Theoretical analysis and experiment study on the acoustic parameters of metal rubber materials

The acoustic parameters of metal rubber materials were theoretically and experimentally investigated. Under the assumption that metal rubber materials were homogenous, isotropic and porous structures, formulas were deduced for the calculations of effective sound velocity, characteristic impedance, propagation constant, structural constant and flow resistivity. The structural constant of metal rubber materials with different structural parameters were obtained and analyzed by using experiments. The experimental and theoretical values of characteristic impedance and propagation constant were compared and analyzed. It is shown that the proposed theoretic method based on the homogenous, isotropic and porous material model is suitable to calculate the acoustic parameters of metal rubber materials.     

Acoustical characteristics of porous materials

The diversity of porous materials is noted. However, this study is particularly relevant to the use of sound absorbent materials in architectural acoustics. The theory of sound propagation within an idealised porous material consisting of a rigid matrix through which run parallel cylindrical pores normal to the surface is reviewed. Extensions to pores of arbitrary orientation and cross-section are achieved by introducing physically-measura ble microstructural constants rather than phenomenological bulk parameters that might be frequency dependent. By comparison of several theories that account for sound propagation within an elastically-framed porous material a basis is laid for an improved formulation, that takes into account both viscosity and heat conduction.The application of various propagation theories to model the reflection and transmission of sound at porous boundaries is considered. Particular attention is paid to the common assumption of local reaction and to the adequacy of modelling the porous interface as that of a quasi-homogeneous fluid. Finally the most widely used methods of measuring acoustical characteristics of porous materials at normal and oblique incidence and of obtaining their values by empirical means are surveyed.     

Sound propagation above a porous road surface with extended reaction by boundary element method

Acoustic impedance of an absorbing interface is easily introduced in boundary element codes provided that a local reaction is assumed. But this assumption is not valid in the case of porous road surface. A two-domain approach was developed for the prediction of sound propagation above a porous layer that takes into account the sound propagation inside the porous material. The porous material is modeled by a homogeneous dissipative fluid medium. An alternative to this time consuming two-domain approach is proposed by using the grazing incidence approximate impedance in the traditional single-domain boundary element method (BEM). It can be checked that this value is numerically consistent with the surface impedance calculated at the interface from the pressure and surface velocity solutions of the two-domain approach. The single-domain BEM introducing this grazing incidence impedance is compared in terms of sound attenuation with analytical solutions and two-domain BEM. The comparison is also performed with the single-domain BEM using the normal incidence impedance, and reveals a much better accuracy for the prediction of sound propagation above a porous interface.     

含气泡液体中声传播的解析解及其强非线性声特性

声波在含气泡的液体中传播时,气泡的受迫振动会引起强的声散射,并且由于振动的非线性,使得气泡产生的次级波不仅含有基频成分,而且还会有高次谐波。本文从理论上描述了气泡个数随尺并给出了含气泡液体的等效非线性声参数Ｂ／Ａ的计算公式理论与已有的实验观测符合较好,文中对含气泡水的声速和声衰减等特性也进行了讨论。     

Recent advances in utilizing acoustics to study surface roughness in agricultural surfaces

The evaluation of surface roughness in agricultural settings is investigated. Previous work has shown that sound propagating in a direction parallel to a smooth porous ground attenuates more rapidly than in a free space. This attenuation is due to absorption of the sound in the air filled pores in the ground. Previous work has also shown that a comparable attenuation phenomenon exists for propagation over a rough surface, albeit from different attenuation mechanisms. It is proposed that these additional attenuation mechanisms can be used to quantify the surface roughness, even on a porous surface. Attempts to model observed data with an effective impedance or reflection coefficient, in order to quantify the surface roughness, have had some success but have met with some problems for certain propagation geometries and surface configurations. Experimental data and modeling results will be presented and discussed for a variety of surfaces ranging in surface properties from impermeable to loosely packed soil and ranging in surface roughness scales from low sloped perturbations to steeply sloped wedges.     

