Acoustical Properties Of Porous Materials Research Articles

Stochastic modeling of porous sound absorbing materials using homogenization method and machine learning

This research introduces a novel approach to investigate porous sound absorbing materials using stochastic modeling techniques. The study employs the homogenization method and machine learning to predict the acoustic properties of porous materials. The homogenization method simplifies the analysis of microstructural properties in porous materials, while machine learning is a data analysis technique that utilizes algorithms to learn from data and make predictions. By integrating these methods, this study quantitatively assesses the impact of microscopic structural randomness on sound absorption properties. The study assumes that microstructural parameters are random variables and calculates the sound absorption coefficient through homogenization method. This dataset serves as input for machine learning. A Gaussian process regression model is developed using the dataset to evaluate the distribution of the sound absorption coefficient via the Gauss-Hermite quadrature method. The study implements Bayesian optimization, utilizing the variance of the resulting probability distribution as the acquisition function, to adaptively update the dataset. By iteratively performing these processes, the probability distribution of the sound absorption coefficient can be predicted efficiently and with high accuracy.

Extended reacting boundary modeling of porous materials with thin coverings for time-domain room acoustic simulations

Modeling of acoustic boundary conditions has a significant impact on the accuracy of room acoustic simulations, which play an important role in the design phase of indoor built environments in order to improve the acoustical comfort. In this work, a numerical framework based on the discontinuous Galerkin (DG) method is presented for modeling extended reacting boundaries of porous absorbers covered by thin materials. The domain decomposition methodology is applied by treating the porous material as a subdomain. Equivalent fluid models are used to depict the acoustic properties of porous materials, whose effective density and compressibility as irrational functions are approximated by multipole rational functions in the frequency domain. By employing the auxiliary differential equation approach to calculate the time convolution, the augmented time-domain governing equations of porous materials can be expressed in the same unified hyperbolic form as the linear acoustic equations, which further enables a consistent upwind numerical flux formulation throughout the whole domain. The numerical coupling across the interface between propagation media is handled by solving the underlying Riemann problem. Compared to existing approaches with the DG method for extended reacting boundaries modeling for room acoustics, the derived upwind numerical flux formulation does not involve the computation of auxiliary variables. The presented framework yield a well-posed linear hyperbolic system with admissible boundary conditions as guided by the “uniform Kreiss condition” (Kreiss, 1970). Acoustic properties of the covering materials are illustrated by considering a limp permeable membrane model. A local time-stepping approach is utilized to improve computational efficiency. Numerical validations against analytical solutions in 1D are performed to verify the desired high-order convergence rate. A 3D case study on modeling spherical wave fronts demonstrates the broadband accuracy of the formulation.

An extended transfer matrix method for measuring acoustical properties of porous materials beyond the cut-off frequency.

In the field of measuring the complex wave number and characteristic impedance of porous materials, available impedance tube approaches assume that only plane wave is propagating such that the maximum frequency is limited below the cut-off frequency of the first higher order mode. This indicates that if measurements at higher frequencies are required, the tube size has to be reduced, as well as the size of porous material sample, which may cause inaccurate results due to tube attenuation and edge-constraint effects. Through simulations, this paper presents an extended transfer matrix method to remove the plane wave assumption based on the fact that the propagation of plane wave through the porous sample can be characterized by the same transfer matrix whether higher order modes exist or not. This method arranges measuring points upstream and downstream the sample for implementing mode decomposition to extract the transfer matrix for plane wave in a multi-modal field. From the matrix elements, the complex wave number and characteristic impedance are determined in the same way as the original transfer matrix method. Based on numerical simulations and the Monte Carlo approach, the method effectiveness and a suitable measuring points layout are studied in this paper.

