Effects of gravity and nonlinearity on the waves in the granular chain (original) (raw)

Nonlinear waves in disordered diatomic granular chains

Physical Review E, 2010

We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin", so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: In low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of disorder, the wave amplitude instead decays as a power law, and the wave transmission becomes insensitive to the level of disorder. We characterize the spatio-temporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for such a transition. Our investigation suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highly nonlinear waves.

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.

NONLINEAR ELASTIC WAVES IN A GRANULAR MEDIUM

The propagation and interaction of elastic waves in the granular medium with regard for its nonlinear properties is considered. This medium is represented by the cubic packing of elastic spheres. The obtained equations allow to describe the nonlinear compression and shear waves in the simple model of granular medium.

Propagation and Backscattering of Mechanical Impulses in a Gravitationally Loaded Chain: Dynamical Studies and Toy Model Based Phenomenology

arXiv (Cornell University), 2005

We recently introduced a simple toy model to describe energy propagation and backscattering in complex layered media (T.R. Krishna Mohan and S. Sen, Phys. Rev. E 67, 060301(R) (2003)). The model provides good qualitative description of energy propagation and backscattering in real soils. Here we present a dynamical study of energy propagation and backscattering in a gravitationally loaded granular chain and compare our results with those obtained using the toy model. The propagation is ballistic for low g values and acquires characteristics of acoustic propagation as g is increased. We focus on the dynamics of the surface grain and examine the backscattered energy at the surface. As we shall see, excellent agreement between the two models is achieved when we consider the simultaneous presence of acoustic and nonlinear behavior in the toy model. Our study serves as a first step towards using the toy model to describe impulse propagation in gravitationally loaded soils.

Observation of Two-Wave Structure in Strongly Nonlinear Dissipative Granular Chains

Physical Review Letters, 2007

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.

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.

Wave propagation in confined granular systems

arXiv (Cornell University), 2004

Solitary waves in the granular chain

Physics Reports, 2008

Solitary waves are lumps of energy. We consider the study of dynamical solitary waves, meaning cases where the energy lumps are moving, as opposed to topological solitary waves where the lumps may be static. Solitary waves have been studied in some form or the other for nearly 450 years. Subsequently, there have been many authoritative works on solitary waves. Nevertheless, some of the most recent studies reveal that these peculiar objects are far more complex than what we might have given them credit for. In this review, we introduce the physics of solitary waves in alignments of elastic beads, such as glass beads or stainless steel beads. We show that any impulse propagates as a new kind of highly interactive solitary wave through such an alignment and that the existence of these waves seems to present a need to reexamine the very definition of the concept of equilibrium. We further discuss the possibility of exploiting nonlinear properties of granular alignments to develop exciting technological applications.

Effects of gravity and nonlinearity on the waves in the granular chain (original) (raw)

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