Time-domain impedance formulation for transmission line matrix modelling of outdoor sound propagation

Outdoor sound propagation modelling has attracted considerable attention in the past and has lead to many analytical and numerical models. More recently, the increase of computational power has led to consider time-domain methods that enable to consider transient phenomena. Among these models, the transmission line matrix (TLM) method has been proposed, but the sound absorption at boundaries appears to be a somewhat underdeveloped aspect of this approach. In this paper, a specific implementation of impedance boundary condition is proposed. The method is based on the approximation of the impedance as a sum of linear systems, which allows the formulation of an equivalent impedance model in the time-domain. The proposed implementation is applied for two common impedance models of porous material. Numerical simulations have been carried out in the case of sound propagation over a flat ground with and without an impedance discontinuity, and for several values of specific airflow resistivity. TLM numerical predictions expressed in terms of excess attenuation relative to free field show a good agreement with analytical solutions.     

An axisymmetric poroelastic finite element formulation.

In the past, various two- and three-dimensional Cartesian, poroelastic finite element formulations have been proposed and demonstrated. Here an axisymmetric formulation of a poroelastic finite element is presented. The intention of this work was to develop a finite element formulation that could easily and efficiently model axisymmetric sound propagation in circular structures having arbitrary, axially dependent radii, and that are lined or filled with elastic porous sound absorbing materials such as foams. The formulation starts from the Biot equations for an elastic porous material expressed explicitly in axisymmetric form. By following a standard finite element development, a u-U formulation results. Procedures for coupling the axisymmetric elements to an adjacent acoustical domain are described, as are the boundary conditions appropriate for unfaced foams. Calculations described here show that the present formulation yields predictions as accurate as a Cartesian, three-dimensional model in much reduced time. Predictions made using the present model are also compared with measurements of sound transmission through cylindrical foam plugs, and the predicted results are shown to agree well with the measurements. Good agreement was also found in the case of sound transmission through a conical foam plug.     

Viscoelastic BISQ Model for Low-Permeability Sandstone with Clay

A modified BISQ （Blot/Squirt） model for wave propagation in low-permeability sandstone is developed by introducing the viscoelastic mechanism of a porous skeleton into Dvorkin＇s model. The linear viscoelasticity of the Kelvin Voigt constitutive law is employed to describe the stress-strain relation of a solid frame with clay while the ultrasonic waves propagate through the fluid-saturated sandstone. The phase velocity and attenuation of two p-waves are given based on the present BISQ model. The comparisons between numerical results and experimental data indicate that our viscoelastic model is more realistic and feasible for wave propagation in the low-permeability sandstone, especially with clay, than traditional BISQ models.     

Analysis of sound attenuation in a duct with a solid or porous splitter

The equivalent singularity method is developed for the analysis of sound propagation in a duct with a thin solid or point-reacting porous splitter of a finite streamwise length. The method consists in representing the splitter by a singular plane of pressure dipoles and mass sources, distributions of which are determined so that the boundary condition at the splitter surfaces is satisfied. The boundary condition is expressed in terms of two admittance parameters giving relations between pressures and normal displacements of fluid particles at the upper and lower surfaces of the splitter. Computed results are presented to illustrate the dependence of the sound power transmitted through the splitter section on the acoustic properties, length and location of the splitter and the flow Mach number. A principal cause of the sound attenuation due to a splitter is found to be the conversion of the acoustic energy into the wake vortex energy convected downstream. A solid splitter or a porous splitter of small admittance shows tuning effects—with a peak or multiple peaks in the attenuation spectrum. The tuning frequencies can be controlled by the splitter location.     

