Nonlinear effects for coda-type elastic waves in stressed granular media

Experimental results and their interpretations are presented on the nonlinear acoustic effects of multiple scattered elastic waves in unconsolidated granular media. Short wave packets with a central frequency higher than the so-called cut-off frequency of the medium are emitted at one side of the statically stressed slab of glass beads and received at the other side after multiple scattering and nonlinear interactions. Typical signals are strongly distorted compared to their initially radiated shape both due to nonlinearity and scattering. It is shown that acoustic waves with a deformation amplitude much lower than the mean static deformation of the contacts in the medium can modify the elastic properties of the medium, especially for the weak contact skeleton part. This addresses the problem of reproducibility of granular structures during and after acoustic excitation, which is necessary to understand in the non destructive testing of the elastic properties of granular media by acoustic methods. Coda signal analysis is shown to be a powerful time-resolved tool to monitor slight modifications in the elastic response of an unconsolidated granular structure

Crista acustica in insect ears modeled by an inhomogenous granular chain

International audienceInsect ears are found on the thorax (in some Hemiptera), the abdomen (in grasshoppers, cicadas, some moths), or the front tibia (in crickets, katydids). Crista acustica -also named Siebold's organs- is the sensory organ linked to tympanum when located in forelegs. It is a collection of individually-tuned scolopidia -the most fundamental unit of mechanoreceptor organs in insects- that can discriminate frequencies. A remarkable geometrical property of the arrangement of the soma or cell body of hearing sensing cells -the inner hair cells in the cochlea of mammals and human beings and the scolopidia in the hearing organs of invertebrates- has not yet been explored. We will focus on the arrangement of the cells of the scolopidia of crista acustica in the fore tibia of certain Orthoptera (eg, grasshoppers, crickets, katydids). It consists of a collection of perfectly aligned sensory cells which forms a crest on top of a hollow tracheal tube behind the tympanum. Such a crest can interestingly be modeled as an inhomogenous granular chain linked to a substrate. We will show that the dynamical response in both time and frequency domains of this neurally tunable chain also strongly depends on its anatomical pre-arrangement

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

Modulation instability in nonlinear flexible mechanical metamaterials

In this paper, we study modulation instabilities (MI) in a one-dimensional chain configuration of a flexible mechanical metamaterial (flexMM). Using the lumped element approach, flexMMs can be modeled by a coupled system of discrete equations for the longitudinal displacements and rotations of the rigid mass units. In the long wavelength regime, and applying the multiple-scales method we derive an effective nonlinear Schr\"odinger equation for slowly varying envelope rotational waves. We are then able to establish a map of the occurrence of MI to the parameters of the metamaterials and the wavenumbers. We also highlight the key role of the rotation-displacement coupling between the two degrees of freedom in the manifestation of MI. All analytical findings are confirmed by numerical simulations of the full discrete and nonlinear lump problem. These results provide interesting design guidelines for nonlinear metamaterials offering either stability to high amplitude waves, or conversely being good candidates to observe instabilities.Comment: 12 pages, 9 figure

Identification of avalanche precursors by acoustic probing in the bulk of tilted granular layers

International audienceUnderstanding the precursors of granular avalanches is important for the prediction of critical events. As part of the dynamics leading to the avalanche, precursors are identified as collective motions of grains on the free surface. When a granular pile is tilted at a constant angular velocity, precursors appear quasi-periodically. In this paper we simultaneously caracterize precursors on the free surface with an optical method and in the bulk with acoustic methods (nonlinear and linear). Surprisingly, the use on nonlinear acoustic method is not necessary to probe rearrangements in the bulk of the granular material. A linear method can also be used provided that the frequency region is the one where the acoustic propagation is sensitive to the solid skeleton formed by the bead-contact network. Our experiments conducted with monodisperse glass beads show that their surface features are by far the most important for the precursor propreties. Our results allow to probe with a few millisecond time resolution (less than 10−2 degree of inclination) the relaxation phenomena associated to each precursor event. Interpretations of different precursors and different experiments provide an interesting train of thought for the understanding of destabilization mechanisms in granular systems

Monitoring of a Large Cracked Concrete Sample with Non-Linear Mixing of Ultrasonic Coda Waves

International audienceA high precision can be achieved with ultrasonic coda waves to monitor the mechanical properties of concrete material (~10-5 in relative). This high sensitivity can be used to detect damage initiation and to closely follow concrete mechanical properties evolution with time. This advantage is counterbalance by the influence of environmental conditions making reproducibility of any experiment in concrete a challenging issue especially when in situ measurements are performed. Indeed thermal and water gradients present in the thickness of the structures (several decimetres) cannot be controlled and must be compensated. In this paper a protocol to remove environmental bias is proposed. Furthermore, to follow the apparition of a tensile crack in a metric size structure, non-linear mixing of coda wave via frequency-swept pump waves is tested. It is shown that, when the crack is closed (by pre-stressing cables), it is still possible to detect its presence. The non-linearity of the cracked zone remains at a high level, comparable to the case when the crack was open

Revealing sub-{\mu}m inhomogeneities and {\mu}m-scale texture in H2O ice at Megabar pressures via sound velocity measurements by time-domain Brillouin scattering

Time-domain Brillouin scattering technique, also known as picosecond ultrasonic interferometry, which provides opportunity to monitor propagation of nanometers to sub-micrometers length coherent acoustic pulses in the samples of sub-micrometers to tens of micrometers dimensions, was applied to depth-profiling of polycrystalline aggregate of ice compressed in a diamond anvil cell to Megabar pressures. The technique allowed examination of characteristic dimensions of elastic inhomogeneities and texturing of polycrystalline ice in the direction normal to the diamond anvil surfaces with sub-micrometer spatial resolution via time-resolved measurements of variations in the propagation velocity of the acoustic pulse traveling in the compressed sample. The achieved two-dimensional imaging of the polycrystalline ice aggregate in-depth and in one of the lateral directions indicates the feasibility of three-dimensional imaging and quantitative characterization of acoustical, optical and acousto-optical properties of transparent polycrystalline aggregates in diamond anvil cell with tens of nanometers in-depth resolution and lateral spatial resolution controlled by pump laser pulses focusing.Comment: 32 pages, 5 figure

Granular Graphene: direct observation of zigzag and armchair edge waves

We propose a mechanical granular graphene obtained by replacing the carbon atoms with macroscopic spherical stainless steel beads in contact. The experimental measured dispersion relation is presented, in conjunction with evidence of the Dirac points. In addition, wave propagation along the zigzag and a robust turning effect of edge waves from the zigzag to the armchair boundary is experimentally revealed, even in the absence of a full band gap for bulk modes. Our work shows that mechanical granular graphene can serve as an excellent experimental platform to study novel Dirac, topological and nonlinear wave phenomena