Stéphane Job

How Hertzian Solitary Waves Interact with Boundaries in a 1D Granular Medium

We perform measurements, numerical simulations, and quantitative comparisons with available theory on solitary wave propagation in a linear chain of beads without static preconstraint. By designing a nonintrusive force sensor to measure the impulse as it propagates along the chain, we study the solitary wave reflection at a wall. We show that the main features of solitary wave reflection depend on wall mechanical properties. Since previous studies on solitary waves have been performed at walls without these considerations, our experiment provides a more reliable tool to characterize solitary wave propagation. We find, for the first time, precise quantitative agreements.

Solitary wave trains in granular chains: experiments, theory and simulations

The features of solitary waves observed in horizontal monodisperse chain of barely touching beads not only depend on geometrical and material properties of the beads but also on the initial perturbation provided at the edge of the chain. An impact of a large striker on a monodisperse chain, and similarly a sharp decrease of bead radius in a stepped chain, generates a solitary wave train containing many single solitary waves ordered by decreasing amplitudes. We find, by simple analytical arguments, that the unloading of compression force at the chain edge has a nearly exponential decrease. The characteristic time is mainly a function involving the grains’ masses and the striker mass. Numerical calculations and experiments corroborate these findings.

Experimental evidence of shock mitigation in a Hertzian tapered chain.

We present an experimental study of the mechanical impulse propagation through a horizontal alignment of elastic spheres of progressively decreasing diameter phi(n): namely, a tapered chain. Experimentally, the diameters of spheres which interact via the Hertz potential are selected to keep as close as possible to an exponential decrease, phi(n+1) = (1-q)phi(n), where the experimental tapering factor is either q(1) approximately equal to 5.60% or q(2) approximately equal to 8.27%. In agreement with recent numerical results, an impulse initiated in a monodisperse chain (a chain of identical beads) propagates without shape changes and progressively transfers its energy and momentum to a propagating tail when it further travels in a tapered chain. As a result, the front pulse of this wave decreases in amplitude and accelerates. Both effects are satisfactorily described by the hard-sphere approximation, and basically, the shock mitigation is due to partial transmissions, from one bead to the next, of momentum and energy of the front pulse. In addition when small dissipation is included, better agreement with experiments is found. A close analysis of the loading part of the experimental pulses demonstrates that the front wave adopts a self-similar solution as it propagates in the tapered chain. Finally, our results corroborate the capability of these chains to thermalize propagating impulses and thereby act as shock absorbing devices.

Wave localization in strongly nonlinear Hertzian chains with mass defect

We report observations of mechanical energy localization in a strongly nonlinear discrete lattice. The experimental setup we consider is a one-dimensional nonloaded horizontal chain of identical spheres interacting via the nonlinear Hertz potential which contains a mass defect. Our experiments show that the interaction of a solitary wave with a light intruder excites a nonlinear localized mode. In agreement with dimensional analysis, we find that the frequency of localized oscillations exceeds the incident wave frequency spectrum and nonlinearly depends on incident wave strength and on mass and size of the intruder. The absence of tensile stress between grains allows some gaps to open, which in turn induces a significant enhancement of the amplitude of oscillations. We performed numerical simulations that precisely describe our observations without any adjusting parameters.

Experimental evidence of solitary wave interaction in Hertzian chains

We study experimentally the interaction between two solitary waves that approach one another in a linear chain of spheres interacting via the Hertz potential. When these counterpropagating waves collide, they cross each other and a phase shift in respect to the noninteracting waves is introduced as a result of the nonlinear interaction potential. This observation is well reproduced by our numerical simulations and is shown to be independent of viscoelastic dissipation at the bead contact. In addition, when the collision of equal amplitude and synchronized counterpropagating waves takes place, we observe that two secondary solitary waves emerge from the interacting region. The amplitude of the secondary solitary waves is proportional to the amplitude of incident waves. However, secondary solitary waves are stronger when the collision occurs at the middle contact in chains with an even number of beads. Although numerical simulations correctly predict the existence of these waves, experiments show that their respective amplitudes are significantly larger than predicted. We attribute this discrepancy to the rolling friction at the bead contact during solitary wave propagation.