3-D printed bulk absorbers

We present results from our recent efforts on the fabrication and acoustic characterization of 3-D printed porous absorbers. The acoustic properties of porous structures are dependent on their cellular microstructural architecture. Thus, controlling their local and global cellular architecture can allow a significant control over the acoustic properties of porous materials. Our focus here is on two different kinds of porous absorbers—open-celled absorbers with novel surface topologies and functional gradients, and bio-inspired fibrous absorbers. First, we apply stereolithographic printing to fabricate open-celled absorbers with novel surface topologies. The effect of parameters such as porosity, relative density, surface topology, and through-thickness porosity gradients on the sound absorption behavior is elucidated. Second, we explore the possibility of fabricating fibrous absorbers using fused deposition modeling. While 3-D printing allows fabrication of complex geometries, printing thin fibrous parts is significantly more challenging. Here, we compare two different techniques of printing such structures and present the effect of the fibrous architecture on the acoustic properties of the structure. The obtained results show that 3-D printing offers a promising new avenue of designing porous structures with tailored acoustic properties.

Equivalent model of spatial random array vibration system on sound-absorbing computing for porous material

Porous materials are currently the most widely used sound absorbing materials. Due to the complex sound absorption mechanism, there is no mature calculation method to analyze its sound absorption performance, which can not provide a theoretical support for the selection, analysis and design of porous sound absorbing materials. Establishing a simple and reasonable equivalent model is a prerequisite for the calculation of the acoustic properties of porous materials. The sound absorption mechanism of porous materials was explored, and the spatial topology of porous materials was reconstructed. According to the spatial characteristics of porous materials, a mass-spring-damped vibration system equivalent model of spatial random array is proposed and established. The boundary conditions of the porous sound absorbing material were studied to be equivalent to the load to analyze the sound absorbing performance. The impedance tube test method is used to verify the equivalent model of the spatial random array vibration system for the sound absorption calculation of porous materials. The results show that the simulation results of the acoustic equivalent model of porous materials are consistent with the experimental results. This research method provides technical support for the study of acoustic theoretical models of porous materials.

Airflow resistance measurement of fibrous materials at high temperatures for acoustical applications

For some industrial applications it is necessary to assess the acoustic properties of porous materials at high temperatures; hence, airflow resistance measurements on fibrous materials have been carried out at temperatures up to 800 °C. A comparison of a high temperature test rig and a test rig satisfying the requirements of ISO 9053-1 indicated no significant difference between the two rigs at room temperature. For measurements in the high temperature test rig at and above 600 °C there were changes in the sample thickness that could be linked to the onset of crystallisation. This meant that regression analysis had to establish relationships between the sample mass (rather than bulk density) and the specific airflow resistance (rather than airflow resistivity). Power law regression for AES, basalt wool and rock wool show that, on average, the specific airflow resistance is proportional to T0.7 (where T is the absolute temperature in Kelvin) at temperatures where there has been no reduction in sample thickness or other material change due to temperature. For fibrous materials, these results provide more evidence that the temperature-dependence is mainly determined by the air viscosity. Measurements on AES at 20 °C indicate negligible change in the specific airflow resistance when measured with flow velocities between 0.5 × 10−3 and 1.83 × 10−3 m/s but significant differences at 800 °C.

Characterization of noise reduction capabilities of porous materials under various vacuum conditions

Noise pollution has been considered as a major challenge for the life of quality and engineering practices for environmental noise control for urban communities is of great importance. In this study, a series of experimental investigations are conducted to investigate the effects of a vacuum on the sound reduction and acoustic properties of porous materials. It is well known that sound cannot be transmitted under a full vacuum. However, a full vacuum condition cannot be realistically achieved in the construction process. Vacuum glass and related products are available in the market but these products can only extract a small degree of vacuum and can hardly withstand atmospheric pressure. Based on current research findings, a porous material with a certain degree of vacuum can achieve better noise reduction. The experimental setups are designed such that various porous materials can be tested, the desired vacuum levels can be maintained, and the ambience noise can be reduced to a sufficiently low level. Laboratory experiments are conducted to measure acoustic responses under various porous materials and vacuum levels. Sound intensities and corresponding frequencies are measured for porous materials with desired vacuum levels. The vacuum in porous materials, even at relatively low vacuum levels, has a significant effect on sound reduction. A vacuum of 10% in glass ball and polystyrene foam can lead to a noise reduction of more than 3 dB. The combination of vacuum and polystyrene foam has a more significant noise reduction effect, which can reach more than 8 dB for 30% vacuum. The research results may contribute to the comprehension of acoustic properties of porous materials under optimal vacuum levels. It is anticipated the research findings may lead to the construction of effective sound reducing products for noise attenuation, increasing insertion loss or improving sound insulation.

