Propagation of sound from a monopole source above an impedance-backed porous layer

In this article, the propagation of sound from a monopole source above an impedance-backed porous layer is examined. The sound fields can be expressed in an integral form that is amenable to further analysis. A standard method of steepest descents is applied to evaluate the integral where the method of pole subtraction is needed to obtain a uniform asymptotic solution for the sound field above the plane surface. To obtain a numerical solution, the location of the pole was determined numerically by means of the Newton-Raphson method. Based on the pole location, the sound fields can then be calculated numerically. It has been demonstrated that the use of a plane wave reflection coefficient to calculate the sound fields is a special case of the asymptotic formula when the pole is located further away from the saddle point.     

Predicted attenuation of sound in a rigid-porous ground from an airborne source

An approximate analytical formula has been derived for the prediction of sound fields in a semi-infinite rigid-porous ground due to an airborne source. The method starts by expressing the sound fields in an integral form, which can subsequently be evaluated by the method of steepest descents. The concept of effective impedance has been introduced by using a physically plausible assumption. The integral can then be simplified and evaluated analytically. The analytical solution can be expressed in a closed form analogous to the classical Weyl-Van der Pol formula that has been used for predicting sound fields above a rigid-porous ground. Extensive comparisons with the wave-based numerical solutions according to the fast field formulation and the direct evaluation of the integral have been conducted. It has been demonstrated that the analytical formula is sufficiently accurate to predict the penetration of sound into a wide range of outdoor ground surfaces.     

Extended sources radiation and laplace type integral representation: Application to wave propagation above and within layered media

In has been shown that the sound field reflected by the plane boundary of a layered ground can always be described by a specularly reflected wave, and layer potentials. Despite its generality, this representation is not quite suitable for numerical computation. Dealing with a very simple case, Weyl, and later on Ingard and Thomasson, proposed a representation of the solution in which the layer potential terms are replaced by the sum of surface wave and a Laplace type integral. Such an integral is very convenient for numerical purposes. In this paper, it is shown that this kind of representation can be obtained for a very wide class of sound propagation problems above or within layered media: a half-space bounded by a locally reacting surface, a finite layer of porous medium, a porous medium with depth-varying porosity, a thin elastic plate; wave propagation in shallow water with an impedance bottom. Many other applications could be developed.     

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.     

Efficient computation of the sound fields above a layered porous ground

An efficient computation of sound fields due to a monopole source placed above a porous layer is presented. This paper examines an improved scheme whereby the steepest descent path is selected for the numerical evaluation of the Sommerfeld integral. Along the steepest descent path, a standard Gaussian-Hermite quadrature can be used to calculate the sound fields effectively. The suggested numerical scheme is accurate at all frequencies except in the very near field. The proposed method is more numerically efficient than other computational schemes, especially at long ranges and high source frequencies.     

Effects of a multi-layered poro-elastic ground on attenuation of acoustic waves and ground vibration

Ground conditions affect the propagation of outdoor sound and vibration. This paper focuses on the interaction between air pressure and porous ground at low frequencies- where mechanisms other than the rigid porous effects used in locally reacting models may be important. A 2-D analytical model has been developed in this study for the calculation of acoustic and acousto-seismic admittances in a multi-layered poro-elastic ground. The model can be used as a prediction tool both for the ground effect on the sound and the generation of ground vibration by the sound. The modelled acoustic admittance is validated successfully against established rigid frame admittance models over a frequency range of 1 Hz-3 kHz. Moreover, the acousto-seismic impedance is verified against full scale airblast field test data measured during the Norwegian Trials full scale field test program. For certain ground types, the predicted acoustic admittance illustrates a different behaviour compared with predictions from the traditional rigid frame acoustic impedance models. This emphasises the importance of including a deformable frame in the model to obtain realistic results for these conditions.     

The diffraction of sound by an impedance sphere in the vicinity of a ground surface

The problem of sound diffraction by an absorbing sphere due to a monopole point source was investigated. The theoretical models were extended to consider the case of sound diffraction by an absorbing sphere with a locally reacting boundary or an extended reaction boundary placed above an outdoor ground surface of finite impedance. The separation of variables techniques and appropriate wave field expansions were used to derive the analytical solutions. By adopting an image method, the solutions could be formulated to account for the multiple scattering of sound between the sphere and its image near a flat acoustically hard or an impedance ground. The effect of ground on the reflected sound fields was incorporated in the theoretical model by employing an approximate analytical solution known as the Weyl-van der Pol formula. An approximation solution was suggested to determine the scattering coefficients from a set of linearly coupled complex equations for an absorbing sphere not too close to the ground. The approximate method substantially reduced the computational time for calculating the sound field. Preliminary measurements were conducted to characterize the acoustical properties of an absorbing sphere made of open cell polyurethane foam. Subsequent experiments were carried out to demonstrate the validity of the proposed theoretical models for various source/receiver configurations around the sphere above an acoustically hard ground and an impedance ground. Satisfactory comparative results were obtained between the theoretical predictions and experimental data. It was found that the theoretical predictions derived from the approximate solution agreed well with the results obtained by using the exact solutions.     

