Effect of Mean Flow on Acoustic Wave Propagation in a Duct with a Periodic Array of Helmholtz Resonators

Sound propagation properties of a duct system with Helmholtz resonators(HRs) are affected by mean flow.Previous studies have tended to focus on the effects of mean flows on acoustic response of a duct system with a finite number of HRs. Employing an empirical impedance model, we present a modified transfer matrix method for studying the effect of mean flow on the complex band structure of an air duct system with an infinite periodic array of HRs. The efficiency of the modified transfer matrix is demonstrated by comparison between an example of transmission response calculation for a finite single HR loaded duct and the finite element simulation result calculated using the COMSOL software. Numerical results are presented to analyze the effect of mean flow on the band structure and transmission loss of the sound wave in the duct system. It is hoped that this study will provide theoretical guidance for acoustic wave propagation of HR silencer in the presence of mean flow.     

An Analysis of Structural-Acoustic Coupling Band Gaps in a Fluid-Filled Periodic Pipe

A periodic pipe system composed of steel pipes and rubber hoses with the same inner radius is designed based on the theory of phononic crystals. Using the transfer matrix method, the band structure of the periodic pipe is calculated considering the structural-acoustic coupling. The results show that longitudinal vibration band gaps and acoustic band gaps can coexist in the fluid-filled periodic pipe. The formation of the band gap mechanism is further analyzed. The band gaps are validated by the sound transmission loss and vibration-frequency response functions calculated using the finite element method. The effect of the damp on the band gap is analyzed by calculating the complex band structure. The periodic pipe system can be used not only in the field of vibration reduction but also for noise elimination.     

Wave propagation in a duct with a periodic Helmholtz resonators array

Helmholtz resonator is often used to reduce noise in a narrow frequency range. To obtain a broader noise attenuation 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.     

Interplay of local resonances and Bragg band gaps in acoustic waveguides with periodic detuned resonators

This letter is concerned with acoustic wave propagation and transmission in acoustic waveguides with periodically grafted detuned Helmholtz resonators. The interplay of local resonances and Bragg band gaps in such periodic systems is examined. It is shown that, when the resonant frequencies of the resonators are tuned close to a Bragg band gap, the behavior of the Bragg band gap can be affected dramatically. Particularly, by introducing appropriately tuned resonators, the bandwidth of a Bragg band gap can be reduced to zero, leading to a very narrow pass band with great wave attenuation performance near both band edges. The band formation mechanisms of such periodic waveguides are further examined, providing explicit formulae to locate the band edge frequencies of all the band gaps, as well as the conditions to achieve very narrow pass bands in such periodic waveguides.     

Double topological edge states investigation in sonic metamaterials

We investigate the topologically protected sound propagation in sonic metamaterials, analogous to quantum spin hall effect (QSHE). The sonic metamaterials consist of circular rods and meta-molecules arranged in air with a honeycomb-lattice. The on-demand inversion in topological phase can be achieved by two ways of scatterer controls at locally resonant frequency and Bragg frequency. The Helmholtz resonators in the structure are contributed to the formation of subwavelength double Dirac cones which are more likely to appear due to local resonance enhancement with more number of resonators. By combining two sonic metamaterials with different topological invariants, we demonstrate the robust sound propagation and pseudospin-dependent one-way acoustic propagation at the interface. Experimental measurement of the topologically protected acoustic wave transmission matches well with the simulation result.     

双层弹性支撑板的水下宽带隔声

为实现水下宽带隔声,提出了一种由弹性元件支撑两块刚性端板构成的双层弹性支撑板结构。采用弹簧振子振动分析法和声传播理论,建立了平面波入射的水下隔声理论模型,分析了结构参数对隔声量的影响规律,结果表明足够小的弹性元件单位面积弹性系数或足够大的端板单位面积质量都可以连续一致地提高隔声量.仿真分析了双层弹性支撑板的振动位移和声输入阻抗,比较了双层弹性支撑板与连续介质层的隔声特性,结果表明,降低弹性元件质量,有助于在低频段消除半波全透射现象.在同厚度、同质量、同静态压缩率条件下,双层弹性支撑板能更好的降低两侧流体的振动及声耦合,隔声频带更宽,带内一致性更好,隔声量更大.      

