Improving low-frequency sound absorption of micro-perforated panel absorbers by using mechanical impedance plate combined with Helmholtz resonators

The traditional Micro-perforated plate (MPP) is a kind of clean and non-polluting absorption structure in the middle and high frequency and has been widely used in the field of noise control. However, the sound absorption performance is dissatisfied at low frequencies when the air-cavity depth is restricted. In this paper, a mechanical impedance plate (MIP) is introduced into the traditional MPP structure and a Helmholtz resonator is attached to the MIP. Mechanical impedance plate (MIP) provides a good absorption at low frequency by using mechanism of mechanical resonance and the acoustic energy is dissipated in the form of heat with viscoelastic material. Helmholtz resonator can fill in the defect of the poor absorption effect between the Micro-perforated plate (MPP) and the mechanical impedance plate (MIP). The acoustic impedance of the proposed sound absorber is investigated by using acoustic electric analogy method and impedance transfer method. The influence of the tube’s length of Helmholtz resonator and the number of Helmholtz resonator on the sound absorption is studied. The corresponding results are in agreement with the theoretical calculation and prove that the composite structure has the characteristics of improving the low frequency sound absorption property.     

内置谐振器的轻薄宽频吸声器结构设计与分析*

微穿孔板吸声器的吸声频带相较于亥姆霍兹谐振器更宽,但其低频吸声的实现需要较大的空气背腔,这对结构尺寸有限制的场合存在一定局限性。本文设计了一种轻薄吸声降噪结构(内置亥姆霍兹谐振器的微穿孔板吸声器,简称MPPHR),将微穿孔板吸声器与亥姆霍兹谐振器进行了结合,提升吸声器的低频吸声性能的同时兼具了微穿孔板宽带吸声的优点。首先基于微穿孔板和亥姆霍兹谐振器理论建立了等效电路模型并计算了结构的声阻抗。然后通过有限元对MPPHR的吸声特性进行了参数研究。最后验证了MPPHR的声阻抗模型和有限元仿真的准确性。研究结果表明：MPPHR结构拥有更宽吸声频带,厚度仅为30mm的MPPHR的半吸收频带可达1294Hz,相较于同等厚度下的微穿孔板吸声器宽近500Hz。此外,MPPHR拥有更好的低频吸声效率。     

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.     

Sound absorption by a Helmholtz resonator

Absorption characteristics of a Helmholtz resonator positioned at the end wall of a circular duct are considered. The absorption coefficient of the resonator is experimentally investigated as a function of the diameter and length of the resonator neck and the depth of the resonator cavity. Based on experimental data, the linear analytic model of a Helmholtz resonator is verified, and the results of verification are used to determine the dissipative attached length of the resonator neck so as to provide the agreement between experimental and calculated data. Dependences of sound absorption by a Helmholtz resonator on its geometric parameters are obtained.     

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。      

水下圆柱形Helmholtz共振器的声学特性分析

理论分析了水下圆柱形Helmholtz共振器的声学特性. 综合考虑壁面弹性和辐射阻抗的影响,基于电-声类比的基本原理,建立了较为完善的水下圆柱形Helmholtz共振器的低频集中参量模型. 利用电路分析的基本方法,得到了系统的输入阻抗和声压传递函数表达式. 仿真分析了主要结构参数对共振器声学特性的影响,得出了一些有意义的结论. 在充水驻波罐中对自制的Helmholtz共振器进行了测量,并对实验结果进行了详细地误差分析. 去除压电水听器对测量结果的影响后,实验与仿真结果基本一致,从而验证了理论分析的正确性. 关键词： Helmholtz共振器 共振频率 传递函数 辐射阻抗     