声波在含气泡液体中的线性传播

为了探讨含气泡液体对声波传播的影响, 研究了声波在含气泡液体中的线性传播. 在建立含气泡液体的声学模型时引入气泡含量的影响,建立气泡模型时引用 Keller的气泡振动模型并同时考虑气泡间的声相互作用,得到了经过修正的气泡振动方程. 通过对含气泡液体的声传播方程和气泡振动方程联立并线性化求解,在满足 (ω R₀)/c << 1 的前提下,得到了描述含气泡液体对声波传播的衰减系数和传播速度. 通过数值分析发现,在驱动声场频率一定的情况下,气泡含量的增加及气泡的变小均会导致衰减系数增加和声速减小;气泡的体积分数和大小一定时, 驱动声场频率在远小于气泡谐振频率的情况下,声速会随驱动频率的增加而减小; 气泡间的声相互作用对声波传播速度及含气泡液体衰减系数的影响不明显.最终认为气泡的大小、 数量和驱动声场频率是影响声波在含气泡液体中线性传播的主要因素. 关键词： 含气泡液体 线性声波 声衰减系数 声速     

NUMERICAL MODELLING OF MEDIAN ROAD TRAFFIC NOISE BARRIERS

Outdoor sound propagation from road traffic is modelled by solving a boundary integral equation formulation of the wave equation using boundary element techniques in two dimensions. In the first model, the source representing a traffic stream can be considered as a coherent line source of sound. The results can then be transformed to derive a pseudo-three dimensional solution to the problem. In the second model the line source is incoherent. For receivers near the ground, the second model predicted significantly higher values of ground attenuation than the first. The first model generally produced better agreement with ground attenuation results obtained using the U.K. traffic noise prediction model. For conditions when a noise barrier was present and the ground was absorbent, the incoherent line source model generally predicted significantly higher values of attenuation than those from the barrier and ground attenuation calculated separately. Over a range of receiver positions and barrier heights a similar, but less marked effect was observed when the coherent line source model was used. On dual carriageway roads, it is possible to incorporate barriers on the central reservation as a noise control measure. These are “median” noise barriers. The incoherent line source model is used to assess the performance of median barriers in reducing noise when installed alone and also with associated roadside barriers. A sound absorbent median noise barrier 1m in height produced consistent values of insertion loss of between 1 and 2dB over the range of receiver positions and ground conditions considered. When the median barrier was used in conjunction with a roadside barrier it produced a consistent improvement in insertion loss of between 1 and 2 dB over the range of conditions considered.     

Long-range sound propagation in the Mediterranean Sea

The data of several experiments on the long-range propagation of explosion-generated and tonal sound signals are analyzed. The experiments are performed by the Acoustics Institute in the Mediterranean Sea with a fully developed sound channel. A substantial difference is observed for the propagation conditions in the western and eastern parts of the sea. This difference concerns the vertical sound speed profiles, the time structures of the sound field in the underwater sound channel, the duration of the explosion-generated signal, and the positions of the convergence zones. The experiment is compared with calculations. The observed difference in the experimental and calculated positions of the first convergence zone is explained by the imperfection of the relation used to recalculate the salinity, water temperature, and hydrostatic pressure to the sound speed. In spite of substantial difference in the propagation conditions on two 600-km paths, the experimental low-frequency attenuation coefficients on these paths (and on some shorter ones) agree well with each other for the frequency band of several kilohertz. The data are also close to those published for another 600-km path. All the paths mentioned run in different parts of the Mediterranean Sea. The frequency dependence of sound attenuation (absorption) can be well described by the relation that accounts for the absorption caused by the boron present in the sea water.     

Noise attenuation in factories

The cost of reducing noise levels in factories by covering large surfaces with sound absorbents is high. It is therefore important to be able to calculate in advance the effectiveness of absorbents and to determine how absorbents may be chosen and distributed for maximal noise reduction for the invested capital. For this purpose a mathematical model of sound propagation and attenuation in factories has been developed on certain simplifying assumptions. The interrelationship between the different parameters is found to be rather intricate and the mathematical model must be evaluated using a computer program. The influence on the noise levels of sound scattering objects, the shape and size of the factory and absorbents on the room surfaces have been studied. Especially if the ceiling is high, acoustic baffles are found to be more efficient than absorbents on the ceiling in reducing noise levels.     

