Materials Testing

International audienceIn recent years, a number of models to calculate the acoustical behaviour of porous materials (sound absorption, sound insulation and vibration damping) have been developed [1]. Although these models are based on physical sound theories, they require a number of material parameters and the output of a calculation will depend on the accuracy of the input parameters. Depending on the complexity of the porous material and the configuration to be modeled, up to seven parameters may be needed

Predictions of angle dependent tortuosity and elasticity effects on sound propagation in cancellous bone

The anisotropic pore structure and elasticity of cancellous bone cause wave speeds and attenuation in cancellous bone to vary with angle. Previously published predictions of the variation in wave speed with angle are reviewed. Predictions that allow tortuosity to be angle dependent but assume isotropic elasticity compare well with available data on wave speeds at large angles but less well for small angles near the normal to the trabeculae. Claims for predictions that only include angle-dependence in elasticity are found to be misleading. Audio-frequency data obtained at audio-frequencies in air-filled bone replicas are used to derive an empirical expression for the angle-and porosity-dependence of tortuosity. Predictions that allow for either angle dependent tortuosity or angle dependent elasticity or both are compared with existing data for all angles and porosities

Acoustic response of a rigid frame porous medium slab with a periodic set of inclusions

The acoustic response of a rigid frame porous slab with a periodic set of inclusions is calculated by use of a multipole method. The acoustic properties, in particular the absorption, of such a structure are then derived and studied. Numerical results together with a modal analysis show that the addition of a periodic set of high-contrast inclusions leads to quasi-modes excitation of both the slab and the gratings, and to a large increase of the acoustic absorption of the initial slab, this being partly due to the quasi-modes excitation.Comment: submitted to Journal of Sound and Vibratio

Characterization of porous acoustic materials

International audienceAn overview of the models and parameters of the acoustic wave propagation in porous media is presented. The most common parameters (the porosity, the permeability or flow resistivity and the densities) can be measured with standard methods. Ultrasonic methods for measuring the other parameters (the tortuosity and characteristic lengths) related to the complex pore micro-structure are reviewed. The ultrasonic methods are based on the transmission or reflection of airborne ultrasonic waves and on the signal analysis in the frequency and/or in the time domains. Ultrasonic scattering is discussed at higher frequencies where the classical models are no longer valid. In order to complete the characterization of porous acoustic materials, new techniques for evaluating the elastic and viscoelastic properties are proposed. These techniques are based on the generation of standing waves in a layer of material and on the spatial Fourier Transform of the displacement profile of the upper surface. Two configurations are proposed: a layer of porous material glued on a rigid substrate and a porous layer under Lamb conditions. Theoretical dispersion curves are fitted to the experimental results and this procedure can provide information on the complex shear modulus and of the complex Poisson ratio in a wide frequency range, typically between 50 Hz and 4 kHz

Ultrasonic wave propagation in reticulated foams saturated by different gases: High frequency limit of the classical models

International audienceTransmission experiments are performed on high porosity reticulated polyurethane foams saturated by different gases at ultrasonic frequencies up to 800 kHz. An excess attenuation is observed at high frequencies, when the wavelength is not sufficiently large compared to the lateral dimensions of the fibers. At lower frequencies, these experiments lead by using classical models of equivalent fluids, to a fast and reliable method for determining the characteristic length $\Lambda$

Characterisation of the elastic properties of porous foams

International audienceAn experimental method for measuring the elastic constants of poroelastic foams as a function of frequency is presented. The method is based on the measurement of phase velocities of guided acoustic waves in a slab of the material. Standing waves are generated in the material and the phase velocities are evaluated using the spatial Fourier Transform of the displacement profile of the upper surface. The displacement is measured with the help of a Laser Doppler vibrometer along a line corresponding to the direction of propagation of plane surface waves. The spatial Fourier Transform provides the wave numbers and the phase velocities are obtained from the relationship between wave number and frequency. The phase velocity of several guided modes could be measured in highly porous foams saturated by air. The modes were also studied theoretically and from the theoretical and experimental results, it was possible to determine the frequency behavior of the real part of the shear modulus and in a frequency range higher than the traditional methods. Experimental results concerning guided waves in isotropic porous materials tend to suggest that information about the anisotropy of the elastic matrix can also be obtained

Prediction and Measurements of the Influence of Boundary Conditions in a Standing Wave Tube

International audienceThe paper concerns a comparison between measurement results of the acoustic absorption coefficient and impedance using two different methods, the standing wave tube (Kundt's tube) and a free field method. The mounting of the sample in the Kundt's tube is known to be very important. In this paper, the effect of the constraints at the tube wall on the absorption coefficient of an elastic porous material is analysed. It will be shown that the effect of the friction offered by the tube wall is to stiffen the material, compared to its behaviour in the free field. Measurement results together with model calculations are presented. The material parameters used in the models have been determined by separate measurements

Measuring the dynamic shear modulus of poroelastic foams in the audible frequency range

International audienceThe prediction of acoustical properties of multilayered systems including poroelastic layers using the full Biot theory is in principle possible but in practice limited by the absence of material data. One of the parameters that is difficult to measure is the dynamic rigidity of the porous frame. Current experimental methods are limited to the lower part of the audible frequency range 1 (typically below 400 Hz) and require special shapes of the sample (cube, cylindrical rod or very thin samples). Since most sound absorbing plastic foams are viscoelastic, the elastic moduli may vary strongly with frequency, a measuring technique in the full audible frequency range is needed. Recently 2 a new method for the measurement of the dynamic shear modulus of the frame of poroelastic foams in the medium and high audible frequency range (1 to 4 kHz) has been presented This method is based on the measurement of the velocity and the damping of a Rayleigh-type surface wave on sample with thickness larger than the Rayleigh wave penetration depth. The Rayleigh wave was excited through direct mechanical excitation of the frame or the porous material and detected using a laser-doppler vibrometer. The velocity of this wave is closely related to the shear velocity, which is directly linked to the shear modulus. The damping of the Rayleigh wave can be used to determine the imaginary part of the shear modulus.In this work a first attempt is made to measure the dynamic shear modulus on a layer of finite thickness. In this way there is no requirement whatsoever concerning the shape of the sample under investigation

Verification of Kramers-Kronig relationship in porous materials having a rigid frame

The propagation of acoustic waves in porous materials having a rigid frame is well described by several models. A doubt about the causality of these models has been raised recently in the literature. A verification of the causality of these models is studied in this paper using the Kramers–Kronig dispersion relations adapted to the frequency power law dependence of the attenuation. It is shown that these models are causal in the high- and low-frequency range. A time domain wave equation and time-causal theory have been treated