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.     

Power flow through machine isolators to resonant and non-resonant beams

The parameters controlling power transmission from a vibrating machine to the seating structure, via spring-like vibration isolators, are investigated. The low frequency range is considered where the machine moves as a rigid body. It is shown that the finite seating structure can be modelled by an equivalent structure of infinite extent for frequency averaged power transmission calculations. Power transmission to a finite and an infinite beam via a mass and spring in series is measured experimentally and compared with theoretical predictions. The power transmission is measured by two proposed methods; the first involves the real component of the seating impedance, and the second the transfer impedance of the isolator.     

Reduction of acoustic radiation by impedance control with a perforated absorber system

A model of sound radiation from an infinite plate with an absorptive facing is proposed and investigated theoretically from the viewpoint of acoustic power. Acoustic characteristics on the plate surface are represented by impedance derived from iso-absorption curves. A parametric study is carried out to clarify the effect of the impedance on the acoustic power. Results derived from this model show that acoustic radiation depends on change in impedance as well as the absorption coefficient, and there is a possibility of reducing the radiation from vibrating surface by introducing an appropriate impedance surface. In order to realize this effect, a model using a perforated board with a back cavity attached to the vibrating surface is proposed, in which the motion of the perforated board is made equal to that of the vibrating surface. To obtain fundamental data, a theoretical study is performed under a simplified condition, assuming an infinite plane piston. The calculated results are compared to experimental data measured by using an acoustic tube. The results, which are in good agreement in the reduction effect, show that this system can achieve the reduction of radiated sound power at arbitrary frequencies.     

圆孔非线性声阻抗三维时域仿真与特性分析

为研究有限振幅声波作用下圆孔的非线性声学特性,提出了基于三维时域计算流体动力学(CFD)仿真的圆孔非线性声阻抗提取方法,通过求解层流方程来模拟声信号在圆孔及上下游的传播,以及采用横向周期性边界条件来考虑高穿孔率时圆孔之间相互作用的影响。研究了不同幅值声波作用下孔径、厚度和穿孔率对声阻抗的影响规律,通过对质点振速幅值、频率和板厚等组成的无量纲参量进行非线性回归分析,得到了圆孔非线性声阻抗的拟合公式,并将其转换为可考虑多频声波影响的时域模型。最后结合声阻抗时域模型和有限差分方法计算了直通穿孔管消声器在小振幅和有限振幅声波作用下的传递损失,通过与实验测量结果的比较,验证了拟合公式的准确性和实用性。     

Efficient calculation of two-dimensional periodic and waveguide acoustic Green's functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.     

The effects on noise of changes in wheel/rail system parameters

An analytical model has been developed that simulates the generation and propagation of wheel/rail noise. In the model, wheel/rail vibrations are induced by running surface roughness. The vibration responses are determined from considering contact stiffness effects and wheel/rail impedance interactions. Near field sound power levels are then calculated by combining the responses with radiation efficiencies, space-averaging the velocity squared on the wheel, and accounting for the decay of vibration along the rail. Finally, the noise levels predicted for the wayside are obtained from an analysis of the propagation that includes the effect of finite ground impedance. Good agreement exists between the analytical model and a series of validation measurements taken at DOT's Transportation Test Center in Pueblo, Colorado. A sensitivity analysis conducted for the parameters of a typical baseline system achieved significant changes in rolling noise only for reductions in wheel/rail contact stiffness, increases in wheel/rail contact area, and decreases in wheel/rail roughness through wheel truing and rail grinding.     

Shadowing of directional noise sources by finite noise barriers

The present study investigates the shadowing effect of barriers of infinite or finite length in the presence of directional noise sources. The diffraction model termed [Directive Line Source Model (DLSM) J. Acoust. Soc. Am. 107 (2000) 2973-2986] is employed. DLSM is appropriately modified and extended to include the effects of ground reflection, diffraction by the side edges of a finite length barrier, and diffraction by directional noise sources. Results obtained are shown to be in good agreement with available experimental data and known analytical solutions. An application of the enhanced DLSM is illustrated using helicopter type noise, which is highly directive. The noise source is modeled as a directional point source with far field directivity data and the enhanced DLSM is employed to compare the noise field with and without the barrier present for three different directivity patterns, various source locations and orientations, as well as, for various barrier lengths.     

Thin film on metal: Resonance effects in light diffraction at the edge

The theory of light diffraction at the impedance step is developed which allows for an additional surface wave. Reflection and transmission coefficients for a surface wave are determined as well as radiative losses at the diffraction of the surface polaritons (SP). Coefficients of transformation of the incident bulk radiation energy to the SP energy are calculated. Resonance effects in the mirror reflection of bulk radiation are investigated. Possible application of the predicted effects for the study of optical properties of thin films and transition layers are discussed.     