Modified two-thickness method for measurement of the acoustic properties of porous materials

In this study, a modified two-thickness method to measure acoustic properties of porous materials using surface acoustic impedance is proposed and compared to those obtained by the four-microphone impedance tube and traditional two-thickness methods. In the two-thickness method, the complex propagation constant and characteristic impedance are estimated from the measured surface acoustic impedances, and the sample thicknesses should have a ratio of two. Through the proposed method, the complex characteristic impedance and wavenumber of a porous material are calculated under arbitrary sample thicknesses condition. The surface acoustic impedances for samples of different thicknesses are measured via the two-microphone impedance tube method to estimate their complex acoustic properties. Sensitivity analysis is performed to analyze the measurement uncertainty on the resulting values. The sensitivity depended on the sample thickness and mount edge constraint in the tube. Using the method proposed in this study, acoustic properties are measured accurately with small differences in thickness and surface acoustic impedance.

Prediction of elastic and acoustic behaviors of calcarenite used for construction of historical monuments of Rabat, Morocco

Natural materials (e.g. rocks and soils) are porous media, whose microstructures present a wide diversity. They generally consist of a heterogeneous solid phase and a porous phase which may be fully or partially saturated with one or more fluids. The prediction of elastic and acoustic properties of porous materials is very important in many fields, such as physics of rocks, reservoir geophysics, civil engineering, construction field and study of the behavior of historical monuments. The aim of this work is to predict the elastic and acoustic behaviors of isotropic porous materials of a solid matrix containing dry, saturated and partially saturated spherical pores. For this, a homogenization technique based on the Mori–Tanaka model is presented to connect the elastic and acoustic properties to porosity and degree of water saturation. Non-destructive ultrasonic technique is used to determine the elastic properties from measurements of P-wave velocities. The results obtained show the influence of porosity and degree of water saturation on the effective properties. The various predictions of Mori–Tanaka model are then compared with experimental results for the elastic and acoustic properties of calcarenite.

A comparison of impedance models for the inverse estimation of the non-acoustical parameters of granular absorbers

An impedance model relates acoustic properties of porous materials with non-acoustical parameters. Although such parameters can be measured, specific equipment is required for each of them, so that numerical methods have been proposed for estimating their value from a more manageable measurement of the normal incidence absorption coefficient in an impedance tube. This inverse procedure requires both an impedance model and an inversion technique. This paper compares four impedance models, Miki, Hamet–Berengier, Johnson–Allard–Champoux and Champoux–Stinson, when Simulated Annealing is used for the inverse estimation of the non-acoustical parameters of three granular materials, consisting of packings of small spherical glass beads of different diameters. Some of these parameters have also been measured, so that they can be compared with these estimated by the proposed inverse method.

Analytical Solution of Biot's Equations Based on Potential Functions Method

In this paper, a new analytical solution for Biot's equations is presented based on potential functions method. The primary coupled Biot's equations have been considered based on fluid and solid displacements in three-dimensional (3D) space. By defining some potential functions, the governing equations have been improved to a simpler form. Then the coupled Biot's equations have been replaced with four-decoupled equations, by doing some mathematical manipulations. For a case study, it is assumed that the incident wave is in xy-plane and for specific boundary conditions; the partial differential equations are converted to ordinary differential equations and solved analytically. Then two foams with different properties have been considered, and acoustical properties of these foams due to the new developed method have been compared with the corresponding results presented by transfer-matrix method. Good agreement between results verifies the new presented solution. Based on the potential function method, not only the acoustical properties of porous materials are calculated, but also the analytical values of all basic field variables, such as pressure, fluid, and solid displacements, are obtained for all points in the porous media. Furthermore, fundamental features, such as damped and undamped natural frequencies, and damping coefficient of porous materials are calculated by considering presented results. The obtained results show that maximum values of field variables, such as pressure, fluid, and solid displacements, happen at the damped natural frequencies of the porous media, as expected. By increasing material thickness, the effect of damping of porous material on damped natural frequency decreases. Damping decreases the first natural frequency of the foam up to 8.5%.

