Adam Sokolow

How Hertzian Solitary Waves Interact with Boundaries in a 1D Granular Medium

We perform measurements, numerical simulations, and quantitative comparisons with available theory on solitary wave propagation in a linear chain of beads without static preconstraint. By designing a nonintrusive force sensor to measure the impulse as it propagates along the chain, we study the solitary wave reflection at a wall. We show that the main features of solitary wave reflection depend on wall mechanical properties. Since previous studies on solitary waves have been performed at walls without these considerations, our experiment provides a more reliable tool to characterize solitary wave propagation. We find, for the first time, precise quantitative agreements.

Solitary wave trains in granular chains: experiments, theory and simulations

The features of solitary waves observed in horizontal monodisperse chain of barely touching beads not only depend on geometrical and material properties of the beads but also on the initial perturbation provided at the edge of the chain. An impact of a large striker on a monodisperse chain, and similarly a sharp decrease of bead radius in a stepped chain, generates a solitary wave train containing many single solitary waves ordered by decreasing amplitudes. We find, by simple analytical arguments, that the unloading of compression force at the chain edge has a nearly exponential decrease. The characteristic time is mainly a function involving the grains’ masses and the striker mass. Numerical calculations and experiments corroborate these findings.

Solitary wave train formation in Hertzian chains

Experiments show that perturbation by an incident striker can generate solitary wave trains in unloaded, monodispersed elastic sphere alignments (Lazaridi A. N. and Nesterenko V. F., Prikl. Mekh. Tekh. Fiz., 3 (1985) 115). We report the first dynamical studies in the elastic regime that confirm and extend upon the results obtained in existing experiments and define the conditions for which controlled generation of solitary wave trains may be possible.

Absorption of short duration pulses by small, scalable, tapered granular chains

Making shock proof layers is an outstanding challenge. Elastic spheres are known to repel softer than springs when gently squeezed but develop strong repulsion upon compression and the forces between adjacent spheres lead to ballistic-like energy transfer between them. Here we demonstrate that a small alignment of progressively shrinking spheres of a strong, light-mass material, placed horizontally in an appropriate casing, can absorb ∼80% (∼90%) of the incident force (energy) pulse. The system can be scaled down in size. Effects of varying the size, radius shrinkage and restitutive losses are shown via computed “dynamical phase diagrams.”

USING MECHANICAL ENERGY AS A PROBE FOR THE DETECTION AND IMAGING OF SHALLOW BURIED INCLUSIONS IN DRY GRANULAR BEDS

Mechanical energy, such as sound waves and impulses, have been used to detect shallow buried objects for more than half a century. Yet, very little is understood about how mechanical energy propagates into one of the simplest kinds of soil, namely, a granular bed. Here we present an overview of the state of the art in our understanding of mechanical energy propagation in granular beds.

Nonlinear breathing processes in granular alignments

A compressive applied force at the zero frequency limit applied on confined granular alignments is shown to result in tunable and higher frequency nonlinear granular breathing. We use extensive dynamical simulations and simple arguments to probe the origins of these breathing processes. In the presence of dissipation, the breathing has a lifetime that is inversely proportional to the dissipation constant. The possible use of the concept of nonlinear granular breathing in recovering the energy released at the beaches by surface gravity waves using a system made largely of nonmoving parts is mentioned as a possible application.

Nonlinear, Statistical and Applied Physics of Solitary Wave‐like Objects in Granular Systems

We consider a simple problem that of a horizontal alignment of identical grains, and insure that the grains are in gentle mutual contact and held between two rigid fixed end walls. Grain‐grain interactions are intrinsically nonlinear according to the Hertz law and hence no sound waves can propagate through this alignment. The discussions here concern the solitary wave nature of propagation of any perturbation and its subsequent dispersion in the same vein as we probe the dispersion of a perturbation in linear response theory in statistical physics. We show that a perturbed granular alignment exhibits both decaying and growing solitary waves and can indeed reach an equilibrium‐like state. We suggest that this equilibrium‐like state may not be the equilibrium state commonly reached in thermodynamics and statistical physics. Moving beyond the effort to develop a deeper understanding of the energy transport problem in granular systems, we discuss a new application of a granular alignment system, that of drive...

Periodic Dynamics in Driven Granular Chain Systems

We consider the dynamical behavior of horizontal alignments of elastic grains placed within confining walls and placed under a constant acceleration that is applied at one end of the system. We show that these systems vibrate under such a compressive force. Certain universal properties of this vibration are mentioned. These systems may be useful in designing devices for filtering out mechanical noise.