Laurens Boeckx

Reproducibility experiments on measuring acoustical properties of rigid-frame porous media (round-robin tests)

This paper reports the results of reproducibility experiments on the interlaboratory characterization of the acoustical properties of three types of consolidated porous media: granulated porous rubber, reticulated foam, and fiberglass. The measurements are conducted in several independent laboratories in Europe and North America. The studied acoustical characteristics are the surface complex acoustic impedance at normal incidence and plane wave absorption coefficient which are determined using the standard impedance tube method. The paper provides detailed procedures related to sample preparation and installation and it discusses the dispersion in the acoustical material property observed between individual material samples and laboratories. The importance of the boundary conditions, homogeneity of the porous material structure, and stability of the adopted signal processing method are highlighted.

Investigation of the phase velocities of guided acoustic waves in soft porous layers.

A new experimental method for measuring the phase velocities of guided acoustic waves in soft poroelastic or poroviscoelastic plates is proposed. The method is based on the generation of standing waves in the material and on the spatial Fourier transform of the displacement profile of the upper surface. The plate is glued on a rigid substrate so that it has a free upper surface and a nonmoving lower surface. The displacement is measured with a laser Doppler vibrometer along a line corresponding to the direction of propagation of plane surface waves. A continuous sine with varying frequencies was chosen as excitation signal to maximize the precision of the measurements. The spatial Fourier transform provides the wave numbers, and the phase velocities are obtained from the relationship between wave number and frequency. The phase velocities of several guided modes could be measured in a highly porous foam saturated by air. The modes were also studied theoretically and, from the theoretical results, the experimental results, and a fitting procedure, it was possible to determine the frequency behavior of the complex shear modulus and of the complex Poisson ratio from 200 Hz to 1.4 kHz, in a frequency range higher than the traditional methods.

Enhancing the absorption coefficient of a backed rigid frame porous layer by embedding circular periodic inclusions

The acoustic properties of a porous sheet of medium static air flow resistivity (around 10,000 N m s(-4)), in which a periodic set of circular inclusions is embedded and which is backed by a rigid plate, are investigated. The inclusions and porous skeleton are assumed motionless. Such a structure behaves like a multi-component diffraction grating. Numerical results show that this structure presents a quasi-total (close to unity) absorption peak below the quarter-wavelength resonance of the porous sheet in absence of inclusions. This result is explained by the excitation of a complex trapped mode. When more than one inclusion per spatial period is considered, additional quasi-total absorption peaks are observed. The numerical results, as calculated with the help of the mode-matching method described in this paper, agree with those calculated using a finite element method.

A description of transversely isotropic sound absorbing porous materials by transfer matrices

A description of wave propagation in transversely isotropic porous materials saturated by air with a recent reformulation of the Biot theory is carried out. The description is performed in terms of a transfer matrix method (TMM). The anisotropy is taken into account in the mechanical parameters (elastic constants) and in the acoustical parameters (flow resistivity, tortuosity, and characteristic lengths). As an illustration, the normal surface impedance at normal and oblique incidences of transversely isotropic porous layers is predicted. Comparisons are performed with experimental results.

Guided elastic waves in porous materials saturated by air under Lamb conditions

The propagation of guided elastic waves in porous materials saturated by air under Lamb conditions is studied theoretically and experimentally. The modes are derived from expressing the boundary conditions on the normal and tangential stresses and the displacements at the interfaces between the porous layer and the surrounding fluid. The stresses and the fluid pressure inside the porous medium are obtained from Biot’s equations of poroelasticity. Symmetrical and antisymmetrical modes are found when the porous layer is loaded by the same fluid on both sides. Damping mechanisms include viscous and thermal exchanges between the solid and the fluid, in addition to the classical structural damping. Using an experimental setup based on the generation of standing waves in the layer and taking the spatial Fourier transform of the displacement profile, the phase velocities of three modes were measured for two porous materials in a frequency range between 80 Hz and 4 kHz. The measurements confirm the theoretical pr...

