Transient Acoustic Wave Propagation in Porous Media

International audienceTransient Acoustic Wave Propagation in Porous Medi

Generalized equation for transient-wave propagation in continuous inhomogeneous rigid-frame porous materials at low frequencies

International audienceThis paper provides a temporal model for the propagation of transient acoustic waves in continuous inhomogeneous isotropic porous material having a rigid frame at low frequency range. A temporal equivalent fluid model in which the acoustic wave propagates only in the fluid saturating the material, is considered. In this model, the inertial effects are described by the inhomogeneous inertial factor [A.N. Norris., J. Wave Mat. Interact. 1 365 (1986)]. The viscous and thermal losses of the medium are described by two inhomogeneous susceptibility kernels which depend on the viscous and thermal permeabilities . The medium is one dimensional and its physical parameters (porosity, inertial factor, viscous and thermal permeabilities) are depth dependent. A generalized wave propagation equation in continuous inhomogeneous material is established and discussed

Ultrasound Measuring of Porosity in Porous Materials

This chapter provides a temporal method for measuring the porosity and the tortuosity of air-saturated porous materials using experimental reflected waves. The direct problem of reflection and transmission of acoustic waves by a slab of porous material is studied. The equivalent fluid model has considered in which the acoustic wave propagates only in the pore-space. Since the acoustic damping in air-saturated porous materials is important, only the reflected waves by the first interface are taken into account, and the multiple reflections are neglected. The study of the sensitivity analysis shows that porosity is much more sensitive than tortuosity to reflection, especially when the incident angle is less than its critical value, at which the reflection coefficient vanishes. The inverse problem is solved using experimental data at a different incidence angle in reflection. Some advantages and perspectives of this method are discussed

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

Propagation acoustique dans les milieux poreux hétérogènes

La modélisation temporelle de la propagation acoustique/élastique dans un milieu poreux à structure rigide (modèle du fluide équivalent) et souple (modèle de Biot) a été étudiée. Le concept de dérivées fractionnaires a été introduit, les fonctions de Green temporelles ainsi que les opérateurs de réflexion et de transmission ont été obtenues. Les problèmes directs et inverses ont été résolus en utilisant des données expérimentables réfléchies et/ou transmises. Une caractérisation complète des milieux poreux a été ainsi effectuée dans le régime asymptotique correspondant aux hautes fréquences et le régime visqueux correspondant aux basses fréquences. Une application expérimentale aux mousses plastiques et aux tissus osseux spongieux a été traitée. Une étude détaillée de la causalité des modèles a été faite suite à un doute dans la littérature concernant l'utilisation de modèles couramment utilisés (Johnson-Allard), les relations de Kramers-Kronig ont été vérifiées dans le domaine des hautes et basses fréquences. La causalité des modèles a été aussi montrée dans le domaine temporel en utilisant les relations généralisées de Hilbert et la théorie des distributions tempérées. Les problèmes ouverts concernant la propagation dans les milieux poreux macroscopiquement inhomogènes ont été soulevés, en évoquant quelques pistes comme la méthodes de séparation d'ondes (Waves splitting) et l'établissement des équations de propagations dans le régime temporel

AN APPROACH TO DIRECT AND INVERSE TIME-DOMAIN SCATTERING OF ACOUSTIC WAVES FROM RIGID POROUS MATERIALS BY A FRACTIONAL CALCULUS BASED METHOD

In this paper direct and inverse time-domain scattering of ultrasonic pulses from a rigid, homogeneous and isotropic porous medium are investigated. The Green's function of the wave propagation of a transient field in one dimensional porous media is established. The solution of direct and inverse problems are given in the time domain by using the concept of fractional derivatives. The viscous and thermal losses of the medium are described by the Johnson and Allard models [1] [2] modified to be usable in the time domain. Experimental and numerical results are given as a validation of our model

Amplitude-modulated acoustic radiation force experienced by elastic and viscoelastic spherical shells in progressive waves

The dynamic acoustic radiation force resulting from a dual-frequency beam incident on spherical shells immersed in an inviscid fluid is examined theoretically in relation to their thickness and the contents of their interior hollow regions. The theory is modified to include a hysteresis type of absorption inside the shells’ material. The results of numerical calculations are presented for stainless steel and absorbing lucite (PolyMethyMethacrylAte) shells with the hollow region filled with water or air. Significant differences occur when the interior fluid inside the hollow region is changed from water to air. It is shown that the dynamic radiation force function Yd deviates from the static radiation force function Yp when the modulation size parameter δx = ∣x2 − x1∣ (x1 = k1a, x2 = k2a, k1 and k2 are the wave vectors of the incident ultrasound waves, and a is the outer radius of the shell) starts to exceed the width of the resonance peaks in the Yp curves

Transient wave propagation in inhomogeneous porous materials : application of fractional derivatives.

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Modélisation temporelle de la propagation acoustique dans un matériau poreux.

ISBN13 : 978-2-7462-1449-

Recovery of Biot's transition frequency of air-saturated poroelastic media using vibroacoustic spectroscopy

International audienceThe transition frequency marks the passage from low-frequency viscosity dominated flow to high-frequency inertia dominated one in porous media. It was one of the principal characteristics predicted by Biot's theory. The transition frequency has been a theoretical concept for which only theoretical expressions have been developed in recent years. A vibroacoustic spectroscopy experimental method to recover the characteristic frequency (fC) and for gaining insight into the frequency response of fluid-saturated porous materials has been developed. Long thin air-saturated porous rods solicited mechanically are employed for the experiment. Changes in the fluid flow profile with excitation frequency results in relative motion between the skeleton and the saturating-fluid. This enhances the frictional viscous forces, which, in turn, increases damping of the skeletal motion. These transitions are signaled by observable cues in the acquired laser-vibrometry spectrum of the rods' longitudinal vibration mode patterns. The resonance peaks exhibit sudden attenuation (increase in damping) and are interrupted at the transition frequencies evoking a change of propagation medium. These patterns are compared with those of two plains, single phase material (viscoelastic) rods whose modes stand out as regularly spaced moderately damped peaks