Nonlinear waves in dry and wet Hertzian granular chains

A one-dimensional dry granular medium, a chain of beads which interact via the nonlinear Hertz potential, exhibits strongly nonlinear behaviors. When such an alignment further contains some fluid in the interstices between grains, it may exhibit new interesting features. We report some recent experiments, analysis and numerical simulations concerning nonlinear wave propagation in dry and wet chains of spheres. We consider first a monodisperse chain as a reference case. We then analyze how the pulse characteristics are modified in the presence of an interstitial viscous fluid. The fluid not only induces dissipation but also strongly affect the intergrain stiffness: in a wet chain, wave speed is enhanced and pulses are shorter. Simple experiments performed with a single sphere colliding a wall covered by a thin film of fluid confirm these observations. We demonstrate that even a very small amount of fluid can overcome the Hertzian potential and is responsible for a large increase of contact stiffness. Possible mechanisms for wet contact hardening are related to large fluid shear rate during fast elastohydrodynamic collision between grains.

Porogranular materials composed of elastic Helmholtz resonators for acoustic wave absorption

A theoretical and experimental study of the acoustic absorption of granular porous media made of non-cohesive piles of spherical shells is presented. These shells are either rigid or elastic, possibly drilled with a neck (Helmholtz resonators), and either porous or impervious. A description is given of acoustic propagation through these media using the effective medium models proposed by Johnson (rigid particles) and Boutin (rigid Helmholtz resonators), which are extended to the configurations studied in this work. A solution is given for the local equation of elasticity of a shell coupled to the viscous flow of air through the neck and the micropores. The models and the simulations are compared to absorption spectra measured in reflection in an impedance tube. The effective medium models and the measurements show excellent agreement for configurations made of rigid particles and rigid Helmholtz resonators that induce an additional peak of absorption at low frequency. A shift of the Helmholtz resonance toward low frequencies, due to the softness of the shells is revealed by the experiments for elastic shells made of soft elastomer and is well reproduced by the simulations. It is shown that microporous shells enhance and broaden acoustic absorption compared to stiff or elastic resonators.

Diffusive transport and Anderson localization of ultrasonic waves in strongly scattering inhomogeneous media

In inhomogeneous media with constituents having very different acoustic properties, very strong multiple scattering of ultrasonic waves can occur, especially when the wavelength is comparable with the length scales over which the constituent properties vary. Such strong multiple scattering can lead to a long “coda” that dominates the observable behaviour in pulsed experiments, and can dwarf the ballistic pulse that travels coherently through the medium. In many cases, the transport of energy by the multiply scattered waves can be well described using the diffusion approximation, which may even seem quite surprising since all interference effects are ignored. An exception occurs when the return probability that the waves scatter back to the same spot becomes enhanced as a result of very strong multiple scattering; then interference plays an important role and can ultimately lead to Anderson localization and the breakdown of wave propagation. Examples of these wave phenomena will be presented in contrasting...

Experimental and Analytical Analysis of Particle Damping

Particle damping is an emerging technology among passive devices for furnishing high damping of structural vibration, particularly in harsh environment, through the use of granular particles filled within an enclosure. In this work, we investigate experimentally the effect of acceleration amplitude, mass ratio, volume package, and type of material on the dynamic behavior of the particle damping to yield a thorough understanding of the attenuation mechanism played within such dampers. Experimental trials are realized within a rigid enclosure attached to a shaker and partially filled with particles. An analytical model based on the inelastic bouncing ball model (IBBM) is also developed in order to describe the nonlinear behavior of particle dampers. Our measurements reveal that the loss factor only relies on the total mass of the incorporated grains and on the driving magnitude. Further scaling of the loss factor, for all measurements, by the mass ratio led to a universal curve dependent only on the acceleration magnitude. A good agreement between the analytic model and the experimental results was verified.

Granular Material for Vibration Suppression

We present preliminary results devoted to study and analyze the main features of particle damping from numerical simulations and experimental procedures. Particle damping is measured for free-free beam with particle filled enclosure attached to their both sides. Particle damping is measured for different amplitude vibration and the goal is to highlight the damping phenomena and to understand such mechanism involved in particle damping.