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 the Shape and Location of a Rigid Cylindrical Body from Experimental Scattered Acoustic Field Data

International audienceThe standard method for solving a boundary-identification inverse problem [2] is to generate a cost functional expressing the discrepancy between the actual (simulated or measured) data and what the estimator predicts the scattered field to be for a set of trial location and boundary parameters of the body; the sought-for parameters are then chosen to be those trial parameters which give rise to the minimum of the cost functional. A major difficulty with this approach, rarely alluded-to in previous studies, is that the cost functional often exhibits not one, but many minima so that the procedure cannot provide a unique solution. We exhibit this fact empirically both for real and simulated data estimated by the ICBA, and observe that the distribution of minima follows a regular pattern, which fact suggests that there exists a simple law relating the position of the minima to some or all of the sought-for parameters

The direct and inverse problems of an air-saturated porous cylinder submitted to acoustic radiation

International audienceGas-saturated porous skeleton materials such as geomaterials, polymeric and metallic foams, or biomaterials are fundamental in a diverse range of applications, from structural materials to energy technologies. Most polymeric foams are used for noise control applications and knowledge of the manner in which the energy of sound waves is dissipated with respect to the intrinsic acoustic properties is important for the design of sound packages. Foams are often employed in the audible, low frequency range where modeling and measurement techniques for the recovery of physical parameters responsible for energy loss are still few. Accurate acoustic methods of characterization of porous media are based on the measurement of the transmitted and/or reflected acoustic waves by platelike specimens at ultrasonic frequencies. In this study we develop an acoustic method for the recovery of the material parameters of a rigid-frame, air-saturated polymeric foam cylinder. A dispersion relation for sound wave propagation in the porous medium is derived from the propagation equations and a model solution is sought based on plane-wave decomposition using orthogonal cylindrical functions. The explicit analytical solution equation of the scattered field shows that it is also dependent on the intrinsic acoustic parameters of the porous cylinder, namely, porosity, tortuosity, and flow resistivity (permeability). The inverse problem of the recovery of the flow resistivity and porosity is solved by seeking the minima of the objective functions consisting of the sum of squared residuals of the differences between the experimental and theoretical scattered field data

Killer whales (Orcinus orca) feeding on schooling herring (Clupea harengus) using underwater tail-slaps: kinematic analyses of field observations

Killer whales (Orcinus orca) feeding on herring (Clupea harengus) in a fjord in northern Norway were observed using underwater video. The whales cooperatively herded herring into tight schools close to the surface. During herding and feeding, killer whales swam around and under a school of herring, periodically lunging at it and stunning the herring by slapping them with the underside of their flukes while completely submerged. The kinematics of tail-slapping were analysed in detail. Tail-slaps were made up of a biphasic behaviour consisting of two phases with opposite angles of attack, a preparatory phase (negative angles of attack) and a slap phase (positive angles of attack). During the slap phase, the mean maximum angle of attack of the flukes was 47 degrees. The maximum speed of the flukes, measured at the notch, increased with whale length (L(w)) and was 2.2 L(w)s(−)(1), while the maximum acceleration of the flukes was size-independent and was 48 m s(−)(2). When killer whales slapped the herring successfully, disoriented herring appeared on the video at approximately the time of maximum fluke velocity, in synchrony with a loud noise. This noise was not heard when the tail-slaps ‘missed’ the target, suggesting that the herring were stunned by physical contact. Killer whales then ate the stunned herring one by one. Of the tail-slaps observed, 61 % were preceded by lunges into the school. We suggest that lunging was aimed at directing the school rather than at capturing the herring, since it occurred at a relatively low speed and there were no observations of the killer whales attempting to capture the herring during lunging behaviour. Given the high performance of the tail-slaps in terms of speed and acceleration, we suggest that tail-slapping by killer whales is a more efficient strategy of prey capture than whole-body attacks, since acceleration and manoeuvrability are likely to be poor in such large vertebrates.</jats:p

Addressing the ill-posedness of multi-layer porous media characterization in impedance tubes through the addition of air gaps behind the sample: numerical validation

International audienceThis paper is concerned with plane wave propagation in multi-layer assemblies of rigid isotropic porous media inside impedance tubes. The focus is placed on the inverse problem, i.e., the retrieval of the intrinsic properties defining the pore micro-structure of each layer: the porosity, the pore mean size and the pore size standard deviation. Each layer is considered isotropic. Such an inverse problem can be ill-posed due to the non-uniqueness of the solution. The technique explored in this work is the consideration of additional acoustic observations, where air gaps are placed behind the multi-layer assembly. The aptitude of this strategy to overcome the ill-posedness of the inverse problem is evaluated on numerical synthetic data, on assemblies made of three layers. For a given fixed amount of input data, inverse problems including different observations with air gaps can yield more accurate results, removing the ill-posedness

Addressing the ill-posedness of multi-layer porous media characterization in impedance tubes through the addition of air gaps behind the sample: numerical validation

International audienceThis paper is concerned with plane wave propagation in multi-layer assemblies of rigid isotropic porous media inside impedance tubes. The focus is placed on the inverse problem, i.e., the retrieval of the intrinsic properties defining the pore micro-structure of each layer: the porosity, the pore mean size and the pore size standard deviation. Each layer is considered isotropic. Such an inverse problem can be ill-posed due to the non-uniqueness of the solution. The technique explored in this work is the consideration of additional acoustic observations, where air gaps are placed behind the multi-layer assembly. The aptitude of this strategy to overcome the ill-posedness of the inverse problem is evaluated on numerical synthetic data, on assemblies made of three layers. For a given fixed amount of input data, inverse problems including different observations with air gaps can yield more accurate results, removing the ill-posedness