Theory of sound propagation in superfluid-filled porous media

The theory of sound propagation in macroscopically isotropic and homogeneous porous media saturated with superfluid ⁴He has been developed neglecting all damping processes. The case when the normal fluid component is locked inside a porous medium by viscous forces is investigated in detail. It is shown that in this case one shear wave and two longitudinal, fast and slow, waves exist. Fast wave as well as slow wave is accompanied with temperature oscillations. The velocities of these waves are obtained.     

Improved sound absorption performance of three-dimensional MPP space sound absorbers by filling with porous materials

Because microperforated panels (MPPs), which can be made from various materials, provide wide-band sound absorption, they are recognized as one of the next-generation absorption materials. Although MPPs are typically placed in front of rigid walls, MPP space sound absorbers without a backing structure, including three-dimensional cylindrical MPP space absorbers (CMSAs) and rectangular MPP space absorbers (RMSAs), are proposed to extend their design flexibility and easy-to-use properties. On the other hand, improving the absorption performance by filling the back cavity of typical MPP absorbers with porous materials has been shown theoretically, and three-dimensional MPP space absorbers should display similar improvements. Herein the effects of porous materials inserted into the cavities of CMSAs and RMSAs are experimentally investigated and a numerical prediction method using the two-dimensional boundary element method is proposed. Consequently, CMSAs and RMSAs with improved absorption performances are illustrated based on the experimental results, and the applicability of the proposed prediction method as a design tool is confirmed by comparing the experimental and numerical results.     

A finite element model for rigid porous absorbing materials

An eight node isoparametric finite element is used to represent a rigid porous absorbing material. Tests on an assembly of these elements for a one dimensional model gave good agreement with an exact solution for the input impedance. Results from a two dimensional model show the effects of transverse propagating modes on the input impedance and indicate that for an absorbent with finite dimensions extended reaction is important.     

Transient acoustic wave propagation in rigid porous media: a time-domain approach

Wave propagation of acoustic waves in porous media is considered. The medium is assumed to have a rigid frame, so that the propagation takes place in the air which fills the material. The Euler equation and the constitutive relation are generalized to take into account the dispersive nature of these media. It is shown that the connection between the fractional calculus and the behavior of materials with memory allows time-domain wave equations, the coefficients of which are no longer frequency dependent, to be worked out. These equations are suited for direct and inverse scattering problems, and lead to the complete determination of the porous medium parameters.     

Quantifying the through-thickness asymmetry of sound absorbing porous materials

A method to quantify the through-thickness asymmetry of a sound absorbing porous material is proposed and discussed. Its calculation only requires impedance tube measurements of the acoustical surface impedance performed on both sides of the tested material. The method may be used for quality control or to assess the level of asymmetry of the material in terms of its acoustic properties. As a first validation, a two-layered porous system seen as an equivalent asymmetrical single porous layer with a sudden change in its physical properties is studied. From this study, a criterion of asymmetry is suggested and experimentally tested.     

Bulk sound velocity of porous materials at high pressures

A correction of Walsh's method for bulk sound velocity calculation for shocked porous materials is accomplished based on the Wu－Jing thermodynamic equation of state. The corrected bulk velocities for solid and porous samples with low porosities are in good agreement with the corresponding experimental data published previously. On the basis of this corrected equation, the influence of thermoelectrons on the bulk velocity of shocked materials is discussed in detail at pressures of 50, 70 and 200 GPa. Some interesting phenomena are revealed, which seem to be the unique features of a dynamic-pressure-loading process and could not be found in static experiments.     

Low-frequency sound propagation in porous media: Glass spheres and pea gravel

The sound propagation properties of two air-filled granular materials: large sifted pea gravel and 10 mm diameter glass spheres have been measured in an impedance tube. The experimental method was essentially the same as reported earlier [Swenson et al. Low-frequency sound wave parameter measurement in gravels. Appl Acoust 2010; 71: 45–51] for two other kinds of gravel: crushed limestone and undifferentiated pea gravel. Additional sampling and processing steps were applied to the microphone signals such that instead of tones, band-limited random noise was used as the input signal, and spectral domain complex pressures are now offered as input to the estimation algorithm. The estimation process extracts the best-fit attenuation coefficient, phase velocity, and characteristic impedance for the material over the signal frequencies, all with better precision than we previously obtained. Quadratic approximations for the acoustical parameters are given over the frequency range 25–160 Hz. The media are both slightly attenuating and dispersive, having attenuation coefficients within 0.13–0.34 Np/m, phase velocities smaller than those in air (180–240 m/s), and characteristic impedance approximately 3–5 times that for air. Pea gravel was more attenuating, and had slightly higher characteristic impedance, but lower phase velocities than the glass spheres.     

