Acoustic identification of a poroelastic cylinder

We show how to cope with the acoustic identification of poroelastic materials when the specimen is in the form of a cylinder. We apply our formulation, based on the Biot model, approximated by the equivalent elastic solid model, to a long bone-like or borehole sample specimen probed by low frequency sound

Ultrasonic propagation of reflected waves in cancellous bone: Application of Biot theory.

International audienceAn ultrasonic propagation in cancellous bone is considered using the Biot theory modified by the Johnson et al. Numerical simulations of reflected waves in the time domain are worked out by varying the modified Biot parameters. The sensitivity of different mechanical parameters : Young modulus and the Poisson ratio of the skeletal frame and physical parameters , porosity , tortuosity and viscous characteristic length are studied showing their effect on the reflected ultrasonic waves of the bone sample. The sensitivity of the modified Biot parameters with respect to the reflected wave depends strongly on the coupling between the solid and fluid phases of the cancellous bone. We show from these simulations that some parameters such as porosity and tortuosity play an important role on reflected wave ; the remaining parameters have low sensitivity compared with the porosity and tortuosity. Experimental results for reflected waves by human cancellous bone samples are given and compared with theoretical predictions

Determination of the flow resistivity and thickness of porous materials with rigid frames via transmitted waves at Darcy's regime

International audienceAn acoustic method is proposed for measuring the flow resistivity and the thickness of air-saturated porous materials. The conventional methods [14, 16, 17] for the measurement of the flow resistivity (or the viscous permeability) require the prior knowledge of the porosity. The method presented in this work is based on a temporal model of the direct problem in which a simplified expression (independent of frequency and porosity) of the transmission coefficient at the Darcy’s regime (low frequency range) is established, this expression depends only on the viscous permeability (or the flow resistivity) and the thickness of a porous sample. The inverse problem is solved based on the leastsquare numerical method using experimental transmitted wave in time domain. Tests are performed using two samples of different thicknesses to same industrial plastic foam, thereby enabling the determination the thickness and flow resistivity of foam plastic. This method has the advantage of being simple, fast and efficient

Fabrication of Capacitive Acoustic Resonators Combining 3D Printing and 2D Inkjet Printing Techniques

International audienceA capacitive acoustic resonator developed by combining three-dimensional (3D) printing and two-dimensional (2D) printed electronics technique is described. During this work, a patterned bottom structure with rigid backplate and cavity is fabricated directly by a 3D printing method, and then a direct write inkjet printing technique has been employed to print a silver conductive layer. A novel approach has been used to fabricate a diaphragm for the acoustic sensor as well, where the conductive layer is inkjet-printed on a pre-stressed thin organic film. After assembly, the resulting structure contains an electrically conductive diaphragm positioned at a distance from a fixed bottom electrode separated by a spacer. Measurements confirm that the transducer acts as capacitor. The deflection of the diaphragm in response to the incident acoustic single was observed by a laser Doppler vibrometer and the corresponding change of capacitance has been calculated, which is then compared with the numerical result. Observation confirms that the device performs as a resonator and provides adequate sensitivity and selectivity at its resonance frequency

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

Inverse estimation of the permeability of porous materials using experimental data via reflected waves at low frequencies

International audienceAn acoustic reflectivity method is proposed for measuring the permeability or flow resistivity of air-saturated porous materials. In this method, a simplified expression of the reflection coefficient is derived in the Darcy's regime (low frequency range), which does not depend on frequency and porosity. Numerical simulations show that the reflection coefficient of a porous material can be approximated by its simplified expression obtained from its Taylor development to the first order. This approximation is good especially for resistive materials (of low permeability) and for the lower frequencies. The permeability is reconstructed by solving the inverse problem using waves reflected by plastic foam samples, at different frequency bandwidths in the Darcy regime. The proposed method has the advantage of being simple compared to the conventional methods that use experimental reflected data, and is complementary to the transmissivity method which is more adapted to low resistive materials (high permeability)

Measuring static viscous permeability of porous absorbing materials

International audienceConventional acoustical methods for measuring the permeability or flow resistivity of a porous material require a priori estimation of the porosity. In this work, an acoustical method is presented in which a simplified expression (independent of both the frequency and porosity) for the transmitted waves at the Darcy’s regime (low frequency range) is derived, and used for the inverse determination of both the viscous static permeability (or flow resistivity) and the thickness of air-saturated porous materials. The inverse problem is solved based on the least-square numerical method using transmitted waves in time domain. Tests are performed using industrial plastic foams. Experimental and numerical validation results of this method are presented, which show theadvantage of measuring the viscous permeability and thickness of a porous slab, without the required prior knowledge of the porosity, but by simply using the transmitted waves

Non-ambiguous recovery of Biot poroelastic parameters of cellular panels using ultrasonic waves

a b s t r a c t The inverse problem of the recovery of the poroelastic parameters of open-cell soft plastic foam panels is solved by employing transmitted ultrasonic waves (USW) and the Biot-Johnson-Koplik-Champoux-Allard (BJKCA) model. It is shown by constructing the objective functional given by the total square of the difference between predictions from the BJKCA interaction model and experimental data obtained with transmitted USW that the inverse problem is ill-posed, since the functional exhibits several local minima and maxima. In order to solve this problem, which is beyond the capability of most off-the-shelf iterative nonlinear least squares optimization algorithms (such as the Levenberg Marquadt or Nelder-Mead simplex methods), simple strategies are developed. The recovered acoustic parameters are compared with those obtained using simpler interaction models and a method employing asymptotic phase velocity of the transmitted USW. The retrieved elastic moduli are validated by solving an inverse vibration spectroscopy problem with data obtained from beam-like specimens cut from the panels using an equivalent solid elastodynamic model as estimator. The phase velocities are reconstructed using computed, measured resonance frequencies and a time-frequency decomposition of transient waves induced in the beam specimen. These confirm that the elastic parameters recovered using vibration are valid over the frequency range of study

Recovery of airflow resistivity of poroelastic beams submitted to transient mechanical stress

International audienceThe airflow resistivities of air-saturated poroelastic slender beams submitted to transient mechanical stress are recovered using fluid and solid borne compressional mode phase velocity expressions drawn from a modified Biot theory. A point where the two dilatational modes intersect and their phase velocities equal, is first sought. This point also corresponds to the Biot transitional frequency indicating the frequency at which the solid and the pore fluid start disassociating due to the weakening of the viscous forces by the thinning of the viscous boundary layer in the pores. A bilinear time-frequency (TF) distribution is used to represent on the time-frequency plane, the captured transient mechanical stress waves from which the point of intersection/separation of the two modes is located. The projection of the Eigenfrequencies obtained from a simple 3D finite element modeling of the thin poroelastic beam, on a (TF) diagram, facilitates the identification of the modes. The transition frequencies for the poroelastic beams thus retrieved are verified through the use of variable frequency, single cycle sine wave bursts. The anisotropy of the foams are also revealed by analyzing the transient responses of the poroelastic beam specimens cut from the same panel but in two perpendicular directions in orientation to each other