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.     

A model comparison of the absorption coefficient of a Microperforated Insertion Unit in the frequency and time domains

The absorption coefficient of acoustic materials can be measured either in the frequency or the time domain. At normal incidence, a sample of the material is fitted within an impedance tube and the absorption coefficient is calculated in the frequency domain from the measurement of the transfer function between two microphones [ISO 10534-2. Acoustics - determination of sound absorption coefficient and impedance in impedance tubes - Part 2: transfer function method. ISO, Geneva, Switzerland; 1996]. When the acoustic material must be characterized at oblique incidence or in situ (noise barriers, for instance) the absorption coefficient is calculated from measurements of the loudspeaker-microphone impulse response in the time domain, both in free field and in front of the sample [CEN/TS 1793-5. Road traffic noise reduction devices - test method for determining the acoustic performance - Part 5: intrinsic characteristics - in situ values of sound reflection and airborne sound insulation. CEN, Brussels, Belgium; 2003, ISO 13472-1. Acoustic measurement of sound absorption properties of road surfaces in situ - Part I: extended surface method. ISO, Geneva, Switzerland; 2002]. Since the absorption is an intrinsic property of the acoustic material, its measurement in either domain must provide the same result. However, this has not been formally demonstrated yet. The aim of this paper is to carry out a comparison between the absorption coefficient predicted by the impedance model of a Microperforated Insertion Unit and the absorption coefficient predicted from a simulated reflection trace taken into account the finite length of the time window.     

高声压级时多孔金属板的吸声特性研究

针对高声压级下有限厚度多孔金属板在线性阻抗背衬条件下(背衬表面声压与声质点速度为线性关系)的吸声问题,提出了一个描述不同声压级下材料层法向吸声性能的一维模型,并给出求解材料层内部声质点速度的线化与差分方法,以预测多孔金属板在高声压级下的非线性吸声特性。在阻抗管中对两块多孔金属板进行了声学测试,得到了材料层法向表面阻抗和吸声系数随入射声压级变化的实验结果。研究表明:实验与理论预测符合良好,验证了模型与数值方法的正确性。本文所提原理和方法,可用于一般硬质多孔材料。      

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.     

Predicting the sound absorption of natural materials: Best-fit inverse laws for the acoustic impedance and the propagation constant

Natural materials are becoming a valid option for sound absorption treatments. In particular, among them, natural fibers have received increasing attention given their good thermal insulation properties, lack of harmful effects on health, and availability in large quantities. This paper discusses an inverse method to predict the acoustical properties of nine natural fibers. Six vegetative fibers: kenaf, wood, hemp, coconut, straw, and cane; one animal fiber, sheep wool; recycled cardboard; and granular cork are investigated. The absorption coefficient and the flow resistance for samples of different thickness have been measured. Moving from the Delany-Bazley model, this study compares the impedance tube results with the theoretically predicted ones. Then, using a least-square fit procedure based on the Nelder-Mead method, the coefficients that best predict both the acoustic impedance and the propagation constant laws are calculated. The inverse approach used in this paper allows to determine different physical parameters and to obtain formulas to include the investigated natural fibers in software modelling for room acoustics applications.     

Measurement of the resistivity of porous materials with an alternating air-flow method

Air-flow resistivity is a main parameter governing the acoustic behavior of porous materials for sound absorption. The international standard ISO 9053 specifies two different methods to measure the air-flow resistivity, namely a steady-state air-flow method and an alternating air-flow method. The latter is realized by the measurement of the sound pressure at 2 Hz in a small rigid volume closed partially by the test sample. This cavity is excited with a known volume-velocity sound source implemented often with a motor-driven piston oscillating with prescribed area and displacement magnitude. Measurements at 2 Hz require special instrumentation and care. The authors suggest an alternating air-flow method based on the ratio of sound pressures measured at frequencies higher than 2 Hz inside two cavities coupled through a conventional loudspeaker. The basic method showed that the imaginary part of the sound pressure ratio is useful for the evaluation of the air-flow resistance. Criteria are discussed about the choice of a frequency range suitable to perform simplified calculations with respect to the basic method. These criteria depend on the sample thickness, its nonacoustic parameters, and the measurement apparatus as well. The proposed measurement method was tested successfully with various types of acoustic materials.     

