Comparison of 1D transfer matrix method and finite element method with tests for acoustic performance of multi-chamber perforated resonator

Multi-chamber perforated resonator (MCPR) is a kind of typical silencer element which can both attenuate broadband noise and satisfy specific installation requirements. The one-dimensional transfer matrix method (TMM) and finite element method (FEM) are widely used to predict the transmission loss of the resonators. This paper mainly focuses on the comparison between 1D TMM and FEM in which detailed perforation modeling is applied for the acoustic modeling of MCPRs. Five resonators with different acoustic attenuation frequency ranges are built for simulation and test. In order to verify the results of the above methods, a transmission loss test facility is designed based on two-load method. Through adjusting the distance between microphones, the facility’s effective measurement frequency can be changed. The results show that despite of the complex modeling and calculation, FEM with detailed perforation modeling shows good consistency with test results in both frequency and amplitude within entire frequency range. In comparison, TMM is limited by the cut-off frequency when calculating transmission losses. Besides, accuracy of TMM in low frequency range is also affected by perforation conditions. However, TMM is time-saving in calculation and structure optimization. In MCPRs’ development process, TMM can be used to quickly design and optimize structure parameters while FEM can be used to verify the acoustic performance before prototyping.     

The impact of the neck material on the sound absorption performance of Helmholtz resonators

Helmholtz resonators with sound absorption materials filling the neck may have an improved sound absorption capacity. In this work, parallel perforated ceramics with different perforation diameters were installed into the neck of a Helmholtz resonator to improve its acoustic impedance to simultaneously achieve a better acoustic absorption coefficient and a wider absorption bandwidth. An experimental system was built to investigate the effect of the perforation diameters on the sound absorption performance of the resonator. It is found that nonlinear effects near the resonance frequency affect the resonator?s neck mouth impedance and further its sound absorption performance significantly. For frequency range 50–500 Hz, a model of the neck mouth impedance is developed based on a revised Forchheimer relationship. The experimental results are in good agreement with the theoretical model.     

On optimal design of half-wave resonators for acoustic damping in an enclosure

Acoustic design parameters of a half-wave resonator are studied experimentally for purely acoustic tuning of the resonator. According to the standard acoustic-test procedures, acoustic-pressure signals in the model enclosure with the resonators are measured. Based on the signals, quantitative acoustic properties of damping factor and sound absorption coefficient are evaluated and thereby, the acoustic-damping capacity of the resonator is characterized. Sound absorption coefficient has the advantages of the damping factor in various aspects. The coefficient indicates clearly the tuning frequency of the resonator, absorption effectiveness as a function of frequency, and overall damping capacity. The diameter and the number of a half-wave resonator, its distribution, and the blockage ratio at its inlet are selected as design parameters for optimal tuning of the resonator in the model enclosure. The resonators with larger diameter have the advantage of those with smaller one with respect to purely acoustic damping at the tuning frequency. The optimum number of resonators or the optimum open-area ratio decreases as boundary absorption decreases. When the open-area ratio exceeds the optimum value, over-damping appears, leading to a decrease in peak absorption coefficient and a broadening of absorption bandwidth. Blockage at the resonator inlet controls both peak absorption coefficient and its absorption bandwidth and it can be considered one of design factors for acoustic tuning.     

A sound absorption panel containing coiled Helmholtz resonators

This study proposes a promising design of sound absorption panels containing acoustic resonators. Each resonator is comprised of one small-sized and one large-sized tubes in series. The former can be viewed as the neck of a Helmholtz resonator, while the latter serves as a resonant chamber. Both tubes are bent up to fit in limited space of the panel. The 3D printing technology is exploited to fabricate samples for measurements. Frequency manipulation for the absorption peak can be achieved by adjusting the geometric parameters of tubes. Moreover, two pairs of resonators with different dimensions can broaden the bandwidth of absorption. Theoretical predictions on absorption characteristics agree well with numerical and experimental results. The proposed structure offers a feasible way of absorbing low-frequency sound without the need to use thick panels.     

