Propagation and Backscattering of Mechanical Impulses in a Gravitationally Loaded Chain: Dynamical Studies and Toy Model Based Phenomenology (original) (raw)
Related papers
Effects of gravity and nonlinearity on the waves in the granular chain
Physical review. E, Statistical, nonlinear, and soft matter physics, 2001
The solitary signal observed in a horizontal granular chain changes its speed and form due to gravity in a vertical chain. We find that all the propagating signals in a vertical chain follow power laws in depth for propagating speed, grain velocity, amplitude, and width. This stems from the power-law type changing of elastic properties in a medium under gravity. The propagation may be separated into two types according to the behavior of the power-law exponents, depending on the strength of the nonlinearity. We show that the power-law exponents are constants in the strength of the impulse in the weakly nonlinear regime, while they depend on the strength of the impulse in the strongly nonlinear regime. We derive power-law exponents for the weakly nonlinear regime analytically and try to understand the behaviors of the strongly nonlinear regime through analytical treatment.
Towards a Mathematical Model for Elastic Wave Propagation in Granular Materials
Engineering, 2012
A theoretical model for the propagation of acoustic waves in dry granular media is presented within the framework of the nonlinear granular elasticity. An essential ingredient is the dependence of the elastic moduli on compression. For the purpose of illustration, we analyze the case of a time-harmonic plane wave propagation under isotropic compression. We derive explicit relations for the wave speed dependence with the confining pressure. The present approach provides an accurate description of acoustic wave propagation in granular packings and represents a powerful tool to interpret the results of current experiments.
Elastic wave propagation in confined granular systems
Physical Review E, 2005
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.
Characterization of wave propagation in elastic and elastoplastic granular chains
Physical Review E, 2014
For short duration impulse loadings, elastic granular chains are known to support solitary waves, while elastoplastic chains have recently been shown to exhibit two force decay regimes [Pal, Awasthi, and Geubelle, Granular Matter 15, 747 (2013).]. In this work, the dynamics of monodisperse elastic and elastoplastic granular chains under a wide range of loading conditions is studied, and two distinct response regimes are identified in each of them. In elastic chains, a short loading duration leads to a single solitary wave propagating down the chain, while a long loading duration leads to the formation of a train of solitary waves. A simple model is developed to predict the peak force and wave velocity for any loading duration and amplitude. In elastoplastic chains, wave trains form even for short loading times due to a mechanism distinct from that in elastic chains. A model based on energy balance predicts the decay rate and transition point between the two decay regimes. For long loading durations, loading and unloading waves propagate along the chain, and a model is developed to predict the contact force and particle velocity.
Acta Acustica united with Acustica, 2008
The problem of the nonlinear reflection of acoustic waves from a mechanically free surface of an unconsolidated granular layer under gravity is solved analytically using the successive approximations method. The theory revealed specific dependencies of the characteristics of the generated acoustic harmonics of longitudinal and shear waves on frequency and the thickness of the granular layer, which are related to a power-law gravity-induced depth stratification of linear and nonlinear mechanical properties of the granular layer. The developed theory could be useful for the analysis of the acoustic experiments directed to the investigation of fundamental mechanical properties of unconsolidated granular media near the jamming transition taking place at zero confining pressure.
Impulse backscattering in granular beds: Introducing a toy model
Physical Review E, 2003
Impulses efficiently propagate into nominally dry granular beds and backscatter from buried inclusions in such beds may be potentially exploited to image shallow buried objects (SBOs). However, reliable imaging of SBOs requires "cleaning up" of surface vibrations, and, in addition to 3D particle dynamics simulations, a phenomenological model to parameterize the bed surface may be useful for field applications. We introduce a 1D mean-field-like toy model with two parameters that allows one to model surface vibrations, is consistent with experiments in a granular bed, and can help estimate the approximate signal transmission properties of the bed.
Wave propagation in confined granular systems
arXiv (Cornell University), 2004
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.
Impulse Propagation in Granular Systems
AIP Conference Proceedings, 2003
We review recent developments on the topic of impulse propagation in assemblies of elastic beads, where the beads interact upon contact via the (nonlinear) Hertz potential. The role of solitary waves in granular systems is emphasized. The effects of impurities, disorder and restitution are discussed. The possible applications of this research in the development of new technologies are mentioned.