Scattering of solitary waves in granular media

A detailed numerical study of the scattering of solitary waves by a barrier, in a granular media with Hertzian contact, shows the existence of secondary multipulse structures generated at the interface of two "sonic vacua", which have a similar structure as the one previously found by Nesterenko and coworkers.Comment: 4 pages, 9 figures (fig 5, replaced). Submitted to PR

Anomalous wave reflection from the interface of two strongly nonlinear granular media

Granular materials exhibit a strongly nonlinear behaviour affecting the propagation of information in the medium. Dynamically self-organized strongly nonlinear solitary waves are the main information carriers in granular chains. Here we report the first experimental observation of the dramatic change of reflectivity from the interface of two granular media triggered by a noncontact magnetically induced initial precompression. It may be appropriate to name this phenomenon the "acoustic diode" effect. Based on numerical simulations, we explain this effect by the high gradient of particle velocity near the interface.Comment: 14 pages, 3 figure

Delayed Scattering of Solitary Waves from Interfaces in a Granular Container

In granular media, the characterization of the behavior of solitary waves around interfaces is of importance in order to look for more applications of these systems. We study the behavior of solitary waves at both interfaces of a symmetric granular container, a class of systems that has received recent attention because it posses the feature of energy trapping. Hertzian contact is assumed. We have found that the scattering process is elastic at one interface, while at the other interface it is observed that the transmitted solitary wave has stopped its movement during a time that gets longer when the ratio between masses at the interfaces increases. The origin of this effect can be traced back to the phenomenon of gaps opening, recently observed experimentally.Comment: To appear in Physical Review E, vol 7

Strongly nonlinear wave dynamics in a chain of polymer coated beads

Strongly nonlinear phononic crystals were assembled from a chain of Parylene-C coated steel spheres in a polytetrafluoroethylene holder. This system exhibits strongly nonlinear properties and extends the range of materials supporting sonic-vacuum-type behavior. The combination of a high density core and a soft (low elastic modulus) coating ensures a relatively low velocity of wave propagation. The bead contact interaction caused by the deformation of the Parylene coating can be described by classical nonlinear elastic Hertz theory with an effective value of the elastic modulus equal to 15 GPa for the contact interaction. Strongly nonlinear solitary waves excited by impacts were investigated experimentally and compared to chains composed of uniform steel beads. Fracture of the polymer coating was detected under relatively large pulse amplitude

Energy trapping and shock disintegration in a composite granular medium

Granular materials demonstrate a strongly nonlinear behavior influencing the wave propagation in the medium. We report the first experimental observation of impulse energy confinement and the resultant disintegration of shock and solitary waves. The medium consists of alternating ensambles of high-modulus vs orders of magnitude lower modulus chains of different masses. The trapped energy is contained within the "softer" portions of the composite chain and is slowly released in the form of weak, separated pulses over an extended period of time. This effect is enhanced by using a specific group assembly and superimposed force.Comment: 15 pages, 2 figure

Shock Wave Structure in a Strongly Nonlinear Granular Lattice with Viscous Dissipation

The shock wave structure in a one-dimensional lattice (e.g. granular chain) with a power law dependence of force on displacement between particles with viscous dissipation is considered and compared to the corresponding long wave approximation. A dissipative term depending on the relative velocity between neighboring particles is included in the discrete model to investigate its influence on the shape of steady shock profiles. The critical viscosity coefficient is obtained from the long-wave approximation for arbitrary values of the exponent n and denotes the transition from an oscillatory to a monotonic shock profile in stronly nonlinear systems. The expression for the critical viscosity coefficient converges to the known equation for the critical viscosity in the weakly nonlinear case. Values of viscosity based on this expression are comparable to the values obtained in the numerical analysis of a discrete particle lattice with a Herzian contact interaction corresponding to n = 3/2. An initial disturbance in a discrete system approaches a stationary shock profile after traveling a short distance that is comparable to the width of the leading pulse of a stationary shock front. The shock front width is minimized when the viscosity is equal to its critical value.Comment: 20 pages, 6 figure

Observation of two-wave structure in strongly nonlinear dissipative granular chains

In a strongly nonlinear viscous granular chain under conditions of loading that exclude stationary waves (e.g., impact by a single grain) we observe a pulse that consists of two interconnected but distinct parts. One is a leading narrow "primary pulse" with properties similar to a solitary wave in a "sonic vacuum." It arises from strong nonlinearity and discreteness in the absence of dissipation, but now decays due to viscosity. The other is a broad, much more persistent shock-like "secondary pulse" trailing the primary pulse and caused by viscous dissipation. The medium behind the primary pulse is transformed from a "sonic vacuum" to a medium with finite sound speed. When the rapidly decaying primary pulse dies, the secondary pulse continues to propagate in the "sonic vacuum," with an oscillatory front if the viscosity is relatively small, until its eventual (but very slow) disintegration. Beyond a critical viscosity there is no separation of the two pulses, and the dissipation and nonlinearity dominate the shock-like attenuating pulse which now exhibits a nonoscillatory front

How Hertzian solitary waves interact with boundaries in a 1-D 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 preconstrain. 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.Comment: Proof corrections, ReVTeX, 11 pages, 3 eps (Focus and related papers on http://www.supmeca.fr/perso/jobs/

Highly nonlinear pulse splitting and recombination in a two-dimensional granular network

The propagation of highly nonlinear signals in a branched two-dimensional granular system was investigated experimentally and numerically for a system composed of chains of spherical beads of different materials. The system studied consists of a double Y-shaped guide in which high- and low-modulus/mass chains of spheres are arranged in various geometries. We observed the transformation of a single or a train of solitary pulses crossing the interface between branches. We report fast splitting of the initial pulse, rapid chaotization of the signal and impulse redirection and bending. Pulse and energy trapping was also observed in the branches. Numerical analysis based on Hertzian interaction between the particles and the side walls of the guide was found in agreement with the experimental data, except for nonsymmetric arrangements of particles excited by a large mass striker

Influence of Controlled Viscous Dissipation on the Propagation of Strongly Nonlinear Waves in Stainless Steel Based Phononic Crystals

Strongly nonlinear phononic crystals were assembled from stainless steel spheres. Single solitary waves and splitting of an initial pulse into a train of solitary waves were investigated in different viscous media using motor oil and non-aqueous glycerol to introduce a controlled viscous dissipation. Experimental results indicate that the presence of a viscous fluid dramatically altered the splitting of the initial pulse into a train of solitary waves. Numerical simulations qualitatively describe the observed phenomena only when a dissipative term based on the relative velocity between particles is introduced.Comment: 4 pages, 3 figures, conference pape