[Propagation des ondes de densité de l’impulsion et formation d’arcs dans l’ondulation d’une couche granulaire mince soumise à des vibrations verticales]
Experimental and theoretical investigations are made on the aspect ratio of the height $\delta $ to wavelength $\lambda $ of the undulations generated in a dry granular layer confined between two parallel vertical planes under vertical vibration of frequency $f$ and amplitude $a$. We elucidated the propagation of the density wave along the layer, which suggests one or two order smaller macroscopic elastic constant ascribed to a configuration change of the constituent particles. Our experiment also suggests the relation $\lambda \propto 1/(p-p_c) $ irrespective of the size of the container, where $p$ ($\propto fa$) is the momentum given by the external forcing, which is reminiscent of the de Broglie wave known in quantum mechanics. We further performed a numerical simulation on the onset and development of undulations using our simplified model, in which horizontal dilatation generated by mutual intrusion of particles near the bottom of the container develops to an arch formation of the granular layer. Influence of the friction of the granular material is examined.
Des études expérimentales et théoriques sont menées sur le rapport d’aspect entre la hauteur $\delta $ et la longueur d’onde $\lambda $ des ondulations générées dans une couche granulaire sèche confinée entre deux plans verticaux parallèles sous l’effet d’une vibration verticale de fréquence $f$ et d’amplitude $a$. Nous avons élucidé la propagation de l’onde de densité le long de la couche, ce qui suggère une constante élastique macroscopique inférieure d’un ou deux ordres de grandeur, attribuée à un changement de configuration des particules constitutives. Notre expérience suggère également la relation $\lambda \propto 1/(p-p_c) $, quelle que soit la taille du conteneur, où $p$ ($\propto fa$) est l’impulsion donnée par la force externe, qui rappelle l’onde de de Broglie connue en mécanique quantique. Nous avons ensuite réalisé une simulation numérique sur l’apparition et le développement des ondulations à l’aide de notre modèle simplifié, dans lequel la dilatation horizontale générée par l’intrusion mutuelle des particules près du fond du conteneur se développe pour former une arche dans la couche granulaire. L’influence du frottement du matériau granulaire est examinée.
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Mots-clés : Couche granulaire vibrée, ondulation, propagation des ondes de densité, transfert d’impulsion, onde de de Broglie
Osamu Sano 1
CC-BY 4.0
@article{CRMECA_2025__353_G1_1201_0,
author = {Osamu Sano},
title = {Density wave propagation of momentum and the formation of arches in the undulation of a vertically vibrated thin granular layer},
journal = {Comptes Rendus. M\'ecanique},
pages = {1201--1224},
year = {2025},
publisher = {Acad\'emie des sciences, Paris},
volume = {353},
doi = {10.5802/crmeca.327},
language = {en},
}
TY - JOUR AU - Osamu Sano TI - Density wave propagation of momentum and the formation of arches in the undulation of a vertically vibrated thin granular layer JO - Comptes Rendus. Mécanique PY - 2025 SP - 1201 EP - 1224 VL - 353 PB - Académie des sciences, Paris DO - 10.5802/crmeca.327 LA - en ID - CRMECA_2025__353_G1_1201_0 ER -
%0 Journal Article %A Osamu Sano %T Density wave propagation of momentum and the formation of arches in the undulation of a vertically vibrated thin granular layer %J Comptes Rendus. Mécanique %D 2025 %P 1201-1224 %V 353 %I Académie des sciences, Paris %R 10.5802/crmeca.327 %G en %F CRMECA_2025__353_G1_1201_0
Osamu Sano. Density wave propagation of momentum and the formation of arches in the undulation of a vertically vibrated thin granular layer. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 1201-1224. doi: 10.5802/crmeca.327
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