Absorption of a rigid frame porous layer with periodic circular inclusions backed by a periodic grating

The acoustic properties of a periodic rigid frame porous layer with multiple irregularities in the rigid backing and embedded rigid circular inclusions are investigated theoretically and numerically. The theoretical representation of the sound field in the structure is obtained using a combination of multipole method that accounts for the periodic inclusions and multi-modal method that accounts for the multiple irregularities of the rigid backing. The theoretical model is validated against a finite element method. The predictions show that the acoustic response of this structure exhibits quasi-total, high absorption peaks at low frequencies which are below the frequency of the quarter-wavelength resonance typical for a flat homogeneous porous layer backed by a rigid plate. This result is explained by excitation of additional modes in the porous layer and by a complex interaction between various acoustic modes. These modes relate to the resonances associated with the presence of a profiled rigid backing and rigid inclusions in the porous layer.

Acoustical measurement of the shear modulus for thin porous layers

Simulations performed with the Biot theory show that for thin porous layers, a shear mode of the structure can be induced by a point-source in air located close to the layer. The simulations show that this mode is present around frequencies where the quarter wavelength of the shear Biot wave is equal to the thickness of the samples and show that it can be acoustically detected from the fast variations with frequency of the location of a pole of the reflection coefficient close to grazing incidence. The mode has been detected with this method for two reticulated plastic foams. For one of the foams studied, the velocity and the damping of the Rayleigh wave have been measured on a thicker layer of the same medium at higher frequencies, giving a real part of the shear modulus close to the one obtained from the measured location of the pole. The strong coupling of the shear mode with the acoustic field in air allows the measurement of the shear modulus without mechanical excitation.

How reproducible is the acoustical characterization of porous media

There is a considerable number of research publications on the characterization of porous media that is carried out in accordance with ISO 10534-2 (International Standards Organization, Geneva, Switzerland, 2001) and/or ISO 9053 (International Standards Organization, Geneva, Switzerland, 1991). According to the Web of ScienceTM (last accessed 22 September 2016) there were 339 publications in the Journal of the Acoustical Society of America alone which deal with the acoustics of porous media. However, the reproducibility of these characterization procedures is not well understood. This paper deals with the reproducibility of some standard characterization procedures for acoustic porous materials. The paper is an extension of the work published by Horoshenkov, Khan, Bécot, Jaouen, Sgard, Renault, Amirouche, Pompoli, Prodi, Bonfiglio, Pispola, Asdrubali, Hübelt, Atalla, Amédin, Lauriks, and Boeckx [J. Acoust. Soc. Am. 122(1), 345-353 (2007)]. In this paper, independent laboratory measurements were performed on the same material specimens so that the naturally occurring inhomogeneity in materials was controlled. It also presented the reproducibility data for the characteristic impedance, complex wavenumber, and for some related pore structure properties. This work can be helpful to better understand the tolerances of these material characterization procedures so improvements can be developed to reduce experimental errors and improve the reproducibility between laboratories.

Near field Rayleigh wave on soft porous layers.

Simulations performed for a typical semi-infinite reticulated plastic foam saturated by air show that, at distances less than three Rayleigh wavelengths from the area of mechanical excitation by a circular source, the normal frame velocity is close to the Rayleigh pole contribution. Simulated measurements show that a good order of magnitude estimate of the phase speed and damping can be obtained at small distances from the source. Simulations are also performed for layers of finite thickness, where the phase velocity and damping depend on frequency. They indicate that the normal frame velocity at small distances from the source is always close to the Rayleigh pole contribution and that a good order of magnitude estimate of the phase speed of the Rayleigh wave can be obtained at small distances from the source. Furthermore, simulations show that precise measurements of the damping of the Rayleigh wave need larger distances. Measurements performed on a layer of finite thickness confirm these trends.

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...