Bernard Castagnède

Evaluation of tortuosity in acoustic porous materials saturated by air

Tortuosity is an important parameter for the prediction of the acoustical properties of porous sound absorbing materials. The evaluation of tortuosity by resistivity measurements is now used in several laboratories, although this method presents several drawbacks. In particular, the complete saturation by a conducting fluid of a porous foam having a high flow resistivity is difficult to obtain without partially damaging the structure of the cells. A simple technique based on ultrasonic wavespeed measurements in a material saturated by air is described. This method has been used previously only for water or superfluid helium saturated materials.Tortuosity is an important parameter for the prediction of the acoustical properties of porous sound absorbing materials. The evaluation of tortuosity by resistivity measurements is now used in several laboratories, although this method presents several drawbacks. In particular, the complete saturation by a conducting fluid of a porous foam having a high flow resistivity is difficult to obtain without partially damaging the structure of the cells. A simple technique based on ultrasonic wavespeed measurements in a material saturated by air is described. This method has been used previously only for water or superfluid helium saturated materials.

Effects of compression on the sound absorption of fibrous materials

Abstract During the compression of a fibrous mat, it is well known that the absorption properties are decreasing. In order to predict this change, some heuristic formulae are proposed which take into account the modifications of the physical parameters (porosity, resistivity, tortuosity and shape factors) which enter the standard “equivalent fluid” model. Numerical predictions are then discussed and compared to experimental data obtained on a fibrous material (uncompressed and then compressed) used in the automotive industry.

Observation of the “Luxemburg–Gorky effect” for elastic waves

An experimental observation of a new nonlinear-modulation effect for longitudinal elastic waves is reported. The phenomenon is a direct elastic wave analogy with the so-called Luxemburg-Gorky (L-G) effect known over 60 years for radio waves propagating in the ionosphere. The effect consists of the appearance of modulation of a weaker initially non-modulated wave propagating in a nonlinear medium in the presence of an amplitude-modulated stronger wave that produces perturbations in the medium properties on the scale of its modulation frequency. The reported transfer of modulation from one elastic wave to another was observed in a resonator cut of a glass rod containing a few small cracks. Presence of such a small damage drastically enhances the material nonlinearity compared to elastic atomic nonlinearity of homogeneous solids, so that the pronounced L-G type cross-modulation could be observed at strain magnitude in the stronger wave down to 10(-7) and smaller. Main features of the effect are pointed out and physical mechanism of the observed phenomena is discussed.

Porous material characterization – ultrasonic method for estimation of tortuosity and characteristic length using a barometric chamber

An ultrasonic method of acoustic parameter evaluation for porous materials saturated by air (or any other gas) is discussed. The method is based on the evolution of speed of sound and the attenuation inside the material when the static pressure of the gas saturating the material is changed. Asymptotic development of the equivalent fluid model of Johnson-Allard is used for analytical description. The method allows an estimation of three essential parameters of the model: the tortuosity, and the viscous and thermal characteristic lengths. Both characteristic lengths are estimated individually by assuming a given ratio between them. Tests are performed with industrial plastic foams and granular substances (glass beads, sea sand) over a gas pressure range from 0.2 to 6 bars at the frequencies 30-600 kHz. The present technique has a number of distinct advantages over the conventional ultrasonic approach: operation at a single frequency, improved signal-to-noise ratio, possibility of saturation the porous media by different gases. In the case when scattering phenomena occur, the present method permits a separate analysis of scattering losses and viscothermal losses. An analytical description of the method is followed by a presentation of the set-up and the measurement procedure. Experimental results and perspectives are discussed.

Hysteresis in response of nonlinear bistable interface to continuously varying acoustic loading.

In many experimental situations it is an equation of the forced relaxator and not of the forced oscillator that describes a variation in the acoustic field of the interface width (i.e. of a characteristic distance between the surfaces composing the interface). The developed theory predicts that some types of the nonlinear relaxators (depending on the structure of the nonlinear interaction force between the surfaces) exhibit hysteresis in their response to continuous acoustic loading of first increasing and then decreasing amplitude. Nonlinear (unharmonic) variation of the interface width starts at threshold amplitude of the incident sinusoidal acoustic wave, which is higher than threshold amplitude for returning to sinusoidal motion. This dynamic hysteresis (and accompanying it bistability) are possible, in particular, if the dependence of the effective interaction force on the interface width admits two quasi-equilibrium positions of the interface (bistable interface) or if the force itself is hysteretic (hysteretic interface). These theoretical predictions are relevant to some recent experimental observations on the interaction of powerful ultrasonic fields with cracks.