Suppression of Helmholtz resonance using inside acoustic liner

When a Helmholtz resonator is exposed to grazing flow, an unstable shear layer at the opening can cause the occurrence of acoustic resonance under appropriate conditions. In this paper, in order to suppress the flow-induced resonance, the effects of inside acoustic liners placed on the side wall or the bottom of a Helmholtz resonator are investigated. Based on the one-dimensional sound propagation theory, the time domain impedance model of a Helmholtz resonator with inside acoustic liner is derived, and then combined with a discrete vortex model the resonant behavior of the resonator under grazing flow is simulated. Besides, an experiment is conducted to validate the present model, showing significant reduction of the peak sound pressure level achieved by the use of the side-wall liners. And the simulation results match reasonably well with the experimental data. The present results reveal that the inside acoustic liner can not only absorb the resonant sound pressure, but also suppress the fluctuation motion of the shear layer over the opening of the resonator. In all, the impact of the acoustic liners is to dampen the instability of the flow-acoustic coupled system. This demonstrates that it is a convenient and effective method for suppressing Helmholtz resonance by using inside acoustic liner.     

Sound absorption of microperforated panel mounted with helmholtz resonators

Microperforated panel (MPP) absorbers have been widely used in noise reduction and are regarded as a promising alternative to the traditional porous materials. However, the absorption bandwidth of a single-layer MPP is insufficient to compete with the porous materials. In order to improve the sound absorption ability of the single-layer MPP, MPP mounted with Helmholtz resonators (MPPHR) is introduced. Based on the MPP, Helmholtz resonators theory and electro-acoustical equivalent circuit principle, sound absorption properties of MPPHR are studied. Simulation and experimental results show that MPPHR have two peak frequencies and one anti-resonant frequency. The low-frequency peak is dependent on the Helmholtz resonators, while the high frequency peak is close to the peak of the single-layer MPP. The low-frequency sound absorption peaks move to low frequency with the neck length and the volume of Helmholtz resonators increasing. The high-frequency sound absorption peaks move to high frequency with the volume of Helmholtz resonators cavity increasing. Multiple Helmholtz resonator parallel MPP structure can provide more sound absorption than single MPPHR at low frequency range due to the introduction of more additional sound absorption peaks.     

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.     

Helmholtz resonator lined with absorbing material

A closed-form, two-dimensional analytical solution is developed to investigate the acoustic performance of a concentric circular Helmholtz resonator lined with fibrous material. The effect of density and the thickness of the fibrous material in the cavity is examined on the resonance frequency and the transmission loss. With the expressions for the eigenvalue and eigenfunction in the cavity, the transmission loss is obtained for a piston-driven model by applying a pressure/velocity matching technique. The results from the analytical methods are compared to the numerical predictions from a three-dimensional boundary element method and the experimental data obtained from an impedance tube setup. It is shown that the acoustic performance of a Helmholtz resonator may be modified considerably by the density and thickness of the fibrous material without changing the cavity dimensions.     

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.     

Acoustic impedance at the interface between a plain and a perforated pipe

This paper considers the effective impedance that pertains as low frequency sound in a plain pipe radiates into a general perforated pipe of equal diameter. A previous theory that considered only the reactance is extended to also include resistance. Experimental measurements are made of the response of a Helmholtz resonator to an external sound field, where the neck of the Helmholtz resonator has both plain and perforated pipe sections. A complete theoretical model of this resonator allows for comparison between measured and predicted results of transfer functions from the external to internal sound fields of the resonator. The Nyquist plot of the admittance transfer function is extremely sensitive to the small resistance values, whereas the pressure transfer function gives more accurate results for resonant frequency and hence reactance than the usual method. In particular the results for resistance are so sensitive that it becomes possible to infer which of the current models for aperture resistance within the perforate is the most appropriate.     

A theoretical model to predict the low-frequency sound absorption of a helmholtz resonator array

A theoretical method based on mutual radiation impedance is proposed to compute the sound absorption performance of a Helmholtz resonator array in the low-frequency range. Any configuration of resonator arrangement can be allowed in the method, while all the resonators may or may not be identical. Comparisons of the theoretical predictions with those done by the past studies or experiments show that the present method can accurately predict the absorption performance in more general cases.     