各向异性渗流条件下弹性波的传播特征

研究了弹性波在非均匀裂纹孔隙介质中的传播特性,建立了各向异性喷射流模型.当弹性波通过裂纹孔隙介质时,由于波的扰动及裂纹和孔隙几何结构的不一致,导致在裂纹内部及裂纹与周边孔隙之间同时存在着流体压力梯度.此时的弹性波波动响应中包含着裂纹内连通性特征和背景孔隙渗透率信息.流体的动态流动过程使得介质的等效弹性参数为复数(非完全弹性),并且具有频率依赖性.当弹性波为低频和高频极限时,介质为完全弹性;当处于中间频段时,波有衰减和频率依赖.裂纹孔隙介质的各向异性连通性(渗透率)对应着各向异性特征频率(当渗流长度等于非均匀尺度时的弹性波频率),波的传播受到裂纹内连通性的影响.在一定频段内,随着裂纹厚度的增加,将出现第二峰值,峰值大小同时受到裂纹厚度和半径的影响.     

Outdoor sound propagation under the influence of wind and temperature gradients

The situation investigated is sound propagation from a monopole point source located over an impedance surface. The sound propagation is assumed to be influenced by wind and temperature gradients. A very accurate calculation method for taking into account the effect of wind and temperature gradients on sound propagation outdoors is presented and used for verification of a new approximate calculation model. This comparison shows that the approximate model is accurate. A series of loudspeaker measurements has been carried out over a grass-covered ground for distances up to 80 m. The measurements were carried out for a wind speed fo 2–2·5 m/s measured 10 m above the ground. The measured data agree very well with the calculated results. Furthermore the results from the approximate calculation model agree with results from previous investigations [1,2]. Hence, the main conclusion is that a simple and powerful approximate model for sound propagation under the influence of wind and temperature gradients has been developed. However, the influence of turbulence is not taken into account in this paper, and the wind and temperature gradients are assumed to be constant as functions of height.     

Ultrasonic studies of attenuation and dispersion in NH4Br near the order-disorder transition

Velocity and attenuation of sound wave propagation along the [100] direction in NH₄Br were measured near its transition temperature T_c = 234.5 K at frequencies of 30–150 MHz. The experimental results for the high-frequency attenuation and the dispersive velocity shifts are found to be in good agreement with the model of a single critical relaxation time.     

The propagation of a nonlinear sound wave in an unconsolidated granular medium

The propagation of a high-intensity sound wave in an unconsolidated medium is considered. Dissipation effects are taken into account on the basis of Buckingham’s theory of a relaxation mechanism of sound attenuation in a saturated sediment. The nonlinear evolution equation for the relaxing medium is obtained, and the solutions of this equation are analyzed. The second-harmonic generation in such a medium decays, as does the linear sound wave of the same frequency. The stationary weak shock profile has a specific form due to relaxation effects.     

On the ultrasonic attenuation in glasses at low temperatures

The ultrasonic attenuation in glasses at low temperatures is calculated using the model proposed by Anderson, Halperin, and Varma. It is found that the resonant absorption of sound by the localized two-level systems saturates and can be observed only if the sound amplitude is extremely small. A second contribution to the sound absorption is derived which arises from the relaxation of the localized excitations and does not saturate. Qualitative agreement with recent measurements of the ultrasonic attenuation in fused silica is obtained.     

A displacement-pressure finite element formulation for analyzing the sound transmission in ducted shear flows with finite poroelastic lining

In the present work, the propagation of sound in a lined duct containing sheared mean flow is studied. Walls of the duct are acoustically treated with absorbent poroelastic foams. The propagation of elasto-acoustic waves in the liner is described by Biot's model. In the fluid domain, the propagation of sound in a sheared mean flow is governed by the Galbrun's equation. The problem is solved using a mixed displacement-pressure finite element formulation in both domains. A 3D implementation of the model has been performed and is illustrated on axisymmetric examples. Convergence and accuracy of the numerical model are shown for the particular case of the modal propagation in a infinite duct containing a uniform flow. Practical examples concerning the sound attenuation through dissipative silencers are discussed. In particular, effects of the refraction effects in the shear layer as well as the mounting conditions of the foam on the transmission loss are shown. The presence of a perforate screen at the air-porous interface is also considered and included in the model.