随机扰动对周期共鸣器阵列性能影响的研究

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

周期亥姆霍兹共鸣器(Helmholtz resonator)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.

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 corre-spondently.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 were 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 was first derived,which would be used to calculate ensemble average transmission loss of the overall structure.Moreover,par-ametric random values of neck length and neck cross-sectional area of the resonator were generated and thenbsp;corresponding average transmission loss was calculated for with the ensemble average TL（transmission loss）.It is shown that the average transmission loss is generally coincident with the ensemble average transmission loss.Fur-thermore,different disturbing degree was 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.