基于声压-质点速度声强探头的材料吸声系数的测量

通过由一个声压换能器和一个质点速度换能器所构成的传感器(p-u声强探头)同时测量材料表面附近的声压和质点振动速度,可直接得到其声学阻抗,进而得到材料的反射因子、吸声系数。本文利用一个p-u探头声强测量系统,在半消声室内测量了三聚氰胺泡沫的吸声系数,分析了声源高度和入射角度、材料样本尺寸和厚度对吸声系数测量的影响,并和阻抗管中测量得到的法向吸声系数进行了对比。最后分析了声阻抗率的幅值和相位误差对吸声系数的影响,推导了它们的误差传递公式。     

Experimental measurements of acoustical properties of snow and inverse characterization of its geometrical parameters

Snow is a sound absorbing porous sintered material composed of solid matrix of ice skeleton with air (+water vapour) saturated pores. Investigation of snow acoustic properties is useful to understand the interaction between snow structure and sound waves, which can be further used to devise non-destructive way for exploring physical (non-acoustic) properties of snow. The present paper discusses the experimental measurements of various acoustical properties of snow such as acoustic absorption coefficient, surface impedance and transmission losses across different snow samples, followed by inverse characterization of different geometrical parameters of snow. The snow samples were extracted from a natural snowpack and transported to a nearby controlled environmental facility at Patsio, located in the Great Himalayan range of India. An impedance tube system (ITS), working in the frequency range 63–6300 Hz, was used for acoustic measurements of these snow samples. The acoustic behaviour of snow was observed strongly dependent upon the incident acoustic frequency; for frequencies smaller than 1 kHz, the average acoustic absorption coefficient was found below than 0.4, however, for the frequencies more than 1 kHz it was found to be 0.85. The average acoustic transmission loss was observed from 1.45 dB cm⁻¹ to 3.77 dB cm⁻¹ for the entire frequency range. The real and imaginary components of normalized surface impedance of snow samples varied from 0.02 to 7.77 and −6.05 to 5.69, respectively. Further, the measured acoustic properties of snow were used for inverse characterization of non-acoustic geometrical parameters such as porosity, flow resistivity, tortuosity, viscous and thermal characteristic lengths using the equivalent fluid model proposed by Johnson, Champoux and Allard (JCA). Acoustically derived porosity and flow resistivity were also compared with experimentally measured values and good agreement was observed between them.     

The impact of the neck material on the sound absorption performance of Helmholtz resonators

Helmholtz resonators with sound absorption materials filling the neck may have an improved sound absorption capacity. In this work, parallel perforated ceramics with different perforation diameters were installed into the neck of a Helmholtz resonator to improve its acoustic impedance to simultaneously achieve a better acoustic absorption coefficient and a wider absorption bandwidth. An experimental system was built to investigate the effect of the perforation diameters on the sound absorption performance of the resonator. It is found that nonlinear effects near the resonance frequency affect the resonator?s neck mouth impedance and further its sound absorption performance significantly. For frequency range 50–500 Hz, a model of the neck mouth impedance is developed based on a revised Forchheimer relationship. The experimental results are in good agreement with the theoretical model.     

Application of the ISO 13472-1 in situ technique for measuring the acoustic absorption coefficient of grass and artificial turf surfaces

This paper presents the applicability of an in situ technique based on ISO 13472-1 standard for measuring the acoustic absorption coefficient of grass and artificial turf surfaces for normal incidence from a sound source. The in situ method is based on acoustic impulse response measurement of the material surface. A maximum length sequence (MLS) signal is played through a loudspeaker and the acoustic response from the surface is recorded using a single microphone. The fast Hadamard transform and fast Fourier transform based digital signal post-processing algorithm provides the acoustic absorption coefficient of the surface under test. The normal incidence acoustic absorption coefficient of a commercial artificial quash surface of Dow Co. obtained from this method was compared with the results from the ASTM E1050 impedance tube method for the same surface. The acoustic absorption coefficients of a test-site grass surfaces were measured for 30 mm and 100 mm length of grass blades in wet and dry soil conditions. Substantial difference in the acoustic absorption coefficient was observed for a similar grass-like artificial surface used for estimating sound power of commercial garden equipments and lawnmowers. The advantage of the in situ method lies in its ability to measure the normal incident acoustic absorption coefficient of any planar surface as installed or in situ. Additionally a quick testing time of less than a minute with the use of a laptop sound card based inexpensive data acquisition system is the main feature of this robust method.     

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.     

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.     