Acoustic performance prediction of Helmholtz resonator with conical neck

There is no accurate analytical approach for the acoustic performance prediction of Helmholtz resonator with conical neck,which has broad band acoustic attenuation performance in the low frequency range.To predict the acoustic performance of the resonator accurately,a general theory model based on the one-dimensional analysis approach with acoustic length corrections is developed.The segmentation method is used to calculate the acoustic parameters for sound propagation in conical tubes.And then,an approximate formula is deduced to give accurate correction lengths for conical tubes with difierent geometries.The deviations of the resonance frequency between the transmission loss results obtained by the general theory with acoustic lengths correction and the results from the finite element method and experiments are less than 2 Hz,which is much better than the results from one-dimensional approach without corrections.The results show that the method of acoustic length correction for the conical neck greatly improved the accuracy of the one-dimensional analysis approach,and it will be quick and accurate to predict the sound attenuation property of Helmholtz resonator with conical neck.     

Temperature-controlled tunable acoustic metamaterial with active band gap and negative bulk modulus

The local resonant band gap and the negative bulk modulus of the acoustic metamaterial with Helmholtz resonators are strongly affected by the temperature of water. In this paper, the acoustic transmission line method (ATLM) is introduced to investigate the influences of the temperature of water on the local resonant band gap and the negative bulk modulus of the acoustic metamaterial. Results show that the relative variations of the local resonant band gap and the negative effective bulk modulus suffering from the change of the temperature of water are approximately equivalent and are up to about 11%. The reason is that the local resonant frequency is proportional to the sound speed of fluid which is strongly effects by the temperature of water. By achieving the unambiguous relationships between these unusual properties of the acoustic metamaterial and the temperature of water, we find that the temperature-controlled acoustic metamaterial with the active band gap and the active negative bulk modulus can be realized in theory. This idea opens a new avenue for the design of the tunable acoustic metamaterial that can modulate the acoustic wave propagation.     

全向入射条件下一维固流周期结构中低频声裂隙变化特性研究

利用传递矩阵法, 从理论上建立了全向入射条件下一维固-流周期结构中的声传播模型, 在此基础上计算、分析并比较了无限周期结构的声能带结构和有限周期结构中的声传输特性. 研究结果表明, 当声波以一定的入射角入射时, 固-流周期结构的低频通带区域存在一个声裂隙, 该声裂隙所对应的入射角大小与构成周期结构的固体层和流体层的密度或结构尺寸无关, 而仅取决于构成该周期性结构材料的波速. 关键词： 传递矩阵 全向入射 固-流周期结构 声裂隙     

内插扩张室声子晶体管路带隙特性研究

声子晶体管路的带隙特性,可以实现管路系统在特定频率下的噪声控制.利用二维模态匹配法推导出单个内插扩张室元胞的传递矩阵,结合Bloch定理,得到声子晶体管路的能带结构计算方法;验证了二维方法在计算能带结构时的准确性.研究发现,内插扩张室声子晶体管路存在布拉格带隙和局域共振带隙.进一步研究了晶格常数以及内插管长度对能带结构的影响,结果表明,晶格常数主要控制布拉格带隙,而内插管长度对局域共振带隙有较大的影响,并研究了两种参数变化下的带隙耦合.研究结果可以为管路降噪设计提供新的思路.     

Attenuation and scattering of axisymmetrical modes in a fluid-filled round pipe with internally rough walls

The attenuation of axisymmetric eigenmodes in a cylindrical, elastic, fluid-filled waveguide with a statistically rough elastic wall is studied. It is shown that small perturbation theory can be used to relate explicitly the statistical characteristics of the internal wall surface roughness of an elastic pipe to the attenuation and scattering coefficients of the acoustic modes in the filling fluid. Analytical expressions for modal attenuation coefficients are obtained. The analysis of the frequency dependent attenuation coefficients and the ratio between the roughness correlation length and the inner radius of the pipe is made for different correlation functions of the roughness. It is shown that two scale parameters control the overall behavior of the modal attenuation coefficients. These are the ratios of the roughness correlation length and the inner pipe radius to the acoustic wavelength. The numerical results for sound propagation in a pipe and in a borehole with statistically rough, elastic walls are obtained and discussed.     

