Radiation impedance of a piston at the wall of a rectangular duct

The radiation impedance of a rectangular piston positioned at the wall of a rectangular duct is theoretically investigated. The dependence of the attached length of the piston on the width of the duct is determined. The dependence shows that, unlike the radiation resistance, the attached length decreases with a decrease in duct width. The results of the study are compared with the data obtained for the attached length of a square orifice in a rectangular baffle in a duct.     

Noise silencer in the form of a Helmholtz resonator at the outlet of an air duct of finite length

A new type of noise silencer with the original design of the air duct-resonator system is proposed. The design is free of the disadvantages that are inherent in the conventional design with a resonator placed inside the air duct. A physical model of the silencer is developed, and its efficiency is calculated for different geometrical and physical parameters of the resonator and the air duct. A comparison between the calculated characteristics and the experimental data is performed, and their agreement is demonstrated.     

On the Helmholtz resonator

This paper develops the theory of the excitation of a Helmholtz resonator by external disturbances located arbitrarily close to the mouth of the resonator. The classical approach of Rayleigh is thereby extended to situations in which the disturbance at the mouth is not necessarily equivalent to a uniform, time dependent pressure perturbation. The analysis involves the derivation of the Green function of the resonator in a manner similar to that described in an earlier paper. The use of the Green function is illustrated by two examples in which the resonator is excited by a low Mach number stream of air. In the first case the air stream has a periodic large scale structure such as may be caused by a Kelvin-Helmholtz type of instability. The second example models the case of excitation by a shear layer possessing a continuous spectrum of turbulent eddies. In both of these applications the orders of magnitude of the sound pressure levels involved are illustrated for a typical resonator.     

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.     

Temperature-dependent photoacoustic spectroscopy with a Helmholtz resonator

We describe and example the Beam Propagation Method (BPM) used to model and simulate nonlinear refractive and absorptive effects in materials with applications to optical limiting and switching. Various scenarios including laser-beam trapping and laser-beam division are investigated, in order to demonstrate the power of the BPM. A novel technique is also described for efficiently modelling the external far-field propagation from nonlinear media, including the propagation of non-Gaussian-shaped spatial profiles. The methods are finally combined with the phenomenon of nonlinear absorption to demonstrate enhanced power limiting in the presence of self-refraction. Optimal parameters for high-fluence power-limiting are subsequently discussed.     

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     

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.     

Nonlinear asymptotic impedance model for a Helmholtz resonator liner

The usual nonlinear corrections for a Helmholtz resonator type impedance do not seem to be based on a systematic asymptotic solution of the pertaining equations. We aim to present a systematic derivation of a solution of the nonlinear Helmholtz resonator equation, in order to obtain analytically expressions for impedances close to resonance, while including nonlinear effects. The amplitude regime considered is such that when we stay away from the resonance condition, the nonlinear terms are relatively small and the solution obtained is of the linear equation (formed after neglecting the nonlinear terms). Close to the resonance frequency, the nonlinear terms can no longer be neglected and algebraic equations are obtained that describe the corresponding nonlinear impedance. Sample results are presented including a few comparisons with measurements available in the literature. The validity of the model is understood in the near resonance and non-resonance regimes.     

Low-frequency sound field in a room with a Helmholtz resonator

The sound field generated by a point source of volume velocity in a room with a Helmholtz resonator is determined. The shift produced by the resonator in the natural frequencies of the room is calculated.     

Calculation of the Kirchhoff coefficients for the Helmholtz resonator

A Helmholtz resonator is a shell Ω_shell separating a compact cavity Ω_int from a noncompact outer domain Ω_out. A small opening Ω ^δ in the shell connects the cavity with the outer domain, causing the transformation of real eigenfrequencies of the Neumann Laplacian in the cavity into the complex scattering frequencies of the full spectral problem for the Neumann Laplacian on Ω = ℝ³\Ω_shell. The Kirchhoff model of 1882, see [21], gives a convenient ansatz

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     

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。     

A multiple degree of freedom electromechanical Helmholtz resonator

The development of a tunable, multiple degree of freedom (MDOF) electromechanical Helmholtz resonator (EMHR) is presented. An EMHR consists of an orifice, backing cavity, and a compliant piezoelectric composite diaphragm. Electromechanical tuning of the acoustic impedance is achieved via passive electrical networks shunted across the piezoceramic. For resistive and capacitive loads, the EMHR is a 2DOF system possessing one acoustic and one mechanical DOF. When inductive ladder networks are employed, multiple electrical DOF are added. The dynamics of the multi-energy domain system are modeled using lumped elements and are represented in an equivalent electrical circuit, which is used to analyze the tunable acoustic input impedance of the EMHR. The two-microphone method is used to measure the acoustic impedance of two EMHR designs with a variety of resistive, capacitive, and inductive shunts. For the first design, the data demonstrate that the tuning range of the second resonant frequency for an EMHR with non-inductive shunts is limited by short- and open-circuit conditions, while an inductive shunt results in a 3DOF system possessing an enhanced tuning range. The second design achieves stronger coupling between the Helmholtz resonator and the piezoelectric backplate, and both resonant frequencies can be tuned with different non-inductive loads.     

Exact solution of resonant modes in a rectangular resonator

The resonant modes of rectangular two-dimensional optical resonators were analyzed exactly. Based on the characteristics of the Bessel function, the resonant frequencies of the rectangular microcavities are expressed in a simple way. In addition, a simple rule to judge when the finite length of a rectangular resonator can be considered infinite is given in realistic applications. The solution that is presented should be useful in possible applications of the rectangular resonators as filters for dense wavelength-division multiplexing.     

Fiber-optic hydrophone using a cylindrical Helmholtz resonator as a mechanical anti-aliasing filter

Two Michelson interferometric fiber-optic hydrophones that use panda polarization-maintaining fibers and devices have been constructed and tested. The low-frequency acoustic sensitivities of both hydrophones are -159 dB re 1 rad/microPa. One of the hydrophones tested has a small cylindrical Helmholtz resonator that has a break point near 1200 Hz and a measured roll-off of approximately 50 dB/octave, and it is a hydrostatic-pressure-insensitive design. This hydrophone is a prototype device for a class of sensors that can be used to eliminate aliasing in future sonar systems. To our knowledge, this is the first time that such a fiber-optic hydrophone has been reported.     

Analysis of the turbulent boundary layer in the vicinity of a self-excited cylindrical Helmholtz resonator

This study investigates the changes in the structure of a turbulent boundary layer downstream of a flow-excited Helmholtz resonator. To this end, a fully developed turbulent boundary layer over a resonator mounted flush with a flat plate was simulated by implementing a large eddy simulation (LES). To assist in understanding the effect of the resonator on the flow structure, a sensitivity study was undertaken by changing the main geometrical parameters of the resonator. The results demonstrated that when the boundary layer thickness equals the orifice length, the cross-stream component of velocity fluctuations penetrates the boundary layer, resulting in a reduction of the turbulence intensity by up to 12%. Therefore, it is concluded that a Helmholtz resonator has the potential to reduce the instabilities within the boundary layer. These investigations also assist in identifying the optimal parameters to delay turbulence events within the grazing flow using Helmholtz resonators.     

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.     

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.