Experim ental investigation of sound propagation from an impulsive source near rigid wedges

The acoustic signal from an impulsive source near an ideal rigidwedge consists of the reflected waves from the inclined plane andthe diffracted waves from the apex of the wedge.There are two theoreti-cal solutions of the problem.The first was obtained by Biot-Tolstoyusing normal coordinates.The second was Trorey's Helmholtz-Kirchhoffsolution.So far the experimental measurements have concentrated on thediffracted wave from the wedge apex and ignored the rest of the solution.The Biot-Tolstoy exact wedge solution is used in this paper to study thesound transmission in wedges of angle 12°and 52°approximately.Thetheory and the experiments are consistent.Also studied is the behaviourof the reflected and diffracted waves from a 270°wedge.Both theoriespredicted the existence a specular"image"reflection when a coincidentsource and receiver are over a half plane.The experimental results showedthat the Biot-Tolstoy theory was accurate and the Trorey solution pro-duced quite large errors.     

Fast asymptotic solutions for sound fields above and below a rigid porous ground

The current study simultaneously addresses the problem of reflection and refraction of sound from a rigid porous ground surface. A more rigorous approach is used to derive more accurate asymptotic solutions that can be cast in a convenient form for ease of numerical implementations. The solutions provide means for rapid computations of the sound fields above and below the rigid porous ground. The improved asymptotic formulas for both situations agree well with numerical results obtained by other numerical schemes, which are more accurate but computationally more intensive. More importantly, the asymptotic solutions can be written in the well-known form of the Weyl-van der Pol formula, which provides a direct correlation between the reflected wave term for the sound field above the porous ground and the transmitted (refracted) wave term for the sound field below.     

On the influence of spatial correlations on sound propagation in concentrated solutions of rigid particles

In a previous paper [J. Acoust. Soc. Am. 121, 3386-3387 (2007)], a self-consistent effective medium theory has been used to account for hydrodynamic interactions between neighboring rigid particles, which considerably affect the sound propagation in concentrated solutions. However, spatial correlations were completely left out in this model. They correspond to the fact that the presence of one particle at a given position locally affects the location of the other ones. In the present work, the importance of such correlations is demonstrated within a certain frequency range and particle concentration. For that purpose, spatial correlations are integrated in our two-phase formulation by using a closure scheme similar to the one introduced by Spelt et al. ['Attenuation of sound in concentrated suspensions theory and experiments," J. Fluid Mech. 430, 51-86 (2001)]. Then, the effect is shown through a careful comparison of the results obtained with this model, the ones obtained with different self-consistent approximations and the experiments performed by Hipp et al. ["Acoustical characterization of concentrated suspensions and emulsions. 2. Experimental validation," Langmuir, 18, 391-404 (2002)]. With the present formulation, an excellent agreement is reached for all frequencies (within the limit of the long wavelength regime) and for concentrations up to 30% without any adjustable parameter.     

Effects of compression on the sound absorption of porous materials with an elastic frame

The absorption characteristics of a porous material are well known to vary during compression. The transfer matrix method is applied with an elastic frame to explore the effect of compression on absorption properties. In this work, the materials are treated as elastic rather than being made of rigid models. The absorption coefficients of the uncompressed and compressed porous material are initially calculated and verified from the experimental measurements. Then, numerical predictions of absorption coefficient are made for the compressed porous material.     

An application of the Peano series expansion to predict sound propagation in materials with continuous pore stratification

This work reports on an application of the state vector (Stroh) formalism and Peano series expansion to solve the problem of sound propagation in a material with continuous pore stratification. An alternative Biot formulation is used to link the equivalent velocity in the oscillatory flow in the material pores with the acoustic pressure gradient. In this formulation, the complex dynamic density and bulk modulus are predicted using the equivalent fluid flow model developed by Horoshenkov and Swift [J. Acoust. Soc. Am. 110(5), 2371-2378 (2001)] under the rigid frame approximation. This model is validated against experimental data obtained for a 140 mm thick material specimen with continuous pore size stratification and relatively constant porosity. This material has been produced from polyurethane binder solution placed in a container with a vented top and sealed bottom to achieve a gradient in the reaction time which caused a pore size stratification to develop as a function of depth [Mahasaranon et al., J. Appl. Phys. 111, 084901 (2012)]. It is shown that the acoustical properties of this class of materials can be accurately predicted with the adopted theoretical model.     