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.     

Normal mode solution for low-frequency sound propagation in a downward refracting atmosphere above a complex impedance plane.

The development of the fast field and parabolic equation solutions to the wave equation has made it possible to solve for the combined effects of refraction in a layered atmosphere and the interaction of sound with a complex impedance ground surface. In many respects the numerical methods have advanced beyond our understanding of the basic phenomena. In an earlier study [J. Acoust. Soc. Am. 89, 107-114 (1991)], the residue series solution for upward refraction was investigated and provided insight into the nature of the interaction of refraction and ground reflection. In this paper results are presented of a similar normal mode solution for downward refraction above a complex impedance ground surface. This model is used to investigate when the surface wave is excited for downward refraction conditions and to develop criteria for the maximum range of cylindrical decay as a function of phase and magnitude of the ground impedance and the magnitude of the sound velocity gradient.     

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.     

Diffraction of sound from a dipole source near to a barrier or an impedance discontinuity

Pierce's formulation for the diffraction of spherical waves by a hard wedge has been extended to the case of the sound field due to a dipole source. The same approach is also used to extend a semiempirical model for sound propagation above an impedance discontinuity due to a dipole source. The resulting formulas have been validated by comparing their numerical solutions with that computed by summing the sound fields due to two closely spaced monopole sources of equal magnitude but opposite in phase. These new formulations are then used to develop a simple model for calculating the dipole sound field diffracted by a barrier above an impedance ground. Applications of these models relate to transportation noise prediction, particularly railway noise abatement, for which dipole sources are commonly used. The numerical predictions have been found to compare reasonably well with indoor measurements using piezoceramic transducers as dipole sources.     

Absorption of a rigid frame porous layer with periodic circular inclusions backed by a periodic grating

The acoustic properties of a periodic rigid frame porous layer with multiple irregularities in the rigid backing and embedded rigid circular inclusions are investigated theoretically and numerically. The theoretical representation of the sound field in the structure is obtained using a combination of multipole method that accounts for the periodic inclusions and multi-modal method that accounts for the multiple irregularities of the rigid backing. The theoretical model is validated against a finite element method. The predictions show that the acoustic response of this structure exhibits quasi-total, high absorption peaks at low frequencies which are below the frequency of the quarter-wavelength resonance typical for a flat homogeneous porous layer backed by a rigid plate. This result is explained by excitation of additional modes in the porous layer and by a complex interaction between various acoustic modes. These modes relate to the resonances associated with the presence of a profiled rigid backing and rigid inclusions in the porous layer.     

一种预测扩散声场在非规则形状刚性壁面附近干涉图样的方法

扩散声场会在反射边界附近形成干涉图样,研究方法包括平面波模型、简正模态分析、渐进模态分析等,但仅适用于尺度远大于声波波长的矩形声腔。提出一种预测扩散声场在非规则刚性壁面结构附近形成的干涉图样的数值方法,表明结构附近“受挡”声压的互谱矩阵取决于:(1)假定该结构在自由空间中振动辐射声音时其表面法向振速到表面及场点声压的边界元系数矩阵;(2)假定结构置于自由空间中且表面刚性时,点声源辐射声波入射到结构表面上产生的散射声场的边界元系数矩阵;(3)扩散声场均方声压。仿真表明,该途径预测的干涉图样与理论值完全吻合。该预测方法还可用于混响环境下声源附近直达声压均方值的空间分布估计,为混响环境下设备的声源定位提供帮助。      

An experimental study on antipersonnel landmine detection using acoustic-to-seismic coupling

An acoustic-to-seismic system to detect buried antipersonnel mines exploits airborne acoustic waves penetrating the surface of the ground. Acoustic waves radiating from a sound source above the ground excite Biot type I and II compressional waves in the porous soil. The type I wave and type II waves refract toward the normal and cause air and soil particle motion. If a landmine is buried below the surface of the insonified area, these waves are scattered or reflected by the target, resulting in distinct changes to the acoustically coupled ground motion. A scanning laser Doppler vibrometer measures the motion of the ground surface. In the past, this technique has been employed with remarkable success in locating antitank mines during blind field tests [Sabatier and Xiang, IEEE Trans. Geosci. Remote Sens. 39, 1146-1154 (2001)]. The humanitarian demining mission requires an ability to locate antipersonnel mines, requiring a surmounting of additional challenges due to a plethora of shapes and smaller sizes. This paper describes an experimental study on the methods used to locate antipersonnel landmines in recent field measurements.     

