Evaluation of the acoustic and non-acoustic properties of sound absorbing materials using a three-microphone impedance tube

This paper presents a straightforward application of an indirect method based on a three-microphone impedance tube setup to determine the non-acoustic properties of a sound absorbing porous material. First, a three-microphone impedance tube technique is used to measure some acoustic properties of the material (i.e., sound absorption coefficient, sound transmission loss, effective density and effective bulk modulus) regarded here as an equivalent fluid. Second, an indirect characterization allows one to extract its non-acoustic properties (i.e., static airflow resistivity, tortuosity, viscous and thermal characteristic lengths) from the measured effective properties and the material open porosity. The procedure is applied to four different sound absorbing materials and results of the characterization are compared with existing direct and inverse methods. Predictions of the acoustic behavior using an equivalent fluid model and the found non-acoustic properties are in good agreement with impedance tube measurements.     

Acoustic response of fibrous absorbent materials to impulsive transient excitations

The parameters used to characterize the acoustic behaviour of fibrous absorbent materials are usually the complex characteristic impedance and the complex wavenumber, which permit the calculation of the airflow resistance and vice versa. Different methods have been satisfactorily used by other authors in order to perform this characterization on the basis of a macroscopic modelling of the behaviour of these materials. In this paper, the suitability of this approach for predicting the acoustic response of absorbent materials to impulsive excitations is evaluated. The constant term of the airflow resistance equation for absorbent materials with different densities is quantified by means of a modified version of the impulse method. These values are then incorporated into one-dimensional acoustic calculations in order to predict the response of absorbing materials to pressure pulse excitation. The very good concordance observed between calculated and measured reflection and transmission coefficients shows the suitability of the proposed procedure for the characterization of absorbent 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.     

Measurement of the bulk acoustic properties of fibrous materials at high temperatures

It is common for fibrous porous materials to be used in high temperature applications such as automotive and gas turbine exhaust silencers. Understanding the effect of temperature on the acoustic properties of these materials is crucial when attempting to predict silencer performance. This requires knowledge of the bulk acoustic properties of the porous materials and so this article aims to quantify the effect of temperature on the bulk acoustic properties of three fibrous materials: rock wool, basalt wool and an E-glass fibre. Measurements are undertaken here using a standard impedance tube that has been modified to accommodate temperatures of up to 500 °C. It is shown that measured data for the bulk acoustic properties may be collapsed using a standard Delany and Bazley curve fitting methodology provided one modifies the properties of the material flow resistivity and air to account for a change in temperature. Moreover, by using a previously proposed power law describing the dependence of the flow resistivity with temperature, one may successfully collapse data measured at every temperature and obtain the Delany and Bazley coefficients in the usual way. Accordingly, to predict the bulk acoustic properties of a fibrous material at elevated temperatures it is necessary only to measure these properties at room temperature, and then to apply the appropriate temperature corrections to the properties of the material flow resistivity and air when using the Delany and Bazley formulae.     

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.     

An application of Kozeny–Carman flow resistivity model to predict the acoustical properties of polyester fibre

Modelling of the acoustical properties of polyester fibre materials is usually based on variations of the Bies and Hansen empirical model [1], which allows the calculation of the air flow resistivity of a porous material. The flow resistivity is the key non-acoustical parameter which determines the ability of this kind of materials to absorb sound. The main scope of this work is to illustrate that an alternative theoretical model based on the Kozeny–Carman equation can be used to predict more accurately the flow resistivity from the fibre diameter and bulk material density data. In this paper the flow resistivity is retrieved from the acoustic absorption coefficient data for polyester fibre samples of different densities and fibre diameters. These data agree closely with the flow resistivity predicted with the proposed Kozeny–Carman model.     