Underwater tunable organ-pipe sound source

A highly efficient frequency-controlled sound source based on a tunable high-Q underwater acoustic resonator is described. The required spectrum width was achieved by transmitting a linear frequency-modulated signal and simultaneously tuning the resonance frequency, keeping the sound source in resonance at the instantaneous frequency of the signal transmitted. Such sound sources have applications in ocean-acoustic tomography and deep-penetration seismic tomography. Mathematical analysis and numerical simulation show the Helmholtz resonator's ability for instant resonant frequency switching and quick adjustment of its resonant frequency to the instantaneous frequency signal. The concept of a quick frequency adjustment filter is considered. The discussion includes the simplest lumped resonant source as well as the complicated distributed system of a tunable organ pipe. A numerical model of the tunable organ pipe is shown to have a form similar to a transmission line segment. This provides a general form for the principal results, which can be applied to tunable resonators of a different physical nature. The numerical simulation shows that the "state-switched" concept also works in the high-Q tunable organ pipe, and the speed of frequency sweeping in a high-Q tunable organ pipe is analyzed. The simulation results were applied to a projector design for ocean-acoustic tomography.     

锥形颈部赫姆霍兹共振器声学性能预测

锥形颈部赫姆霍兹共振器具有更好的低频消声能力,而其声学性能尚无准确解析预测方法。为了研究其声学性能,在声学长度修正的基础上,利用一维解析方法建立了用于计算传递损失的一维修正模型。运用分割法计算锥形管内部声传播的声学长度修正,并给出了声学修正长度计算公式。采用得到的锥形管声学修正长度和一维修正模型,计算出的锥形颈部赫姆霍兹共振器频率与有限元及实验测试结果偏差在2 Hz以内,明显优于不修正的计算结果。表明锥形管声学长度修正法提高了一维解析方法的精度,从而可以快捷准确的预测锥形颈部赫姆霍兹共振器的消声性能。      

Sound attenuation of a periodic array of micro-perforated tube mufflers

The wave propagation in a periodic array of micro-perforated tube mufflers is investigated theoretically, numerically and experimentally. Because of the high acoustic resistance and low mass reactance due to the sub-millimeter perforation, the micro-perforated muffler can provide considerable sound attenuation of duct noise. Multiple mufflers are often used to enhance attenuation performance. When mufflers are distributed periodically in a duct, the periodic structure produces special dispersion characteristics in the overall sound transmission loss. The Bloch wave theory and the transfer matrix method are used to study the wave propagation in periodic micro-perforated tube mufflers and the dispersion characteristics of periodic micro-perforated mufflers are examined. The results predicted by the theory are compared with finite element method simulation and experimental results. The results indicate that the periodic structure can influence the performance of micro-perforated mufflers. With different periodic distances, the combination of the periodic structure and the micro-perforated tube muffler can contribute to the control of lower frequency noise with a broader frequency range or improvement of the peak transmission loss around the resonant frequency.     

可听声频段的声学超材料

制作了一维周期排列的亥姆霍兹共振器超材料,在空气环境下测试了其在可听声频段声学透射行为.实验结果表明,在2.1—3.5 kHz附近该材料具有透射衰减的吸收峰,利用声传输线理论（ATLM）计算的透射率和实验结果一致,同时由计算的等效阻抗分析可知,实验中出现的吸收峰是由HRs共振的回波反射引起的.另外,实验测试的样品中透射信号分布进一步验证了材料的共振效应,也就是会出现与外加激励反相响应.基于前述的共振模型计算出该材料的等效弹性模量为负. 关键词： 亥姆霍兹共振器 声传输线 吸收峰 等效弹性模量     