Impedance tube experiments as a tool to teach acoustics of porous media

As a practical matter, sound propagation in many everyday situations includes interactions with porous materials. Such materials include textiles, foams, gravel, grass-covered ground, asphalt, and trees. Modeling sound propagation in complex environments, such as passenger cabins or urban spaces, with porous materials like these is essential to understanding realistic acoustics problems. The theory behind the sound absorption in porous material is not typically included in introductory acoustics courses. This is, at least in part, attributable to the mathematical complexity of the topic. Despite this barrier, acoustic properties of porous material can be easily introduced to typical undergraduate students using simple experiments to demonstrate the acoustic effects of different materials. This presentation describes acoustic property measurements of rigid-frame porous material with straight cylindrical pores as well as foam and soil included in an “Introduction to Acoustics” class at the Catholic University of America. The apparatus is composed of a LabVIEW measurement interface, a pair of microphones, and a simple aluminum impedance tube. The modular design allows students to adapt the software or hardware for other experiments. These hands-on experiences are intended to impart a conceptual understanding of the theory of sound absorption and the acoustic performance of sound absorbing (porous) media.

Beranek's porous material model: Inspiration for advanced material analysis and design

In 1942, Leo Beranek presented a model for predicting the acoustic properties of porous materials [J. Acoust. Soc. Am. 13, 248 (1942)]. Since then, research into many types of porous materials has grown into a broad field. In addition to Beranek's model, many other models for predicting the acoustic properties of porous materials in terms of key physical material parameters have been developed. Following a brief historical review, this work concentrates on studying porous materials and microperforated panels—pioneered by one of Beranek's early friends and fellow students, Dah-You Maa. Utilizing equivalent fluid models, porous material and microperforated panel theories have recently been unified. In this work, the Bayesian inference framework is applied to single- and multilayered porous and microperforated materials. Bayesian model selection and parameter estimation are used to guide the analysis and design of innovative multilayer acoustic absorbers.

On the modification of Delany and Bazley fomulae

It is well known that the formulae developed by Delany and Bazley for characterising the acoustic properties of porous materials should not be extended to low frequencies. Accordingly, a low frequency correction is required when finding the surface impedance or absorption coefficient of a porous material. This article reviews corrections of a type originally proposed by Miki [J. Acoust. Soc. Japan, 1990;11:19–24] and concludes that there is no physical basis behind these methods and that they should not be used. Instead, a number of alternative methods are available that maintain the correct limiting behaviour for the fundamental properties of a porous material at low frequencies, and two of these methods are briefly reviewed here.

Acoustics of porous materials with partially opened porosity.

A theoretical and experimental study of the acoustic properties of porous materials containing dead-end (or partially opened) porosity was recently proposed by Dupont, Leclaire, Sicot, Gong, and Panneton [J. Appl. Phys. 110, 094903 (2011)]. The present article provides a description of partially opened porosity systems and their numerous potential applications in the general context of the study of porous materials, the classical models describing them, and the characterization techniques. It is shown that the dead-end pore effect can be treated independently and that the description of this effect can be associated with any acoustic model of porous media. Different theoretical developments describing the dead-end porosity effect are proposed. In particular, a model involving the average effective length of the dead-end pores is presented. It is also shown that if the dead-end effect can be treated separately, the transfer matrix method is particularly well suited for the description of single or multilayer systems with dead-end porosity.