弯曲圆盘驱动的双Helmholtz共振腔换能器

使用双面同相振动的弯曲圆盘换能器驱动双Helmholtz共振腔,既放大了弯曲圆盘换能器弯曲共振频率以下频段的声输出,又利用两个Helmholtz共振腔的同相声源辐射模型实现了在Helmholtz共振频率处的"∞"字形垂直指向性,实现了低频指向性声发射。阐述了换能器实现"∞"字形低频指向性发射的机理,研究了腔体长度、金属圆片厚度及弯曲圆盘边缘简支厚度等关键结构参数对Helmholtz共振频率的影响,求解了换能器的发送电压响应、指向性等参数。依据仿真结果制作了实验样机,在消声水池中进行了电声性能测试。测试结果显示,指向性形状及液腔共振频率与仿真结果基本相符。这种由弯曲圆盘驱动的双Helmholtz共振腔水声换能器为实现水声换能器小尺寸、低频指向性发射提供了一种技术手段。      

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.     

腔壁弹性对水下小型圆柱形亥姆霍兹共振器共振频率的影响

理论和实验研究了腔壁弹性对水下小型圆柱形亥姆霍兹共振器共振频率的影响.基于电-声类比理论,建立了小型共振器的简化模型,利用电路分析方法得到了便于计算的共振频率一般表达式.分别仿真分析了共振器壁面厚度和材料对共振频率的影响,得到了不同尺寸的小型共振器的近似刚性条件.在充水驻波罐中对不同壁厚、不同材料的小型圆柱形亥姆霍兹共振器的共振频率进行了测量,实验结果较好地验证了理论分析和近似刚性条件的正确性.所得结果对小型圆柱形亥姆霍兹共振器的设计和水下应用具有较好的参考价值. 关键词： 亥姆霍兹共振器 共振频率 传递函数 辐射阻抗     

Design, simulation and structural optimization of a longitudinal acoustic resonator for trace gas detection using laser photoacoustic spectroscopy (LPAS)

The design of the acoustic resonator is critical for the optimization of the sensitivity of laser photoacoustic spectroscopy (LPAS) in trace gas detection applications. In this paper, an LC circuit model is used for the simulation of a 1D acoustic resonator. This acoustic resonator is designed for CO photoacoustic spectroscopy. The effects of the structural parameters, quality factor and resonant frequency on the performance of the device are theoretically analyzed. The role of the buffer volume as an acoustic filter is investigated and optimized dimensions of the buffer volume, to achieve minimum noise transmission coefficient, are calculated. The effects of the ambient temperature, variety of pressure and gas flow velocity on the resonant frequency of photoacoustic resonator and PA signal are simulated. The temperature dependence of the microphone sensitivity is also introduced.     

Quality enhancement and insertion loss reduction of a rectangular resonator by employing an ultra-wide band gap diamond phononic crystal

We report on an ‘in plane mode’ band gaps investigation of a novel diamond CRS (circle-rectangle-square) shaped holey phononic crystals in the desired operating frequency ranges. An ultra-wide band gap for diamond in the ‘in plane mode’ is observed. We also investigate an ultra-wide acoustic band gap for a finite one-dimensional (1D) diamond CRS phononic crystal (PnC) in the ‘out of plane mode’, and an ultra-wide acoustic band gap of a finite two-dimensional (2D) diamond CRS phononic crystal (PnC) in the ‘out of plane mode’ based on the FEA (Finite Element Analysis) method. We analyze that the transmission response of diamond in the length extension and width extension manner is more reasonable. Ultra-wide peak attenuations in the transmission spectra of a CRS shaped diamond phononic crystal successfully reveal the complete band gaps. The wide band gap of a CRS shaped diamond phononic crystal and the wide peak attenuation strongly agree in the same frequency region. It is analyzed that when a CRS-diamond phononic crystal is employed for MEMS resonators with different tether widths the quality Q of the resonators improved, and the energy losses decrease with extremely low insertion loss. In addition, it is observed that the vibrational displacement of a resonator is reduced by employing a diamond phononic crystal.     

