Multiple Scattering and Visco-Thermal Effects on 2D Phononic Crystal

In this paper, we are interested in the transition between regimes here either visco-thermal or multiple scattering effects dominate for the propagation of acoustic waves through a 2D regular square array of rigid cylinders embedded in air. An extension of the numerical method using Schl\"omilch series is performed in order to account for visco-thermal losses. Comparison withexperimental data and results from classical homogenization theory allows to study the transition between a low frequency limit (where viscous and thermal effects dominate) and a high frequency regime (where multiple scattering effects become predominant). For this particular geometry, a large frequency domain where visco-thermal and multiple scattering effects coexist is found

Ultrasonic Measurements by Means of Continuous Waves in Porous Materials Saturated with Air

The study of porous materials has always been of great interest. Several characterization methods have been developed by means of ultrasonic waves, mainly because of their non-invasive behavior. A typical set-up involves transmission and reflection measurements through the test material using pulse signals. The received echoes are analyzed and compared with analytical models in order to estimate some specific acoustic properties of the sample itself. The main drawback of this approach is the low signal-to-noise ratio recorded when testing highly attenuating materials. This disadvantage is even more pronounced for measurements in air. The present work aims to overcome these limitations, replacing the excitation signals by continuous muti-harmonic waves. These signals have been developed by optimizing the phase of each harmonic, resulting in a low crest factor and consequently in a better signal-to-noise ratio [1,2]. Moreover their frequency content can be easily adapted to the different transducers used during the test. The method has been used to test a foam saturated with air, performing ultrasonic measurements in transmission/reflection, at different angles of incidence. The results show a significant improvement of the measurements, facilitating the estimation of the foam acoustics properties

Characterising poroelastic materials in the ultrasonic range - A Bayesian approach

Acoustic fields scattered by poroelastic materials contain key information about the materials' pore structure and elastic properties. Therefore, such materials are often characterised with inverse methods that use acoustic measurements. However, it has been shown that results from many existing inverse characterisation methods agree poorly. One reason is that inverse methods are typically sensitive to even small uncertainties in a measurement setup, but these uncertainties are difficult to model and hence often neglected. In this paper, we study characterising poroelastic materials in the Bayesian framework, where measurement uncertainties can be taken into account, and which allows us to quantify uncertainty in the results. Using the finite element method, we simulate measurements where ultrasonic waves are incident on a water-saturated poroelastic material in normal and oblique angles. We consider uncertainties in the incidence angle and level of measurement noise, and then explore the solution of the Bayesian inverse problem, the posterior density, with an adaptive parallel tempering Markov chain Monte Carlo algorithm. Results show that both the elastic and pore structure parameters can be feasibly estimated from ultrasonic measurements.Comment: Published in JSV. https://doi.org/10.1016/j.jsv.2019.05.02

Surface waves in granular phononic crystals

The existence of surface elastic waves at a mechanically free surface of granular phononic crystals is studied. The granular phononic crystals are made of spherical particles distributed periodically on a simple cubic lattice. It is assumed that the particles are interacting by means of normal, shear and bending contact rigidities. First, Rayleigh-type surface acoustic waves, where the displacement of the particles takes place in the sagittal plane while the particles possess one rotational and two translational degrees of freedom, are analyzed. Second, shear-horizontal-type waves, where the displacement of the particles is normal to the sagittal plane while the particles possess one translational and two rotational degrees of freedom are studied. The existence of zero-group velocity surface acoustic waves of Rayleigh-type is theoretically predicted and interpreted. A comparison with surface waves predicted by the Cosserat theory is performed, and its limitations are established

Nonlocal dynamics of dissipative phononic fluids

We describe the nonlocal effective properties of a two-dimensional dissipative phononic crystal made by periodic arrays of rigid and motionless cylinders embedded in a viscothermal fluid such as air. The description is based on a nonlocal theory of sound propagation in stationary random fluid/rigid media that was proposed by Lafarge and Nemati [Wave Motion 50, 1016 (2013)WAMOD90165-212510.1016/j.wavemoti.2013.04.007]. This scheme arises from a deep analogy with electromagnetism and a set of physics-based postulates including, particularly, the action-response procedures, whereby the effective density and bulk modulus are determined. Here, we revisit this approach, and clarify further its founding physical principles through presenting it in a unified formulation together with the two-scale asymptotic homogenization theory that is interpreted as the local limit. Strong evidence is provided to show that the validity of the principles and postulates within the nonlocal theory extends to high-frequency bands, well beyond the long-wavelength regime. In particular, we demonstrate that up to the third Brillouin zone including the Bragg scattering, the complex and dispersive phase velocity of the least-attenuated wave in the phononic crystal which is generated by our nonlocal scheme agrees exactly with that reproduced by a direct approach based on the Bloch theorem and multiple scattering method. In high frequencies, the effective wave and its associated parameters are analyzed by treating the phononic crystal as a random medium.United States. Office of Naval Research (N00014-13-1-0631