Seven-hole hollow polyester fibers as reinforcement in sound absorption chlorinated polyethylene composites

A series of thin, lightweight and low-cost sound absorption composites consisting of chlorinated polyethylene (CPE) and seven-hole hollow polyester fibers (SHPF) were fabricated. The sound absorption property of the fiber composites was tested in an impedance tube, the morphology was characterized by a scanning electron micrographs (SEM) and the mechanical property of fiber composites was measured by strength tester. The effect of fiber content, composite thickness, and cavity depth on the sound absorption property, and the effect of fiber content on mechanical property and micro-structure were investigated. The results demonstrated that acoustical characteristics of porous materials were exhibited by mixing with SHPF. Acoustical absorption of materials increased significantly with increasing SHPF content. Furthermore, the acoustic property of composite with 20% SHPF concentration and 3 mm thickness was noted in the low frequency range, giving a sound absorption coefficient peak, 0.695 at 2500 Hz. Composite with air back cavity had resonance characteristics of a lamella with an absorption peak only occurring at a specific frequency. Compared with pure CPE of similar thickness, mechanically CPE/SHPF composite at the 1 mm thickness and 20% SHPF exhibited 228% higher tensile stress and 96% lower breaking strain. It appears from these results that CPE/SHPF composites have potential for engineering applications especially as sound absorbers.     

Model and estimation method for predicting the sound radiated by a horn loudspeaker - With application to a car horn

This paper deals with a new car horn device made of a sound synthesizer and an electrodynamic horn loudspeaker. It presents an one-dimensional model allowing to predict the loudspeaker efficiency and a specific method to estimate experimentally the model parameters. First, this model aims at reducing the time spent in the design process. Second it aims at correcting the sound emitted by the sound synthesizer in order that the listener hears the sound designed for creating the warning message. The study gives a survey of the vast loudspeaker literature. It is based on the conventional electroacoustic approach used for electrodynamic loudspeakers and on wave propagation models used for characterizing acoustic horns. The estimation of the model parameter values is performed using measurements of the electrical impedance of the loudspeaker and of the acoustic impedance of the horn. The model is assessed by comparing the calculated and measured electrical impedances and horn efficiencies. Results show that the model predicts well the horn efficiency up to 2500 Hz, the limitation being due to the horn radiation impedance modelization.     

Neural networks for prediction of acoustical properties of polyurethane foams

This paper presents a study of neural networks for prediction of acoustical properties of polyurethane foams. The proposed neural network model of the foam uses easily measured parameters such as frequency, airflow resistivity and density to predict multiple acoustical properties including the sound absorption coefficient and the surface impedance. Such a model is quite robust in the sense that it can be used to develop models for many different classes of materials with different sets of input and output parameters. The current neural network model of the foam is empirical and provides a useful complement to the existing analytical and numerical approaches.     

The acoustical properties of consolidated expanded clay granulates

The paper presents a systematic study of acoustic and non-acoustic properties of consolidated porous samples of expanded clay granulates. The effect of the particle size on the acoustic performance of consolidated expanded clays is investigated experimentally and theoretically. This work involves a comparison of the measured and predicted values of the absorption coefficient and normalised acoustic surface impedance data. It is demonstrated that the values of tortuosity and standard deviation in the pore size distribution do not depend significantly on the size of the material aggregate. An empirical expression which links the flow resistivity of the consolidated granular mix has been derived from the measured data. These results pave the way for the development of a simple practical model which will be able to link the acoustic properties of a consolidated granular mix with the characteristic particle dimension and the porosity data. These materials are structurally robust and easy to integrate in buildings and highway structures to control the levels of environmental noise and improve the acoustic quality of spaces.     

General regression neural network for prediction of sound absorption coefficients of sandwich structure nonwoven absorbers

In this paper, we propose a more general forecasting method to predict the sound absorption coefficients at six central frequencies and the average sound absorption coefficient of a sandwich structure nonwoven absorber. The kernel assumption of the proposed method is that the acoustics property of sandwich structure nonwoven absorber is determined by some easily measured structural parameters, such as thickness, area density, porosity, and pore size of each layer, if the type of the fiber used in nonwoven is given. By holding this assumption in mind, we will use general regression neural network (GRNN) as a prediction model to bridge the gap between the measured structural parameters of each absorber and its sound absorption coefficient. In experiment section, one hundred sandwich structure nonwoven absorbers are particularly designed with ten different types of meltblown polypropylene nonwoven materials and four types of hydroentangled E-glass fiber nonwoven materials firstly. Secondly, four structural parameters, i.e., thickness, area density, porosity, and pore size of each layer are instrumentally measured, which will be used as the inputs of GRNN. Thirdly, the sound absorption coefficients of each absorber are measured with SW477 impedance tube. The sound absorption coefficient at 125 Hz, 250 Hz, 500 Hz, 1000 Hz, 2000 Hz, 4000 Hz and their average value are used as the outputs of GRNN. Finally, the prediction framework will be carried out after the desired training set selection and spread parameter optimization of GRNN. The prediction results of 20 test samples show the prediction method proposed in this paper is reliable and efficient.     