Frequency up-conversion and frequency down-conversion of acoustic waves in damaged materials

Experimental results have been obtained on thermally damaged thick glass plates. A study of nonlinear phenomena with different amounts of damages from the virgin (undamaged) case to a strongly cracked configuration has been performed. The cascade process of harmonic excitation, interaction of a high-frequency wave with a low-frequency one (nonlinear parametric receiving antenna) and demodulation of the amplitude modulated high-frequency wave (nonlinear parametric emitting antenna) have been implemented. One observes a dramatic increase in generation of the second harmonic as well as the demodulation signals versus the pump wave amplitude. A clear correlation exists between these nonlinear signatures and the amount of damages. Preliminary determinations of the coefficient of quadratic nonlinearity have been achieved. The results in the configuration of parametric emitting antenna are believed to be the very first on cracked materials.

Experimental Study of Nonlinear Acoustic Effects in a Granular Medium

Results of a series of experimental studies of nonlinear acoustic effects in a granular medium are presented. Different effects observed in the experiments simultaneously testify that the nonlinearity of granular media is governed by the weakest intergrain contacts. The behavior of the observed dependences suggests that the distribution function of contact forces strongly increases in the range of forces much smaller than the mean force value, which is inaccessible for conventional experimental measuring techniques. For shear waves in a granular medium, the effects of demodulation and second harmonic generation with conversion to longitudinal waves are studied. These effects are caused by the nonlinear dilatancy of the medium, i.e., by the nonlinear law of its volume variation in the shear stress field. With the use of shear waves of different polarizations, the anisotropy of the nonlinearity of the medium is demonstrated. The observation of the cross-modulation effect shows that the nonlinearity-induced modulation components of the probe wave are much more sensitive to weak nonstationary perturbations of the medium, as compared to the linearly propagating fundamental harmonic. The nonlinear effects under study offer promise for diagnostic applications in laboratory measurements and in seismic monitoring systems.

Ultrasonic characterization of plastic foams via measurements with static pressure variations

A method for ultrasonic characterization of plastic foams by changing the static pressure of air that saturates the foam has been proposed. The method is based on high frequency asymptotic expressions of the standard Johnson–Allard equivalent fluid model. It is shown, both experimentally and theoretically, that the real part of squared acoustical refractive index and logarithm of the transmission coefficient depend linearly on the inverse of the square root of applied static pressure. These linear relations provide a simple and convenient way to determine experimentally the constitutive parameters. The method is illustrated with industrial open-cell foams. Advantages, limitations, and perspectives are discussed.

Ultrasonic characterization of the anisotropic behavior of air-saturated porous materials

Abstract This paper provides a comprehensive review of the propagation of ultrasonic waves in anisotropic porous materials. The equivalent fluid model (or Allard-Johnson theory) which is relevant for air-saturated porous media is described. It takes into account viscous and thermal losses occurring during the movement of the fluid within the motionless solid frame. When the skeleton is moving as well, the coupled Biot theory should instead be used. This theory becomes intricate when anisotropy is considered due to a very large number of physical parameters to be determined. A strong formal correspondence between the anisotropic Biot wave and the thermal wave of dynamic thermoelasticity in non-porous media is outlined. Standard ultrasonic methods, generally used at low frequency (i.e. 20–500 kHz) are very effective in order to characterize anisotropy in porous media. Both reflection and transmission configurations have been used. Special attention has been devoted to the measurements of the anisotropic tortuosity, but also to the viscous and thermal characteristics lengths. Finally, some inverse problems related to these measurements are solved and others, which are still open, are presented.

Observation of nonlinear interaction of acoustic waves in granular materials: demodulation process

Abstract Experimental study of the demodulation effect of ultrasonic waves in glass beads are reported. Both impulsive (burst) and continuous regime have been studied for amplitude modulated signals with its carrier frequency of 100 kHz. It is shown that two low frequency acoustical modes corresponding to the modulation frequency (in the range of few kHz) are excited due to the nonlinear processes in the granular medium. The excitation of a first mode propagating mainly through the beads (solid-based mode) and the excitation of a second mode propagating mainly through the air saturating the granular material (fluid-based mode) are observed. Possible physical mechanisms of generation and regimes of propagation in the granular assemblages are discussed.