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。      

Experimental investigation of the sound absorption performance of compartmented Helmholtz resonators

An experiment was derived in the present study to investigate the effects of coupling up two Helmholtz resonators on their overall sound absorption performance. The effect of compartmenting the cavity of a resonator on its sound absorption property was also discussed. Such cavity compartmentation in fact creates a coupled resonator with a front and a rear resonator. The results show that the coupling in many cases can improve the sound absorption capacity and widen the working bandwidth of the resonators provided that the uncoupled resonance frequency of the front resonator is larger than or equal to that of the rear resonator. Results also suggest that the best compartmentation is that with these uncoupled resonance frequencies very close to each other. It is also found that the undamped plane wave approach is sufficient to predict the resonance frequencies of the coupled resonators within engineering tolerance.     

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.     

吸声型薄膜声学超材料低频宽带吸声性能研究*

本文根据吸声型薄膜声学超材料的吸声机理，在传统的吸声型薄膜声学超材料结构的基础上引入质量非对称结构， 优化了不同厚度质量片的排布方式，并根据优化结果制备了能够实现低频宽带吸声效果的薄膜声学超材料样品。对其进行声学实验的测试结果显示，样品在 100-1000Hz 频率范围内的平均吸声系数达 0.25，并在 250-800Hz 频率范围内出现了多个共振吸收峰，且实验测得的吸声系数曲线与仿真曲线的趋势有较高的一致性。因此该样品实现了低频宽带吸声。     

微穿孔介电弹性体薄膜的吸声性能试验分析*

针对普通薄膜型降噪结构的吸声性能较差和吸声带宽较窄的问题,本文设计了一种微穿孔的介电弹性体薄膜吸声结构。该结构由穿孔的介电弹性体薄膜与背腔组合而成,目的是拓宽介电弹性体薄膜低频率段的吸声带宽。针对微穿孔的介电弹性体薄膜吸声结构,从试验角度分析穿孔薄膜初始厚度、穿孔孔径及穿孔间距对结构吸声性能的影响。分析结果可知：通过适当增加薄膜的初始厚度,薄膜的整体吸声性能得到有效提升,最大可将319Hz吸声频带的吸声系数从0.2提升至0.7;减小薄膜的穿孔孔径能够有效拓宽穿孔薄膜的吸声频带,可使吸声系数0.4以上的吸声带宽由304Hz拓宽至432Hz;适当控制穿孔间距能够达到更好的吸声效果。     

A study on the multi-freedom broadband impedance model for time-domain simulations

The purpose of this paper is to construct a general broadband impedance model, which is suited for predicting acoustic propagation problems in time domain.A multi-freedom broadband impedance model for sound propagation over impedance surfaces is proposed and the corresponding time domain impedance boundary condition is presented.Basing on the extended Helmholtz resonator,the multi-freedom impedance model is constructed through combing with a sum of rational functions in the form of general complex-conjugate pole-residue pairs and it is proved that the impedance model is well posed.The impedance boundary condition can be implemented into a computational aeroacoustics solver by a recursive convolution technique, which results in a fast and computationally efficient algorithm.The two dimensional and three dimensional benchmark problems are selected to validate the accuracy of the proposed impedance model and time domain simulations.The numerical results are in good agreement with the reference solutions.It is demonstrated that the proposed impedance model can be used to describe the broadband characteristics of acoustic liners,and the corresponding time domain impedance boundary condition is viable and accurate for the prediction of sound propagation over broadband impedance surfaces.     

Experimental and computational investigation of coupled resonator–cavity systems

Launch vehicle noise is broadband in nature and the noise transmitted into the payload fairing is reduced by treating its interior with an acoustic absorption layer. The latest generation payload fairings are made from composite material which offer poor noise attenuation at low frequencies. One possible solution for reducing the low frequency noise is to use Helmholtz resonators tuned to a few of the dominant low frequency components, such as shell ring frequency or the first few cavity modes of the fairing. The paper presents a simplified modelling approach for numerical simulation of a coupled cavity–resonator system which is validated by experiments. The influence of damping and resonator volume fraction on the coupled system performance, to suppress the first axial mode in a cylindrical cavity, is shown and the resonator volume fraction required for significantly (more than 5 dB) suppressing the cavity axial mode is established.