Propagation ultrasonore dans des gels modélisant les tissus biologiques

Dans le cadre de l'application à la destruction des tumeurs cancéreuses par ultrasons de forte intensité (projet ANR cavitherapus), nos travaux portent sur l'étude de la propagation des ondes ultrasonores dans des gels qui se comportent comme des tissus biologiques. Afin de valider un modèle\ud de propagation acoustique, une étude expérimentale des propriétés acoustiques et thermiques de différents gels est menée

Diffusion multiple en fluide visco-thermique, cas du cristal phononique à deux dimensions

An accurate modelization of acoustic waves propagation and absorption by porous media is of great interest notably due to their numerous applications in industry. During the past years, important progresses lead to acoustic behavior description of porous media in the long wavelength domain (audible frequencies) by means of classical homogenization theory. In this domain, the description is assumed considering important visco-thermal effects which occur inside the medium and so, gives its absorption ability. When the wavelength reduces enough (ultrasonic frequencies), multiple scattering effects appear due to interactions between microstructure and acoustic waves. These effects are not considered by classical models owing to geometrical complexity of porous media at microstructure scale.For this reason, the study is restricted to the case of a two-dimensional periodic lattice containing rigid cylinders (aluminium) surrounded with a visco-thermal fluid (air). This simple geometry, also called "phononic crystal", can exhibits frequency regions where propagation is forbidden (band gaps). This well known phenomenon arises from multiple scattering effects (interferences). Band gaps locations and widths are predicted by many numerical methods taking into account multiple scattering without dissipation. In this work, the sizeable consideration of dissipation effects are discussed. Extensions of multiple scattering models allowing for visco-thermal effects are introduced. On the one hand, these extensions underline dissipation effects impact on propagation at high frequencies. For that, comparisons are performed between transmission coefficients theoretically predicted and experimentally measured on different samples. On the other hand, a numerical study on the transition between a visco-thermal regime (entirely) and multiple scattering effects emergence when wavelength reduces is carried out. This analysis points out the high frequency limit of classical homogenization theory for porous media characterization.Une modélisation précise de la propagation et de l'absorption d'ondes acoustiques dans les matériaux poreux est un enjeu majeur notamment dans la lutte contre les nuisances sonores.Des modèles issus de l'homogénéisation et permettant de décrire le comportement de telsmatériaux ont été développés depuis plusieurs années, qui s'intéressent à leur capacité d'absorption résultant d'effets visco-thermiques importants aux grandes longueurs d'onde (fréquences audio). Lorsque les longueurs d'ondes diminuent suffisamment (fréquences ultrasonores), des effets de diffusion multiple, entre la microstructure du matériau et l'onde acoustique le traversant, interviennent. Ces effets, qui ne sont pas considérés par les modèles classiques, ne sont pas faciles à introduire en raison de la complexité géométrique des matériaux poreux (à l'échelle microscopique).Pour cette raison, nous nous sommes limités à considérer un réseau périodique à deux dimensions constitué de cylindres rigides (aluminium) entourés d'un fluide dissipatif (air). Cette géométrie simple, aussi appelée "cristal phononique", présente des domaines fréquentiels dans lesquels aucune onde ne peut se propager (bandes interdites). Ce phénomène, connu et largement étudié, résulte d'effets de diffusion multiple (interférences). Les positions et les largeurs des bandes interdites sont prédites par de nombreuses méthodes de calcul tenant compte des effets de diffusion multiple en fluide non dissipatif. Dans ce travail, le problème de l'importance, non négligeable, des effets dissipatifs est soulevé. Des extensions permettant d'intégrer les effets visco-thermiques dans un modèle de diffusion multiple sont proposées. Elles permettent dans un premier temps, de mettre en évidence l'influence de ces effets dissipatifs sur la propagation dans un régime hautes fréquences. Pour cela, une comparaison entre les coefficients de transmission prédits et ceux, obtenus expérimentalement sur différents échantillons est réalisée. Dans un second temps, une étude numérique permet d'analyser la transition entre un domaine fréquentiel dominé par des effets visco-thermiques (exclusivement) et l'émergence des effets de diffusion multiple lorsque la fréquence augmente. Cette analyse montre notamment la limite de validité des modèles classiques issus de la théorie d'homogénéisation, pour la caractérisation acoustique des matériaux poreux

Diffusion multiple en fluide visco-thermique, cas du cristal phononique à deux dimensions