A linearized Eulerian sound propagation model for studies of complex meteorological effects

Outdoor sound propagation is significantly affected by the topography (including ground characteristics) and the state of the atmosphere. The atmosphere on its part is also influenced by the topography. A sound propagation model and a flow model based on a numerical integration of the linearized Euler equations have been developed to take these interactions into account. The output of the flow model enables the calculation of the sound propagation in a three-dimensionally inhomogeneous atmosphere. Rigid, partly reflective, or fully absorptive ground can be considered. The linearized Eulerian (LE) sound propagation model has been validated by means of four different scenarios. Calculations of sound fields above rigid and grass-covered ground including a homogeneous atmosphere deviate from analytic solutions by < or = 1 dB in most parts of the computed domain. Calculations of sound propagation including wind and temperature gradients above rigid ground agree well with measured scale model data. Calculations of sound propagation over a screen including ground of finite impedance show little deviations to measured scale model data which are probably caused by an insufficient representation of the complex ground impedance. Further calculations included the effect of wind on shading by a screen. The results agree well with the measured scale model data.     

A coherent model for predicting noise reduction in long enclosures with impedance discontinuities

A theoretical model has been developed for the prediction of sound propagation in a rectangular long enclosure with impedance discontinuities. Based on the image-source method, the boundaries are assumed to be geometrically reflective. An infinite number of image sources are generated by multiple reflections. The sound pressure of each image is obtained by an approximate analytical solution, known as the Weyl-van der Pol formula. The total sound field is then calculated by summation of the contribution from all images. The phase information of each image and the phase change upon reflection are included in the model. A single change of impedance in a two-dimensional duct is focused on as the fundamental problem of the current study. The diffraction effect at the impedance discontinuity is proved to be insignificant, and it is ignored in the formulation. On the assumption that the diffraction effect is not important, the investigation is moved on to a rectangular long enclosure. Measurements are conducted in two model tunnels to validate the proposed prediction model. The predictions are found to give good approximations of the experimental results. The theoretical model serves as the first attempt to optimize the position and pattern of sound absorption materials in a long enclosure, such as an underground railway station or a building corridor, for the reduction of noise and improvement of sound quality.     

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.     

Controlled experiments of the diffraction of sound by a curved surface

Controlled measurements of the sound field from a point source above a curved surface are described. The measurements were made in the frequency range between 0.3 and 10 kHz, in the case of a rigid boundary and a surface of finite impedance. Receiver positions include all of the area within, and above, the shadow zone and for various source heights. Particular attention is given to the region across the shadow boundary. The measurements are compared to diffraction theory expressed in terms of a residue series, or creeping wave solution. The calculation is extended by removing restrictive approximations and by carrying the computation to higher-order terms. A numerical algorithm allows the extension to the general case of a finite impedance. Above the shadow boundary, the sound field is calculated using geometrical theory that accounts for reflections from a curved surface. Deep within the shadow, theory and measurements agree to, typically, 0.5 dB. The same agreement is obtained between measurements and the geometrical theory well above the shadow boundary. In the vicinity of the shadow boundary, both theories agree to within 0.5 dB but differ from the measured results by 2 to 5 dB. Finally, the theory is compared to measurements obtained outdoors above a grass covered curved ground with no refraction and above flat ground with refraction.     

A BEM approach to validate a model for predicting sound propagation over non-flat terrain

A two-dimensional boundary element model for sound propagation in a homogeneous atmosphere above non-flat terrain has been constructed. An infinite impedance plane is taken into account in the Green's function in the underlying integral equation, so that only the non-flat parts of the terrain need to be discretised in the boundary element model. This Green's function is undefined for points below the impedance plane, and therefore valleys and hollows are taken into account by coupling the exterior domain above the ground with one or several interior domains below the ground, as suggested in a recent paper [J. Sound Vibrat. 223 (1999) 355]. The resulting BEM model, which can handle arbitrary combinations of barriers and hollows, has been used for validating a ray model for various difficult configurations, including combinations of valleys and barriers.     

Radiation of tangential dipoles at the boundary of semiinfinite planar impedance systems

A factorization method is used to solve a group of electrodynamic problems involving the radiation of dipoles at a straight discontinuity in the surface impedance specified on an infinite plane and at the edge of an impedance halfplane tangential to these systems.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 4, pp. 50–55, April, 1969.     

