通讯联系人,E-mail:wangxn@saes.sh.cn

A study on the effect caused by random disturbance on the performance of periodic resonator array

Wang Xiaonan1,2*   

  • Online:2015-11-14 Published:2015-11-14
  • About author:(1. Shanghai Acadamy of Environmental Sciences, Shanghai, 200233, China; 2. Shanghai Engineering Research Center of Urban Environmental Noise Control, Shanghai, 200233, China)

摘要: 周期亥姆霍兹共鸣器(Helmholtzresonator)阵列可以看作一类比较特殊的声子晶体,通过调节共鸣器个体与周期间隔之间的关系,可以获得一个由布拉格(Bragg)反射与共鸣器谐振共同作用的禁带.该禁带同时具备宽带和低频的特性.然而在很多情况下,该结构的周期性并不是完美的,可能存在一定的扰动或者缺陷.通过理论建模和数值仿真的方式详细探讨了当该阵列单元存在随机扰动的情况,主要选取了共鸣器短管长度以及短管口面积两个参数进行研究,通过求解共鸣器阻抗统计平均值,得到系统的统计平均传递损失,并且生成随机扰动的特例与系统统计平均传递损失进行对比,发现与统计平均传递损失的趋势基本吻合.本文同时研究了系统参数不同程度的扰动对禁带的影响.对比于单个共鸣器结构,周期共鸣器阵列以及存在扰动的共鸣器阵列结构在低频宽带噪声控制以及声学滤波等方向都存在着潜在的应用价值.

Abstract: Periodic Helmholtz resonators array can be regarded as a typical sonic crystal. By properly tuning the geometries of the resonators and the periodic distance between each two periodic cell, a low-frequency broad forbidden band resulted from both Bragg reflection and the resonance of Helmholtz resonator can be obtained correspondently. However, the periodicity of the structure cannot be perfect as disturbance or defect in the structure may exist. This paper considers the random disorder in a periodic duct-resonator system theoretically and numerically. Two cases are investigated: the disorder in neck length of Helmholtz resonators and the disorder in neck cross-sectional area of Helmholtz resonators. The expectation of the acoustic impedance of Helmholtz resonator is first derived, which further leads to the calculation of ensemble average transmission loss of the overall structure. Moreover, parametric random values of neck length and neck cross-sectional area of the resonator are generated and the corresponding average transmission loss is calculated for with the ensemble average TL. It is shown that the average transmission loss is generally coincident with the ensemble average transmission loss. Furthermore, different disturbing degree is also considered. It turns out that, by comparing with a single Helmholtz resonator, both periodic resonator array and resonator array with disorder have potential application in low frequency broadband noise control as well as in acoustic filtering.

[1] N.Sugimoto, T.Horioka. Dispersion characteristics of sound waves in a tunnel with an array of Helmholtz resonators. Journal of the Acoustical Society of America, 1995, 97(3):1446-1459.
[2] Mead DJ. A general theory of harmonic wave propagation in linear periodic systems with multiple coupling. Journal of Sound and Vibration, 1973, 27(2):235-60.
[3] 刘聪,徐晓东,王敬时等. 三明治型声子晶体中LAMB波传播特性的研究. 南京大学学报(自然科学), 2012, 48(5): 531-536.
[4] 丁红星,沈中华,戴丽莉等.侧面周期嵌入空气柱薄板中兰姆波带隙研究. 南京大学学报(自然科学), 2013, 49(1): 58-63.
[5] 刘红星,吴九汇,沈礼等. 声子晶体结构低频降噪机理研究及应用. 南京大学学报(自然科学), 2013, 49(4): 531-537.
[6] Xu Wang, Dongxing Mao, Wuzhou Yu, et al. Sound barriers from material of inhomogeneous impedance. Journal of the Acoustical Society of America, 2015, 137:3190-3197.
[7] Wang X, Mak CM. Wave propagation in a duct with a periodic Helmholtz resonators array. Journal of the Acoustical Society of America, 2012, 131(2):1172–82.
[8] Wang X, Mak CM. Acoustic performance of a duct loaded with identical resonators. Journal of the Acoustical Society of America, 2012, 131(4):EL316–22.
[9] Sigalas M M. Elastic wave band gaps and defect states in two-dimensional composites. Journal of the Acoustic Society of America, 1997, 101(3): 1256~ 1261.
[10] Kafesaki M, Sigalas M M, Garcfa N. Frequency Modulation in the Transmitivity of Wave Guides in Elastic-Wave Band-Gap Materials. Physical Review Letters, 2000, 85(19): 4044~4047.
[11] 高东宝,曾新吾,周泽民等. 一维亥姆霍兹共振腔声子晶体中缺陷模式的实验研究. 物理学报, 2013, 62(9): 094304-1-6.
[12] Wang X, Mak CM. Disorder in a periodic Helmholtz resonators array. Applied Acoustics, 2014 ,82:1-5
[13] Langley RS. Wave transmission through one-dimensional near periodic structures: optimum and random disorder. Journal of Sound and Vibration, 1995, 188:717–743.
[14] 盛骤,谢式千,潘承毅论与数理统计.第四版.北京:高等教育出版社,2008,50.
[15] Johnson N.L., Kotz S., Balakrishnan N. Continuous Univariate Distributions, Volume 1, Wiley, 1994, 10.1.
[16] Thompson LL. A review of ?nite-element methods for time-harmonic acoustics. Journal of the Acoustic Society of America, 2006, 119(3):1315–1330.
[17] Chunqi Wang, Lixi Huang. Analysis of absorption and reflection mechanisms in a three-dimensional plate silencer. Journal of Sound and Vibration, 2008, 313:510-524.
[18] U.Ingard. On the theory and design of acoustic resonators. Journal of the Acoustical Society of America, 1953, 25:1037-1061.
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