Experimental study of wood acoustic absorption characteristics

Abstract The objective of this study was to determine normal impedance on the surface as well as sound absorption coefficients for several wood species from Europe and from the tropical zone. The mathematical models of Miki, Attenborough, and Allard – dealing with acoustic properties of porous materials – have also been compared. The air flow resistivity exhibits a distinct link between fiber dimensions and wood porosity. The highest sound absorption coefficient was found for oak, ash, sapeli, and pine woods at 2 kHz frequency. The Attenborough model provides results closest to laboratory measurements, although it still requires significant improvements. The Miki and Allard models have some drawbacks and should be applied with reservation for the determination of wood acoustic properties.

Acoustic methods for measuring the porosities of porous materials incorporating dead-end pores

The acoustic properties of porous materials containing dead-end (DE) pores have been proposed by Dupont et al. [J. Appl. Phys. 110, 094903 (2011)]. In the theoretical description, two physical parameters were defined (the dead-end porosity and the average length of the dead-end pores). With the knowledge of the open porosity (measured with non-acoustic methods), and the measurement of kinematic porosity (also called the Biot porosity in this article), it is possible to deduce the dead-end porosity. Two acoustic methods for measuring the Biot porosity for a wide range of porosities are proposed. These methods are based on acoustic transmission and on the low and high frequency behaviors of acoustic indicators. The low frequency method is valid for high porosities. It involves measurements in a transmission tube and the knowledge of the theoretical asymptotic behavior of the phase velocity at high frequencies. The high frequency method is based on ultrasonic measurements and on the high frequency asymptotic behavior of the transmission coefficient. It is well adapted for material with relatively low values of porosity. Good precision was found for both methods and materials containing dead end porosity were tested.

Thermoacoustic properties of fibrous materials

The thermoacoustic properties of fibrous materials are studied using a computational fluid simulation as a test of proposed analytical models for propagation in porous materials with an ambient temperature gradient. The acoustic properties of porous materials have been understood in terms of microstructural models that approximate the material as an array of pores with empirical shape factors used to fit the pore theory to the material. An extension of these theories of acoustics to the thermoacoustic case with an ambient temperature gradient has been proposed by Roh et al. [J. Acoust. Soc. Am. 121, 1413-1422 (2007)] and a model based on Wilson's relaxation approximation for porous acoustics [J. Acoust. Soc. Am. 94, 1136-1145 (1993)] is proposed herein, but the predictions of these analytical models have not been tested successfully against measurements. Accurately characterizing the effects of the applied temperature gradient in a wide bandwidth laboratory setup have proven difficult; as a result, the authors conducted a numerical simulation of propagation within a fibrous geometry in order to test the predictions of the analytical models. The results for several fibrous samples show that the models yield a reliable prediction of thermoacoustic performance from the shape factors and relaxation times.

Anisotropy effects on the acoustical properties of porous materials

Porous materials are now widely used in noise control for their acoustic properties in sound absorption and transmission. These properties are function of the internal porous medium structure. Generally, most of the models assume that the porous medium is isotropic. Mineral wools (as well as some foams) clearly present an anisotropic structure. This communication is concerned with the adaptation of recent works on isotropic materials to the case of anisotropic porous materials. The general theory will be exposed for sound absorbing materials with anisotropic acoustical and mechanical parameters. The case of transverse isotropic materials (with fibers organized in planes running parallels one to each other) will then be detailed in particular in the case when the plane of fibers is not the same than the normal plane of the sample. The influence on the acoustical properties anisotropic porous materials will then be presented. Illustrations are then provided with measurements performed on wools and it will b...

Comparison of errors in the three- and four-microphone methods used in the measurement of the acoustic properties of porous materials

The three-microphone and four-microphone methods have been shown useful for measuring the characteristic impedance and propagating wavenumber of porous materials. In this paper the effects of uncertainties in the apparatus and pressure transfer function measurements are analyzed using Monte Carlo methods. It is shown that for materials with low flow resistivities the four-microphone method is appreciably more accurate than the three-microphone method at low frequencies. The dominant contributors to the overall error are uncertainty in the magnitude and phase of the transfer function measurement.