Use of a hybrid adaptive finite element/modal approach to assess the sound absorption of porous materials with meso-heterogeneities

The paper discusses the sound absorptive performance of a porous material with meso-perforations inserted in a rectangular waveguide using a numerical hybrid adaptive finite element-modal method. Two specific applications are investigated: (i) the improvement of porous materials noise reduction coefficient using meso-perforations (ii) the effects of lateral air gaps on the normal incidence sound absorption of mono-layer and two-layer porous materials. For the first application, a numerical design of experiments is used to optimize the sound performance of a porous material with meso-perforations with a reduced number of numerical simulation. An example in which the optimization process is carried out on the thickness and size of the perforation is presented to illustrate the relevance of the approach. For the second application, a set of twenty fibrous materials spanning a large flow resistivity range is used. Practical charts are proposed to evaluate the influence of air gaps on the average sound absorption performance of porous materials. This is helpful to both the experimenter regarding characterization of porous material based on Standing Wave Tube measurements and for the engineer to quantifying the impact of air gaps and for designing efficient absorbers.     

梯度穿缝型双孔隙率多孔材料的吸声性能

在传统单一孔隙率多孔材料中引入宏观尺度的周期性梯度穿缝结构设计,构造出梯度穿缝型双孔隙率多孔材料,其包含多孔材料基体微孔尺度与穿缝尺度两个尺度。采用分层等效的理论建模方法,将复杂梯度渐变问题变为多层均匀等效层叠加问题。针对不同特征尺寸的多孔材料薄层,分别采用低、高两种渗透率对比度双孔隙率理论,给出了其等效密度和动态压缩系数,再应用传递矩阵方法得到了相邻薄层之间的声压和质点速度传递关系并求得其表面声阻抗,从而建立了梯度穿缝型双孔隙率多孔材料的吸声理论模型。发展了多尺度材料声学有限元数值模型,在所考虑的100~3000 Hz频段范围内数值模拟结果完全吻合理论模型结果。理论与模拟分析了多尺度结构参数对双孔隙率多孔材料吸声性能的影响,结果表明引入多尺度梯度结构设计能够显著提高单一孔隙率多孔材料的吸声性能,且穿缝尺度比穿缝梯度影响更为显著;精细数值模拟获得的声压和能量密度分布云图揭示了多尺度结构设计的吸声增强机制。该工作可用于指导双孔隙率多孔材料的多尺度结构设计,从而提高多孔材料的中低频吸声性能。      

Sound absorption performance of gradiently slit-perforated double-porosity materials

A gradiently slit-perforated double-porosity material is proposed by introducing macro-scale periodic gradient slit-perforations into traditional porous materials with singleporosity.This material is one kind of multiscale material since it includes two scales of matrix micro-pore size and slit-perforation size.A theoretical model is developed for the sound absorption of the gradiently slit-perforated double-porosity material.In the model,the material is divided into lots of thin layers and each layer is approximated to be straight slit-perforated material.The equivalent density and dynamic compressibility of each thin layer are given by using the low or high permeability contrast double-porosity theory.Then the sound pressure and particle velocity relations between adjacent thin layers are obtained by employing the transfer matrix method.Finally,the surface acoustic impedance and the sound absorption of the gradiently slit-perforated porous material can be calculated.A finite element model is further established to validate the accuracy of the theoretical model.In the considered frequency range of 100-3000 Hz,the simulation results agree well with theoretical results.The influence of multiscale structural parameters on the sound absorption performance of the porous materials is analyzed theoretically and numerically.It is proved that the multiscale structure design can significantly improve the sound absorption performance of porous materials.Compared to the slit-perforation gradient,the slit-perforation width plays a more significant influence on sound absorption.The sound absorption enhancement mechanism of the multiscale structure design is revealed by the analysis of the sound pressure and energy dissipation distributions in the material.This work provides a multiscale structural design method for improving the sound absorption performance of traditional porous materials at broadband frequency.     