Vortex sound under the influence of a piecewise porous material on an infinite rigid plane

The vortex dynamics and the sound generation by an inviscid vortex in the presence of a finite length porous material on an otherwise rigid plane are studied numerically in the present study in an attempt to understand the sound generation near the surface of a wall lining in a lined duct. The combined effects of the effective fluid density and flow resistance inside the porous material, and the length and thickness of the porous material on the sound generation process are examined in detail. Results obtained demonstrate the sound pressure is longitudinal dipole and show how seriously the above-mentioned parameters are affecting the vortex sound pressure under the influence of the porous material.     

Shallow water sound propagation with surface waves

The theory of wavefront modeling in underwater acoustics is extended to allow rapid range dependence of the boundaries such as occurs in shallow water with surface waves. The theory allows for multiple reflections at surface and bottom as well as focusing and defocusing due to reflection from surface waves. The phase and amplitude of the field are calculated directly and used to model pulse propagation in the time domain. Pulse waveforms are obtained directly for all wavefront arrivals including both insonified and shadow regions near caustics. Calculated waveforms agree well with a reference solution and data obtained in a near-shore shallow water experiment with surface waves over a sloping bottom.     

On the use of perforations to improve the sound absorption of porous materials

The concept of meso-perforations in appropriately chosen porous media can help enhance their sound absorption performance. The meso-perforated materials are also referred to as “double porosity materials” since they are made up of two interconnected networks of pores of different characteristic size. Several theoretical, numerical and experimental works have been accomplished on the subject by the authors. The purpose of this paper is to give a synthetic review of these works and establish practical design rules to develop optimized noise control solutions based on this concept. The paper presents two complementary models to deal with this kind of materials: an analytical model based on homogenization techniques and a numerical model relying on a finite element discretization of the domains. The limits of these models are discussed. The choice of the design parameters is then been investigated in order to provide practical design rules. This choice relies on a criterion which is evaluated from the knowledge of the resistivity, porosity and tortuosity of the micropous medium, and the calculation of a geometrical parameter defined from the chosen mesoscopic structure. Experimental and numerical results regarding the influence of the mesopore profile along the thickness performed in a appropriately chosen substrate microporous medium are presented. The agreement between the models and the experiments is satisfactory. Results show that significant enhancements of the absorption properties can be obtained over a selected frequency band by adjusting the mesopore profile. It is also shown that interesting absorbing properties can be obtained when coating a double porosity medium with an impervious screen.     

Applicability of locally reacting boundary conditions to porous material layer backed by rigid wall: Wave-based numerical study in non-diffuse sound field with unevenly distributed sound absorbing surfaces

To clarify the applicability of locally reacting boundary conditions in wave-based numerical analyses of sound fields in rooms, we numerically analyzed a non-diffuse sound field in a room with unevenly distributed sound absorbing surfaces and investigated the differences between the extended and local reactions. Each absorbing surface was a porous material layer backed by a rigid wall. Simulations were performed by the fast multipole boundary element method, a highly efficient boundary element method using the fast multipole method. At low frequencies, the extended and local reactions yielded similar reverberation decay curves because of the influence of the room. However, when the random incidence absorption coefficients were small at low frequencies or frequencies were high, the difference was greater than expected from the corresponding Eyring decay lines. We conclude at high frequencies, the locally reacting boundary conditions lead to a longer reverberation time than that expected from the absorption coefficient differences between the extended and local reactions. These differences were similar in sound-pressure-level and sound-intensity-level distributions, and in the oblique incidence absorption coefficient of the absorbing surfaces, but were increased at low frequencies.     

含有孔隙的层状材料中声表面波传播特性的理论研究

研究含有孔隙的层状材料中Rayleigh波的传播特性。采用本征函数展开法,并利用孔隙率与材料的弹性常数和密度之间的关系,模拟了不同孔隙率情况下铁基氧化铝层状材料中Rayleigh波的相速度色散曲线,分析了孔隙率对铁基氧化铝层状材料中Rayleigh波相速度的影响。Rayleigh波色散曲线的变化规律能同时反映层状材料中弹性模量、泊松比、密度和孔隙率的信息,为含有孔隙的层状材料参数的反演提供了理论依据。