Pulse velocity in a granular chain

Rosas, Alexandre; Lindenberg, Katja

doi:10.1103/physreve.69.037601

Cited by 79 publications

(72 citation statements)

References 20 publications

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“…These chains have been shown to support the emergence of nonlinear traveling waves, which have been described through different types of partial differential equation models (see, e.g., [13]) or even by binary collision particle models (see, e.g., [14]). Although these waves are treated as compactly supported in the continuum approximations, they decay with a doubly exponential power law [23,24] (i.e.…”

Section: Introductionmentioning

confidence: 99%

Interaction of traveling waves with mass-with-mass defects within a Hertzian chain

et al. 2013

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We study the dynamic response of a granular chain of particles with a resonant inclusion (i.e., a particle attached to a harmonic oscillator, or a mass-with-mass defect). We focus on the response of granular chains excited by an impulse, with no static precompression. We find that the presence of the harmonic oscillator can be used to tune the transmitted and reflected energy of a mechanical pulse by adjusting the ratio between the harmonic resonator mass and the bead mass. Furthermore, we find that this system has the capability of asymptotically trapping energy, a feature that is not present in granular chains containing other types of defects. Finally, we study the limits of low and high resonator mass, and the structure of the reflected and transmitted pulses.

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Section: Introductionmentioning

confidence: 99%

Interaction of traveling waves with mass-with-mass defects within a Hertzian chain

et al. 2013

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“…The problem of the propagation of a pulse in a 1D granular chain has been considered by many authors [5,43,44,45,46,47,48] but the majority of the work is concentrated on analyzing an initially uncompressed chain. In this case the nonlinear force law plays an important role, as well as the fact that there are no restoring forces between the balls which initially just touch.…”

Section: A 1d Chainmentioning

confidence: 99%

Elastic wave propagation in confined granular systems

et al. 2005

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We present numerical simulations of acoustic wave propagation in confined granular systems consisting of particles interacting with the three-dimensional Hertz-Mindlin force law. The response to a short mechanical excitation on one side of the system is found to be a propagating coherent wavefront followed by random oscillations made of multiply scattered waves. We find that the coherent wavefront is insensitive to details of the packing: force chains do not play an important role in determining this wavefront. The coherent wave propagates linearly in time, and its amplitude and width depend as a power law on distance, while its velocity is roughly compatible with the predictions of macroscopic elasticity. As there is at present no theory for the broadening and decay of the coherent wave, we numerically and analytically study pulse-propagation in a one-dimensional chain of identical elastic balls. The results for the broadening and decay exponents of this system differ significantly from those of the random packings. In all our simulations, the speed of the coherent wavefront scales with pressure as p 1/6 ; we compare this result with experimental data on various granular systems where deviations from the p 1/6 behavior are seen. We briefly discuss the eigenmodes of the system and effects of damping are investigated as well.

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“…The (red) solid line is for the actual (numerical) granular lattice dynamics, the (blue) dashed line is the plain superposition of two Toda one-soliton solutions of Eqn. (15), and the green dash-dotted line represents the numerical evolution of the Toda chain. …”

Section: Lemma 3 Let R Denote a Toda Two-soliton Solutionmentioning

confidence: 99%

“…Granular crystals are material systems based on the assembly of particles in one-, two-and three-dimensions inside a matrix (or a holder) in ordered closely packed configurations in which the grains are in contact with each other [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The fundamental building blocks constituting such systems are macroscopic particles of spherical, toroidal, elliptical or cylindrical shapes [20], arranged in different geometries.…”

Section: Introductionmentioning

confidence: 99%

Characterizing traveling-wave collisions in granular chains starting from integrable limits: The case of the Korteweg–de Vries equation and the Toda lattice

et al. 2014

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Our aim in the present work is to develop approximations for the collisional dynamics of traveling waves in the context of granular chains in the presence of precompression. To that effect, we aim to quantify approximations of the relevant Hertzian FPU-type lattice through both the Korteweg-de Vries (KdV) equation and the Toda lattice. Using the availability in such settings of both 1-soliton and 2-soliton solutions in explicit analytical form, we initialize such coherent structures in the granular chain and observe the proximity of the resulting evolution to the underlying integrable (KdV or Toda) model. While the KdV offers the possibility to accurately capture collisions of solitary waves propagating in the same direction, the Toda lattice enables capturing both copropagating and counter-propagating soliton collisions. The error in the approximation is quantified numerically and connections to bounds established in the mathematical literature are also given.

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Pulse velocity in a granular chain

Cited by 79 publications

References 20 publications

Interaction of traveling waves with mass-with-mass defects within a Hertzian chain

Interaction of traveling waves with mass-with-mass defects within a Hertzian chain

Elastic wave propagation in confined granular systems

Characterizing traveling-wave collisions in granular chains starting from integrable limits: The case of the Korteweg–de Vries equation and the Toda lattice

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