A theoretical analysis and experimental study of the behaviour of sound in corridors

The acoustic ray image theory is developed to predict relative sound levels along a corridor or in adjacent rooms caused by a sound source in the corridor. From experimental results in full-size corridors and in an acoustic scale model, general comments about the behaviour of sound in corridors—and the effect of small intruding walls and the position of absorbent material on sound levels in the corridor—are made.     

A simple empirical model of polyester fibre materials for acoustical applications

A new empirical model has been developed by the authors to predict the flow resistivity, acoustic impedance and sound absorption coefficient of polyester fibre materials. The parameters of the model have been adjusted to best fit the values of airflow resistivity and sound absorption coefficient measured over a set of 38 samples. Calculated results are compared with normal incidence measurements carried out using two different techniques: the transfer-function method in an impedance tube (ISO 10534-2) and the free-field impulse response method (ISO 13472-1). Measurements performed on polyester fibre materials with different density and thickness values, and diameter ranging from 18 to 48 μm, are in good agreement with the predictions of the new model. It is concluded that the new model can predict the basic acoustic properties of common polyester fibre materials with any practical combination of thickness and density².     

Effect of porous material compression on the sound transmission of a covered single leaf panel

In this paper, the authors examine the effect of compressing a poroelastic fibrous layer lined with an isotropic plate on the sound transmission loss (TL). For this purpose, a 2-in. thick fibrous material and two isotropic plates with critical frequencies around 2300 Hz and 9700 Hz were used. The transfer matrix method was applied and the porous layer was assumed to have either a rigid, limp or elastic frame. Current models of compression are outlined, and measurements of the airflow resistivity as a function of compression show that these models are suitable only for low compression rates. TL predictions are compared next to experimental data in a range between 100 Hz and 10000 Hz for three compression rates, corresponding to 0%, 20% and 50%. The fibrous is uniformly compressed over 100% of its surface. Our experiments showed that compression reduces the TL by a maximum of 5 dB for a 50% compression, mainly at the mid-frequency range, around 800 Hz. This is due to a resonance in the thickness of the porous material, increasing the radiation efficiency of the structure at mid-frequencies. Moreover, reduction of the porous thickness and increase of the airflow resistivity with compression are the variations influencing the most the TL of the structure. These trends were also detected with the limp and rigid frame models but with a lower degree of accuracy compared to the elastic frame model.     

A network approach for analysis of silencers with/without absorbent material

The object of this work is to establish a general approach that can analyze the performance of most of the silencers with/without sound absorbent material. Under the assumption of plane wave propagation, the transfer matrices between the two ends of straight pipe and two-duct perforated section are derived and taken as the basic elements. Based on the conditions of continuity of pressure and of mass velocity, the silencer is modeled as a network formed by the two basic elements. Then the sound attenuation characteristic of the silencers can be investigated. With this scheme the multiply connected acoustic filters can also be analyzed. Further, the porous sound absorbent material is also included in this scheme. The effect of sound absorption material on the performance of silencers is analyzed and discussed.     

A low order flow/acoustics interaction method for the prediction of sound propagation using 3D adaptive hybrid grids

A low-order flow/acoustics interaction method for the prediction of sound propagation and diffraction in unsteady subsonic compressible flow using adaptive 3-D hybrid grids is investigated. The total field is decomposed into the flow field described by the Euler equations, and the acoustics part described by the Nonlinear Perturbation Equations. The method is shown capable of predicting monopole sound propagation, while employment of acoustics-guided adapted grid refinement improves the accuracy of capturing the acoustic field. Interaction of sound with solid boundaries is also examined in terms of reflection, and diffraction. Sound propagation through an unsteady flow field is examined using static and dynamic flow/acoustics coupling demonstrating the importance of the latter.     