Helmholtz水声换能器弹性壁液腔谐振频率研究

针对传统Helmholtz水声换能器设计中刚性壁假设的局限性,将Helmholtz腔体的弹性计入到液腔谐振频率计算中,实现低频弹性Helmholtz水声换能器液腔谐振频率精确设计.基于细长圆柱壳腔体的低频集中参数模型,导出了腔体弹性引入的附加声阻抗表达式,得到了弹性壁条件下Helmholtz水声换能器等效电路图,给出了考虑了末端修正的弹性壁Helmholtz共振腔液腔谐振频率计算公式.利用ANSYS软件建立了算例模型,仿真分析了不同材质、半径、长度时的Helmholtz共振腔液腔谐振频率.结果对比表明弹性理论值与仿真值符合得很好,相比起传统的刚性壁理论计算结果,本文的弹性壁理论得出的液腔谐振频率值有所降低,与真实情况更加接近.本文的结论可以为精确设计低频弹性Helmholtz水声换能器提供理论支持.     

封闭腔体噪声控制中亥姆霍兹共振器的优化设计方法

提出用亥姆霍兹共振器控制声腔内噪声时计算共振器最优阻尼比和最优工作带宽的理论公式,并进行实验验证。首先,建立共振器与待控腔体的声学耦合方程,以最小化腔体内目标声压幅值为参考,对共振器的阻尼比和工作带宽进行理论分析,求出最优阻尼比和最优工作带宽的计算公式。接着,提出在声腔噪声控制中使用最优亥姆霍兹共振器的实施步骤。最后,以一维声学腔体内的噪声为控制对象,通过对比控制前后的理论结果与实测数据,验证最优阻尼比和最优工作带宽的理论公式。结果表明,本文开发的亥姆霍兹共振器优化设计方法能准确地预报共振器的最优阻尼比与最优工作带宽,在声腔中低频噪声控制中有广泛的应用前景。      

超材料型周期管路声传播特性及低频宽带控制

船舶管路系统噪声的低频宽带控制是船舶设计和制造中亟待解决的关键问题之一。将超材料理论引入船舶管路系统的结构设计,构造了具有低频声波带隙的一维周期管路结构,并给出了周期管路声波带隙和声波透射系数的计算方法。计算结果表明,该周期管路同时存在声波布拉格带隙和局域共振带隙。在这两种带隙频率范围内,声波在系统中的传播将被衰减抑制。进一步发现,布拉格和局域共振带隙在一定条件会发生耦合,出现带隙耦合展宽现象,且两种带隙存在精确耦合条件。利用带隙耦合的展宽效应和低频设计,可实现声波在低频范围内的传播操控,从而达到船舶管路系统低频噪声宽带控制的目的。      

基于低频吸声超构材料的复合消声器研究*

针对管道内低频噪声难以抑制的问题，本文基于亥姆霍兹共振腔（HR）阵列吸声板和穿孔管消声器组合，设计了一种复合式宽带消声器。首先利用有限元法仿真分析传统穿孔管消声器，发现中低频消声能力较差，通过嵌入HR阵列吸声板吸收中低频噪声。采用仿真与实验的方式研究吸声板的声学性能：在400-1000 Hz频段内的平均吸声系数达到了0.88。然后对复合式消声器进行数值模拟及3D打印阻抗管实验测试对比：复合式消声器在400-1718Hz频率范围内的平均传递损失为18.15 dB ，最终实现了管道内全频带噪声有效控制。     

Disorder in a periodic Helmholtz resonators array

This paper considers the disorder in a periodic duct–resonator system. The transfer matrix method is used to investigate wave propagation in the duct. Two cases are investigated: the disorder in periodic distance and the disorder in the geometries of Helmholtz resonators. Different from the original attenuation characteristic brought about by pure periodic system, it is found that the disorder in the geometries of resonators with the periodic distance being kept unchanged provides a useful way for the design of such a system to achieve a relatively wide noise attenuation band and to track some narrow noise peaks within it.