Nonlinear Coherent Structures in Granular Crystals

This paper reports on the study of the dynamics of 1D magneto-granular phononic crystals composed of a chain of spherical steel beads inside a properly designed magnetic field. This field is induced by an array of permanent magnets, located in a holder at a given distance from the chain. The theoretical and experimental results of the band gap structure are displayed, including all six degrees of freedom for the beads, i.e. three translations and three rotations. Experimental...

We report on the strongly nonlinear dynamics of an array of weakly coupled, non-compressed, parallel granular chains subject to a local initial impulse. The motion of the granules in each chain is constrained to be in one direction which coincides with the orientation of the chain. We show that in spite of the fact that the applied impulse is applied to a one of the granular chains, the resulting pulse that initially propagating only in the excited chain gets gradually equi-p...

Granular materials are ubiquitous in our daily lives. While they have been a subject of intensive engineering research for centuries, in the last decade granular matter attracted significant attention of physicists. Yet despite a major efforts by many groups, the theoretical description of granular systems remains largely a plethora of different, often contradicting concepts and approaches. Authors give an overview of various theoretical models emerged in the physics of granu...

We experimentally study a one-dimensional uncompressed granular chain composed of a finite number of identical spherical beads with Hertzian interactions. The chain is harmonically excited by an amplitude- and frequency-dependent boundary drive at its left end and has a fixed boundary at its right end. Such ordered granular media represent an interesting new class of nonlinear acoustic metamaterials, since they exhibit essentially nonlinear acoustics and have been designated ...

The arrangements of particles and forces in granular materials have a complex organization on multiple spatial scales that ranges from local structures to mesoscale and system-wide ones. This multiscale organization can affect how a material responds or reconfigures when exposed to external perturbations or loading. The theoretical study of particle-level, force-chain, domain, and bulk properties requires the development and application of appropriate physical, mathematical, ...

We study impulse response in 1-D homogeneous micro-granular chains on a linear elastic substrate. Micro-granular interactions are analytically described by the Schwarz contact model which includes nonlinear compressive as well as snap-to/from-contact adhesive effects forming a hysteretic loop in the force deformation relationship. We observe complex transient dynamics, including disintegration of solitary pulses, local clustering and low- to high-frequency energy transfers re...

Propagation of primary pulse through an un-compressed granular chain subject to external on-site perturbation is studied. Analytical procedure predicting the evolution of the primary pulse is devised for the general form of the on-site perturbation applied on the chain. The validity of the analytical model is confirmed with several specific granular setups such as, chains mounted on the nonlinear elastic foundation, chains perturbed by the dissipative forces as well as random...

We show by computer simulation of a two-dimensional crystal confined by corrugated walls that confinement can be used to impose a controllable mesoscopic superstructure of predominantly mechanical elastic character. Due to an interplay of the particle density of the system and the width D of the confining channel, "soliton staircases" can be created along both parallel confining boundaries, that give rise to standing strain waves in the entire crystal. The periodicity of thes...

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic po...

We explore a recently proposed locally resonant granular system bearing harmonic internal resonators in a chain of beads interacting via Hertzian elastic contacts. In this system, we propose the existence of two types of configurations: (a) small-amplitude periodic traveling waves and (b) dark-breather solutions, i.e., exponentially localized, time periodic states mounted on top of a non-vanishing background. We also identify conditions under which the system admits long-live...