Une modélisation précise de la propagation et de l'absorption d'ondes acoustiques dans les matériaux poreux est un enjeu majeur notamment dans la lutte contre les nuisances sonores. Des modèles issus de l"homogénéisation et permettant de décrire le comportement de tels matériaux ont été développés depuis plusieurs années, qui s'intéressent à leur capacité d'absorption résultant d'effets visco-thermiques importants aux grandes longueurs d'onde (fréquences audio). Lorsque les longueurs d'ondes diminuent suffisamment (fréquences ultrasonores), des effets de diffusion multiple, entre la microstructure du matériau et l'onde acoustique le traversant, interviennent. Ces effets, qui ne sont pas considérés par les modèles classiques, ne sont pas faciles à introduire en raison de la complexité géométrique des matériaux poreux (à l'échelle microscopique). Pour cette raison, nous nous sommes limités à considérer un réseau périodique à deux dimensions constitué de cylindres rigides (aluminium) entourés d'un fluide dissipatif (air). Cette géométrie simple, aussi appelée cristal phononique, présente des domaines fréquentiels dans lesquels aucune onde ne peut se propager (bandes interdites). Ce phénomène, connu et largement étudié, résulte d'effets de diffusion multiple (interférences). Les positions et les largeurs des bandes interdites sont prédites par de nombreuses méthodes de calcul tenant compte des effets de diffusion multiple en fluide non dissipatif. Dans ce travail, le problème de l'importance, non négligeable, des effets dissipatifs est soulevé. Des extensions permettant d'intégrer les effets visco-thermiques dans un modèle de diffusion multiple sont proposées. Elles permettent dans un premier temps, de mettre en évidence l'influence de ces effets dissipatifs sur la propagation dans un régime hautes fréquences. Pour cela, une comparaison entre les coefficients de transmission prédits et ceux, obtenus expérimentalement sur différents échantillons est réalisée. Dans un second temps, une étude numérique permet d'analyser la transition entre un domaine fréquentiel dominé par des effets visco-thermiques (exclusivement) et l'émergence des effets de diffusion multiple lorsque la fréquence augmente. Cette analyse montre notamment la limite de validité des modèles classiques issus de la théorie d'homogénéisation, pour la caractérisation acoustique des matériaux poreux.An accurate modelization of acoustic waves propagation and absorption by porous media is of great interest notably due to their numerous applications in industry. During the past years, important progresses lead to acoustic behavior description of porous media in the long wavelength domain (audible frequencies) by means of classical homogenization theory. In this domain, the description is assumed considering important visco-thermal effects which occur inside the medium and so, gives its absorption ability. When the wavelength reduces enough (ultrasonic frequencies), multiple scattering effects appear due to interactions between microstructure and acoustic waves. These effects are not considered by classical models owing to geometrical complexity of porous media at microstructure scale. For this reason, the study is restricted to the case of a two-dimensional periodic lattice containing rigid cylinders (aluminium) surrounded with a visco-thermal fluid (air). This simple geometry, also called phononic crystal, can exhibits frequency regions where propagation is forbidden (band gaps). This well known phenomenon arises from multiple scattering effects (interferences). Band gaps locations and widths are predicted by many numerical methods taking into account multiple scattering without dissipation. In this work, the sizeable consideration of dissipation effects are discussed. Extensions of multiple scattering models allowing for visco-thermal effects are introduced. On the one hand, these extensions underline dissipation effects impact on propagation at high frequencies. For that, comparisons are performed between transmission coefficients theoretically predicted and experimentally measured on different samples. On the other hand, a numerical study on the transition between a visco-thermal regime (entirely) and multiple scattering effects emergence when wavelength reduces is carried out. This analysis points out the high frequency limit of classical homogenization theory for porous media characterization.LE MANS-BU Sciences (721812109) / SudocSudocFranceF

Nonlocal macroscopic theory of sound propagation in rigid-framed porous materials

International audienceMacroscopic acoustic properties of rigid-framed fluid-saturated porous materials are generally well described by the existing Equivalent-fluid macroscopic theory. This (local) theory, however, is incomplete. Indeed, it describes temporal dispersion but not spatial dispersion. In particular, it is in error when the wavelengths reduce so as to become comparable to the size of an elementary representative volume. This may always be the case at high enough frequencies. This may also be the case at lower frequencies, near resonances, when the material contains structured elements such as Helmholtz resonators. We propose here a new (nonlocal) macroscopic Equivalent-fluid theory that is intended to describe both temporal and spatial dispersion. As such, this theory is expected to be more generally applicable than the conventional one. Here, we solve it by the method of finite elements and compute the wavenumber of the least attenuated mode for a 2D porous medium made of a viscothermal fluid saturating a square array of identical cylindrical-circular rigid solid inclusions. The same least attenuated mode wavenumber is independently computed using a direct multiple scattering technique. Excellent agreement betweeen the two is obtained, validating our proposed new nonlocal Equivalent-fluid theory. Finally, this new theory is illustrated for the case of materials with Helmholtz resonators