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。      

An extended neck versus a spiral neck of the Helmholtz resonator

This paper focuses on improving the noise attenuation performance of the Helmholtz resonator (HR) at low frequencies with a limited space. An extended neck or a spiral neck takes the place of the traditional straight neck of the HR. The acoustic performance of the HR with these two types of necks is analyzed theoretically and numerically. The length correction factor is introduced through a modified one-dimensional approach to account for the non-planar effects that result from the neck being extended into the cavity. The spiral neck is transformed to an equivalent straight neck, and the acoustic performance is then derived by a one-dimensional approach. The theoretical prediction results fit well with the Finite Element Method (FEM) simulation results. Without changing the cavity volume of the HR, the resonance frequency shows a significant drop when the extended neck length or the spiral neck length is increased. The acoustic characteristics of HRs with these two different neck types have a potential application in noise control, especially at low frequencies within a constrained space.     

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.     

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。      

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.     

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.     

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.     

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.     

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.     

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.     

Inertial attached neck length of Helmholtz resonators

We studied the inertial attached neck length (end correction) of different Helmholtz resonator configurations based on numerical calculations by the finite element method. First, we determined the eigenfrequency of the resonator, then on its basis, we calculated the attached neck length of the resonator. We analyzed the dependence of the attached neck length on the geometric parameters of the Helmholtz resonator. Using numerical calculations, we approximated the obtained dependences as analytic expressions.     

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.     

Transfer matrix methods for sound attenuation in resonators with perforated intruding inlets

A resonator with perforated intruding inlet (PII) is a superior silencer element, since the use of perforated inlet extensions can dramatically improve the acoustic performance. In this work, both a one-dimensional (1D) and a two-dimensional (2D) transfer matrix methods are developed to predict the transmission loss of the resonator without considering the mean flow. Based on the two groups of comparisons with tests, it is found out that the applicability of 1D method is limited by the resonator geometry even when the frequency is below the cut-off value of plane wave. Whereas the 2D approach is much more accurate while predicting the transmission losses within entire frequency range. Subsequently, five groups of resonators are chosen to determine the effects of structure parameters to transmission loss based on the 2D approach. The resonant frequency decreases and more resonant peaks appear when the length of inlet extension increases. A higher perforation rate leads to a shift of resonant peak towards higher frequencies. Besides, better acoustic performance could be obtained with the perforation being properly designed. Reducing the inlet/outlet radius can obviously improve the transmission loss without changing the frequency of resonant peak. The theories and conclusions in this study can be used for the design and optimization of resonators in various engineering applications.     

基于可调频亥姆霍兹共振器的封闭空间噪声自适应半主动控制

针对实际中声场激励频率可能发生变化的情况,研究采用自适应频率可调的亥姆霍兹共振器吸声器来跟踪激扰频率从而控制封闭空间噪声。建立了封闭声腔与亥姆霍兹共振器耦合的频域模型与时域控制模型,并给出了三种频率调谐控制算法,即亥姆霍兹共振器开口处声压幅值最小和内部声压幅值最大,以及判断内部声压幅值和开口处声压幅值的点积值趋零(点积值法)。理论分析和数值计算结果表明点积值法调频效果明显优于其它两种算法。采用并设计一种颈部面积可调的可调频亥姆霍兹共振器,利用点积值调频算法进行了单频和带宽信号激励下封闭空间噪声控制仿真和单频激励下实验研究,结果表明:点积值调频算法具有较好的频率调节性能和调节精度,并取得了理想的噪声控制效果,验证了理论模型正确性及调频算法的有效性。      

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.     

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.     

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     

Propagation of acoustic waves in a fluid-filled pipe with periodic elastic Helmholtz resonators

Helmholtz resonators are widely used to reduce noise in a fluid-filled pipe system. It is a challenge to obtain lowfrequency and broadband attenuation with a small sized cavity. In this paper, the propagation of acoustic waves in a fluid-filled pipe system with periodic elastic Helmholtz resonators is studied theoretically. The resonance frequency and sound transmission loss of one unit are analyzed to validate the correctness of simplified acoustic impedance. The band structure of infinite periodic cells and sound transmission loss of finite periodic cells are calculated by the transfer matrix method and finite element software. The effects of several parameters on band gap and sound transmission loss are probed.Further, the negative bulk modulus of periodic cells with elastic Helmholtz resonators is analyzed. Numerical results show that the acoustic propagation properties in the periodic pipe, such as low frequency, broadband sound transmission, can be improved.     

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。     

材料非线性衰减系数的二次谐波测量方法研究

采用有限幅值法测量材料在基波和非线性引起的二次谐波作用下的衰减系数:利用准线性下的KZK方程推导基波和二次谐波的声压分布,并提取波束修正系数;采用短纯音信号进行非线性实验,对检测得到的基波和二次谐波声压进行衍射修正处理,有效抑制衍射对衰减系数测量的不利影响,继而通过线性拟合的方法计算得到更精确的基波和二次谐波的衰减系数。以水为例进行实验,研究了实验测量所得衰减系数的频率依赖关系,结果表明在非线性条件下水的衰减系数与频率间存在较强的线性关系,而线性条件下衰减系数随频率呈现二次方增长的特性则不适用于非线性条件。该研究提出了准确测量非线性声波衰减系数的方法,为更有效地应用非线性超声检测提供理论依据。