Acoustic attenuation of hybrid silencers

The acoustic attenuation of a single-pass, perforated concentric silencer filled with continuous strand fibers is investigated first theoretically and experimentally. The study is then extended to a specific type of hybrid silencer that consists of two single-pass perforated filling chambers combined with a Helmholtz resonator. One-dimensional analytical and three-dimensional boundary element methods (BEM) are employed for the predictions of the acoustic attenuation in the absence of mean flow. To account for the wave propagation in absorbing fiber, the complex-valued characteristic impedance and wave number are measured. The perforation impedance facing the fiber is also presented in terms of complex-valued characteristic impedance and wave number. The effects of outer chamber diameter and the fiber density are examined. Comparisons of predictions with the experiments illustrate the need for multi-dimensional analysis at higher frequencies, while the one-dimensional treatment provides a reasonable accuracy at lower frequencies, as expected. The study also shows a significant improvement in the acoustic attenuation of the silencer due to fiber absorption. Multi-dimensional BEM predictions of a hybrid silencer demonstrate that a reactive component such as a Helmholtz resonator can improve transmission loss at low frequencies and a higher duct porosity may be effective at higher frequencies.     

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。      

直通穿孔管消声器声学特性预测的数值模态匹配法

将数值模态匹配法应用于计算横截面为任意形状的直通穿孔管抗性消声器的声学特性。应用二维有限元法计算横截面的本征值和本征向量,应用模态匹配技术求解模态幅值系数,进而得到所需的声学量。对于圆形和椭圆形直通穿孔管消声器的传递损失,数值模态匹配法计算结果与三维有限元计算结果和相应的实验测量结果吻合良好,表明数值模态匹配法能够精确计算直通穿孔管消声器的声学特性。计算结果表明,穿孔管的偏移影响消声器在中高频段的消声特性,同轴结构消声器的消声性能好于非同轴结构。      

一维亥姆霍兹共振腔声子晶体中缺陷模式的实验研究

基于亥姆霍兹共振腔单元设计并制作了一种一维局域共振型声子晶体, 针对结构中存在点缺陷的情况, 进行了实验研究. 实验结果表明, 由于点缺陷的存在, 局域共振型声禁带中出现了缺陷模式, 并且在缺陷单元周围引起了能量的局域现象, 与理论结果符合较好. 缺陷单元从两个不同的方向趋近于完美单元时, 缺陷模式分别按照不同的规律变化, 但是越靠近禁带边缘, 所局域的能量就越多. 另外, 当缺陷单元共振频率小于完美单元共振频率时, 局域能量主要集中在声波导内; 反之, 局域能量则主要集中在共振腔内. 本研究对设计新型低频声滤波装置及高声强集中装置具有一定意义. 关键词： 亥姆霍兹共振腔 声子晶体 缺陷模式 能量局域化     

An extension of the transfer matrix method to analyzing acoustic resonators with gradually varying cross-sectional area

The transfer matrix method was used to analyze the acoustical properties of stepped acoustic resonator in the previous paper. The present paper extends the application of the transfer matrix method to analyzing acoustic resonators with gradually varying cross-sectional area. The transfer matrices and the resonant conditions are derived for acoustic resonators with four different kinds of gradually varying geometric shape: tapered, trigonometric, exponential and hyperbolic. Based on the derived transfer matrices, the acoustic properties of these resonators are derived, including the resonant frequency, phase and radiation impedance. Compared with other analytical methods based on the wave equation and boundary conditions, the transfer matrix method is simple to implement and convenient for computation.     

双通带异向平板波导的特性

提出了一种基于平板波导的新型异向谐振结构——交叉椅型谐振结构,通过理论分析和数值计算,说明和验证了单个交叉椅型谐振结构加载的平板波导具有双通带特性和异向特性;设计了一种由多个交叉椅型谐振结构周期加载的异向平板波导结构,并通过仿真实验验证了其负折射特性。交叉椅型谐振结构的全金属半封闭式结构和其特殊的电磁谐振方式,使得此类2维异向平板波导与传统的由金属开口谐振环与金属线正交阵列而成的2维异向介质相比,具有双通带、无介质损耗、功率容量大等特异性质;单个交叉椅型谐振结构加载的平板波导作为一种新型的滤波器结构,具有良好的双通带特性,尺寸较小。     