Experimental investigation of holes interaction effect on the sound absorption coefficient of micro-perforated panels under high and medium sound levels

This paper experimentally investigates the holes interaction effect on the sound absorption coefficient of micro-perforated panels under high and medium sound levels. The theoretical formulations are based on a semi-empirical approach and the use of Fok’s function to model the acoustic surface impedance. For the high sound level regime, an empirical power law involving three coefficients is adapted. It is shown theoretically and experimentally that these coefficients can lead to optimized absorption performance and particularly, a formula relating the critical Reynolds number (Reynolds number value after which the absorption coefficient decreases with the increase of sound level) and the center-to-center distance between the perforations is derived. It is demonstrated that the first coefficient of the nonlinear acoustic resistance strongly depends on the separation distance between the apertures and decreases with a decrease of this latter distance. Analysis of the data reveals the fact that even with Holes Interaction Effect (HIE), the nonlinear reactance dependence on velocity is still very low compared to the resistance-velocity dependence. Four perforated panels of 1.5 mm thickness with different separation distances between the holes (from widely to closely separation) were built and tested. Experimental results performed with an impedance tube are compared with the described model for HIE. To test the dependence of the coefficients on frequency, the experiments are carried out for two different excitation frequencies (292 Hz and 506 Hz). The results can be used for designing optimal perforated panels for ducts, silencers and for the automotive industry.     

Improving the Sound Absorption Properties of Flexible Polyurethane (PU) Foam using Nanofibers and Nanoparticles

Polyurethane foam as the most well-known absorbent materials has a suitable absorption coefficient only within a limited frequency range. The aim of this study was to improve the sound absorption coefficient of flexible polyurethane (PU) foam within the range of various frequencies using clay nanoparticles, polyacrylonitrile nanofibers, and polyvinylidene fluoride nanofibers. The response surface method was used to determine the effect of addition of nanofi- bers of PAN and PVDF, addition of clay nanoparticles, absorbent thickness, and air gap on the sound absorption coefficient of flexible polyurethane foam (PU) across different frequency ranges. The absorption coefficient of the samples was measured using Impedance Tubes device. Nano clay at low thicknesses as well as polyacrylonitrile nanofibers and polyvinyl fluoride nanofibers at higher thicknesses had a greater positive effect on absorption coefficient. The mean sound absorption coefficient in the composite with the highest absorption coeffi- cient at middle and high frequencies was 0.798 and 0.75, respectively. In comparison with pure polyurethane foam with the same thickness and air gap, these values were 2.22 times at the middle frequencies and 1.47 times at high frequencies, respectively. Surface porosity rose with increasing nano clay, but decreased with increasing polyacrylonitrile nanofibers and polyvinyl fluoride nanofibers. The results indicated that the absorption coefficient was elevated with increasing the thickness and air gap. This study suggests that the use of a combination of nanoparticles and nanofibers can enhance the acoustic properties of flexible polyurethane foam.     

0-3型压电复合材料覆盖层水下 吸声性能的理论研究

目前压电分流阻尼技术在振动和噪声领域的应用得到了广泛的关注. 本文尝试将压电分流阻尼技术应用于水下吸声领域, 以提高覆盖层的吸声性能. 将压电覆盖层厚度模态的机电方程和声波传播的传递矩阵相结合, 建立一维电声模型. 该模型可以用于分析多层压电和非压电水下吸声覆盖层的吸声性能. 采用该模型分析了0-3型压电复合材料覆盖层的水下吸声性能. 压电复合材料的参数是采用Furukawa的模型计算的. 研究结果表明, 采用合适的分流电阻, 负电容分流电路可以在较宽的频率范围显著提高覆盖层的吸声性能. 其原理可以从阻抗匹配的角度解释, 负电容分流电路可以调整压电覆盖层的表面声阻抗, 使之与水的特性声阻抗相匹配.