Active noise cancellation of a spherical multipole source using a radially vibrating spherical baffled piston

The creation of quiet zones in a diffuse sound field due to a multipole spherical primary source by means of a radially vibrating surface set in the side of a rigid sphere (secondary source) is investigated in this article. The formulation utilizes the appropriate wave field expansions along with the translational addition theorems for spherical wave functions to develop a closed-form solution in the form of an infinite series. The numerical results reveal that using a baffled spherical piston model as a secondary source instead of a monopole control source will obviously improve the sound minimization efficiency of such noise-control systems in all cases, especially for a dipolar primary source.     

采用振速测量的改进统计最优近场声全息方法

针对常规统计最优近场声全息在空间多源声场重建过程中所需波函数项数多、重建精度不理想的问题,本文提出了一种基于振速测量的改进统计最优近场声全息算法。与常规算法不同,改进算法主要根据声源特点选取合适的波函数组合来计算声场传递矩阵。通过数值仿真初步验证了该方法的准确性和有效性,并与常规算法进行了详细的对比分析。仿真结果表明,改进算法重建精度高,随频率的变化相对误差波动较小,且随着频率的增大相对误差有逐渐减小的趋势;此外,不同的波函数组合,重建效果差异很大,当选取的波函数与声源共形且数量一致时重建效果最好。     

Rigorous solutions for sound radiation from circular ducts with hyperbolic horns or infinite plane baffle

A rigorous treatment is presented of sound radiation from circular ducts with either a hyperbolic horn or an infinite plane baffle. In the analysis hyperboloidal wave functions are used, which are defined here, for the first time, as a class of eigensolutions of the wave equation for oblate spheroidal co-ordinates. The numerical results include the complex conversion (or reflection) coefficients and the radiation directivity for various incident wave modes, spinning modes as well as axisymmetric modes. The solutions are valid for the whole frequency range including frequencies above and below the cut-off frequencies of the duct modes involved.     

Sound propagation over ground: Analytical approximations and experimental results

Approximations of the sound field emitted by a point source in the presence of the ground have recently been developed [1]. In this paper, these analytical expressions, slightly improved for computation, are compared with an exact representation of the sound pressure and two kinds of experimental results. The approximations, easy to compute, provide a reasonable accuracy for predictions of the sound levels in the asymptotic and intermediate (preceding the asymptotic) regions. Furthermore, numerical techniques (an optimization method) are presented for obtaining the “best value” of the ground normal impedance, from data obtained in Kundt's tube and far field measurements.     

瞬态波位移场计算方法在相控阵声场模拟中的实验验证

通过实验研究了声束偏转不同角度和声场半径变化时线性相控阵的声场特性,并与基于瞬态波位移解析解的相控阵声场计算方法得到的理论结果进行了对比。首先研究了基于半圆圆弧离面瞬态位移的声场计算方法,并进行了数值计算可靠性的优化。然后建立了一套相控阵瞬态波位移场的测量系统,以半圆形钢板为试件,纵波传感器为接收传感器,测量了偏转角度为-10°,-30°,-50°,-70°,及声场半径为50 mm,75 mm,100 mm和125 mm时线性超声相控阵的声束指向性;同时以基于瞬态波位移解析解的相控阵声场计算方法,计算了相同条件下该相控阵的声束指向性。最后将实验结果与理论结果进行了对比,取得了较好的一致。说明基于瞬态波位移的相控阵声场计算方法可以较好地计算线阵的声场,对于声束偏转较大角度和声场半径变化时也同样有效。      

A mode matching approach for modeling two dimensional porous grating with infinitely rigid or soft inclusions

This work investigates the acoustical properties of a multilayer porous material in which periodic inclusions are embedded. The material is assumed to be backed by a rigid wall. Most of the studies performed in this field used the multipole method and are limited to circular shape inclusions. Here, a mode matching approach, more convenient for a layered system, is adopted. The inclusions can be in the form of rigid scatterers of an arbitrary shape, in the form of an air-filled cavity or in the form of a porous medium with contrasting properties. The computational approach is validated on simple geometries against other numerical schemes and with experimental results obtained in an anechoic room on a rigid grating embedded in a porous material made of 2 mm glass beads. The method is used to study the acoustic absorption behavior of this class of materials in the low frequency range and at a range of angles of incidence.