Noise control in enclosures: modeling and experiments with T-shaped acoustic resonators

This paper presents a theoretical and experimental study of noise control in enclosures using a T-shaped acoustic resonator array. A general model with multiple resonators is developed to predict the acoustic performance of small resonators placed in an acoustic enclosure. Analytical solutions for the sound pressure inside the enclosure and the volume velocity source strength out of the resonator aperture are derived when a single resonator is installed, which provides insight into the physics of acoustic interaction between the enclosure and the resonator. Based on the understanding of the coupling between the individual resonators and enclosure modes, both targeted and nontargeted, a sequential design methodology is proposed for noise control in the enclosure using an array of acoustic resonators. Design examples are given to illustrate the control performance at a specific or at several resonance peaks within a frequency band of interest. Experiments are conducted to systematically validate the theory and the design method. The agreement between the theoretical and experimental results shows that, with the help of the presented theory and design methodology, either single or multiple resonance peaks of the enclosure can be successfully controlled using an optimally located acoustic resonator array.     

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.     

基于新型三环谐振器的诱导透明效应分析

针对谐振式微腔的应用需求, 提出了一种新型三环谐振式微腔结构, 类似于原子系统中的电磁诱导透明, 耦合诱导透明(CRIT)效应在一个新的光学微腔系统中已被实验证明. 该结构在硅基上由三个尺寸完全一样的微环腔组成, 通过理论分析、制备和实验测试, 能够观察到CRIT现象, 其频谱具有低群速的狭窄透明峰, 与光栅耦合器的耦合效率为34%, 并且谐振器的品质因数达到了0.65×10⁵, 同时, 失谐的谐振波长可以通过温度变化来控制, 这在旋转传感、光滤波器、光存储器等方面的应用有重要意义.     

Panel of resonators with variable resonance frequency for noise control

The article focuses on acoustic resonators made of perforated sheets bonded onto honeycomb cavities. This kind of resonators can be used in adverse conditions such as high temperature, dirt and mechanical constraints. For all these reasons, they are, for example, widely used in aeronautic applications. The acoustic properties are directly linked to the size, shape and porosity of holes and to the thickness of air gaps. Unfortunately, the acoustic absorption of these resonators is selective in frequency and conventional acoustic resonators are only well adapted to tonal noises. In case of variable tonal noise, the efficiency is limited if the resonators are not tunable. One common solution is to control the depth of cavities based on the noise to be attenuated. This article proposes another technology of tunable resonators with only a very small mass and size increase. It consists of two superposed and identically perforated plates associated with cavities. One plate is fixed and bonded to the cavities and the other plate is mobile. The present concept enables to change the internal shapes of the holes of the perforated layers. The article describes this system and gives a theoretical model of the normal incidence acoustic impedance that allows to predict the acoustic behavior, in particular the resonance frequency. The model shows that the resonance frequency varies with hole profiles and that the absorption peak moves towards the lower frequencies. The proposed model is validated by measurements on various configurations of resonators tested in an impedance tube. The perspectives of this work are to adapt the hole profiles using an actuator in order to perform active control of impedance.     

Theoretical model and analytical approach for a circular membrane–ring structure of locally resonant acoustic metamaterial

Recently developed locally resonant acoustic metamaterials (LRAM) display useful sound attenuation properties over narrow frequency bands. In this study, we present a theoretical model and analytical approach to investigate transmission loss of a circular membrane–ring structure of LRAM. As a degeneration of the ring inner radius being zero, the present model and approach is also suited for acoustic response analysis of the membrane–central-mass structure. Analytical results are compared with the ones from the finite element method to show a quite good agreement. The transmission loss characteristics dependence on the material and geometrical properties of the membrane–ring structure are obtained and discussed. It is indicated that multi-peak transmission loss profile can occur in the membrane–ring structure of LRAM, while the peak transmission loss frequency and bandwidth can be tuned by varying the ring mass location, surface density and ring numbers on the membrane.