Acoustical impedance models for outdoor ground surfaces

A theory which predicts the acoustical characteristics of rigid porous materials in terms of four physical parameters is used to provide impedance versus frequency models for various types of ground surface. It is found possible to obtain tolerable agreement with measurements of surface normal impedance for grass-covered ground, bare ground and layered forest floor when measured values of flow resistivity and porosity and estimated values of the other two parameters are used. The agreement with measured acoustical data is shown to be superior to that obtainable with the single-parameter, semi-empirical model that is widely used to predict ground effect even when the single parameter is adjusted for best-fit. A low frequency/high flow resistivity approximation is derived in a form that requires the adjustment of only a single parameter when fitting impedance versus frequency data. This model predicts that the real part of the surface normal impedance, or resistance, and imaginary part, or reactance, are equal and decrease as the inverse square root of frequency. The low frequency/high flow resistivity approximation makes possible the derivation of a two-parameter impedance versus frequency model for a medium with a porosity that decreases exponentially with depth. If the two parameters are considered to be adjustable for best-fit, then some measurements of surface impedance are found to be explicable by means of such a model. The low frequency/high flow resistivity approximation is used, together with the assumption of layer thickness small compared with internal wavelength, to derive another simple two-parameter model for grounds that behave acoustically as thin hard-backed porous layers. Examples of the validity of this model are provided. Both of the two-parameter models predict values of reactance which are greater than those of resistance over the audio-frequency range. Methods of adjusting the two parameters of each model in fitting short-range excess-attenuation data are suggested as alternatives to the single-parameter method, and as the basis for predicting ground effect at long range and low frequencies.     

Combined effects of admittance optimisation on both barrier and ground

The focus of this paper is on the problem of finite impedances on both ground and barrier. Using a boundary element approach the surface treatment of the barrier and finite parts of the ground have been optimised to yield maximum insertion loss at multiple frequencies simultaneously. A 1 m high T-shaped barrier optimised in this way gives up to 8 dB higher insertion loss than a rigid barrier of equal shape. Optimisation of the acoustical properties of the ground below the source as well as those of the barrier improves the insertion loss dramatically for all receiver heights. The ground close to the source is the part of the ground that influences the insertion loss most, and in such a way that the radiation properties of the source are altered, and the radiated sound power is reduced. Having an optimised admittance only on the ground close to the barrier gives only a minor effect. A barrier-ground combination with specialised treatment on the ground close to the source and on the barrier top gives an increase in insertion loss that is comparable to the optimised results. The main conclusion of this paper is that specialised surface treatments provide largest effect if they are used on the ground surface.     

非对称阻抗插入管消声器的Chebyshev-变分法建模与求解

针对非对称阻抗插入管消声器三维理论建模与求解问题,提出了一种半解析变分建模和求解方法,试验及有限元结果验证了理论模型和求解结果的正确性,开展了模态频率、声压响应及传递损失等声场特性的预测分析.首先构建插入管消声器内部子声场拉格朗日泛函,基于声压与质点振速连续性条件,得到插入管消声器三维理论模型.随后,将子声场声压展开为...     

基于传输线模型的高阻表面反射相位分析

采用传输线模型对高阻表面表面阻抗进行建模,准确计算垂直入射条件下高阻表面的反射相位.在垂直入射条件下,过孔的影响可以忽略,将高阻表面等效为具有容性的贴片阵与具有感性的介质层的并联,利用传输线原理求得高阻表面的反射系数,再得到其反射相位.计算了不同参数的高阻表面反射相位,传输线模型计算反射相位与数值方法计算结果符合较好.制作了不同参数的高阻表面并测量其反射相位,实验结果表明传输线模型计算反射相位结果与测量结果基本符合,证明了传输线模型的正确性. 关键词： 高阻表面 反射相位 传输线模型     

Influence of acoustic leakage at fluid–solid interface on interferometric detection of surface acoustic wave

When using laser interferometer to detect surface acoustic wave at fluid–solid interface, there are two factors which will cause the optical path length variation of the probe laser beam: interface deformation, and refractive index changes in fluid induced by acoustic leakage. Influence of acoustic leakage on laser interferometric detection for surface acoustic wave is researched here. A metal plate immersed in an infinite fluid is used as a physical model. Interface deformation due to laser-induced acoustic wave and pressure in fluid due to acoustic leakage are computed for select cases by finite element method. The optical path length variation caused by the two factors are calculated respectively and compared. The results show that the influence of acoustic leakage increases with the increasing acoustic impedance matching of fluid and solid, the peak-to-peak of influence degree increases linearly with the increasing acoustic impedance of fluid, and that decreasing the distance between the interferometer and interface can effectively reduce the influence of acoustic leakage.