On the influence of frequency-dependent elastic properties in vibro-acoustic modelling of porous materials under structural excitation

The aspects related to modelling the frequency dependence of the elastic properties of air-saturated porous materials have been largely neglected in the past for several reasons. For acoustic excitation of porous materials, the material behaviour can be quite well represented by models where the properties of the solid frame have little influence. Only recently has the importance of the dynamic moduli of the frame come into focus. This is related to a growing interest in the material behaviour due to structural excitation. Two aspects stand out in connection with the elastic-dynamic behaviour. The first is related to methods for the characterisation of the dynamic moduli of porous materials. The second is a perceived lack of numerical methods able to model the complex material behaviour under structural excitation, in particular at higher frequencies. In the current paper, experimental data from a panel under structural excitation, coated with a porous material, are presented. In an attempt to correlate the experimental data to numerical predictions, it is found that the measured quasi-static material parameters do not suffice for an accurate prediction of the measured results. The elastic material parameters are then estimated by correlating the numerical prediction to the experimental data, following the physical behaviour predicted by the augmented Hooke?s law. The change in material behaviour due to the frequency-dependent properties is illustrated in terms of the propagation of the slow wave and the shear wave in the porous material.     

An impulse test technique with application to acoustic measurements

A method is described for measuring the acoustic properties of an absorbent material and a duct/nozzle system (with or without airflow) in which a high voltage spark discharge is used as an impulse source of sound. The cross-spectra of the incident, reflected and transmitted acoustic pressure transients are analyzed by way of a FFT digital processor in the form of complex transfer functions. These transfer functions have a direct relationship to the termination impedance and radiation directivity. The impulse method has been justified by comparisons that show excellent agreement with data obtained from existing methods (both experimental and theoretical).     

Measuring flow resistivity of porous materials at low frequencies range via acoustic transmitted waves

An acoustic transmissivity method is proposed for measuring flow resistivity of porous materials having rigid frame. Flow resistivity of porous material is defined as the ratio between the pressure difference across a sample and the velocity of flow of air through that sample per unit cube. The proposed method is based on a temporal model of the direct and inverse scattering problem for the diffusion of transient low-frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. The transmission scattering operator for a slab of porous material is derived from the response of the medium to an incident acoustic pulse. The flow resistivity is determined from the solution of the inverse problem. The minimization between experiment and theory is made in the time domain. Tests are performed using industrial plastic foams. Experimental and numerical results, and prospects are discussed.     

Influence of gas law on ultrasonic behaviour of porous media under pressure

This paper deals with the influence of gas law on ultrasonic behaviour of porous media when the saturating fluid is high pressured. Previous works have demonstrated that ultrasonic transmission through a porous sample with variations of the static pressure (up to 18 bars) of the saturating fluid allows the characterization of high damping materials. In these studies, the perfect gas law was used to link static pressure and density, which is disputable for high pressures. This paper compares the effects of real and perfect gas laws on modeled transmission coefficient for porous foams at these pressures. Direct simulations and a mechanical parameters estimation from minimization show that results are very similar in both cases. The real gas law is thus not necessary to describe the acoustic behaviour of porous media at low ultrasonic frequencies (100 kHz) up to 20 bars.     

Inverse acoustical characterization of natural jute sound absorbing material by the particle swarm optimization method

For modeling of jute as acoustic material, knowledge of its non-acoustical parameters like porosity, tortuosity, air flow resistivity, thermal and viscous characteristic lengths is a prime requisite. Measurement of these non-acoustical parameters is not straightforward and involves a dedicated measurement setup. So in order to overcome this issue, the inverse acoustical characterization can be used. In this paper, the particle swarm optimization method (PSO) is used as an optimization method. This method estimates the non-acoustical parameters of jute material in felt form by minimizing the error between experimental and theoretical sound absorption data. In this work, the impedance prediction models for fibrous materials like Johnson–Champoux–Allard model with rigid and limp frame and Garai–Pompoli model is used for sound absorption coefficient calculation by the transfer matrix method along with the PSO. The inverse estimated non-acoustical parameters for jute material are then compared with estimated and experimentally measured parameters for jute felts. Using these inversely predicted parameters, sound absorption of multilayer sound absorbers is also studied.