Effective particles and classification of the dynamics of homogeneous granular chains with no precompression

Yuli Starosvetsky, K. R. Jayaprakash, Alexander F. Vakakis, Gaëtan Kerschen, Leonid I. Manevitch

Research output: Contribution to journalArticle

Abstract

We develop a systematic methodology for classifying the periodic orbits of homogeneous ordered granular chains with no dissipation, under the assumption that all granules oscillate with the same frequency. The analysis is based on the idea of balancing linear momentum for sets of auxiliary models consisting of "effective particles." The auxiliary models may be defined for any given finite, ordered granular chain composed of n identical granules (beads) that interact with each other through strongly nonlinear Hertzian interaction law. In turn, the auxiliary models may be effectively used for theoretically predicting the total number of periodic orbits and the corresponding amplitude ratios of the granules. Good correspondence between the theoretical models and results of direct numerical simulations is reported. The results presented herein can be used to understand the complex intrinsic dynamics of ordered granular media, and to systematically study the generation of mode localization in these strongly nonlinear systems. The derived analytical models can be utilized to predict the response of the effective particles, and based on that, to predict primary pulse transmission in periodic layered media with granular interfaces. Moreover, our analysis can be extended to the general class of nonlinear chains of particles with smooth interacting potentials and possible separation between particles during the motion.

Original languageEnglish (US)
Article number036606
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume85
Issue number3
DOIs
StatePublished - Mar 28 2012

Fingerprint

Periodic Orbits
Layered Media
Predict
Granular Media
Nonlinear Interaction
orbits
Balancing
Theoretical Model
Analytical Model
Dissipation
classifying
nonlinear systems
direct numerical simulation
Correspondence
Nonlinear Systems
Momentum
beads
Model
dissipation
Motion

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Effective particles and classification of the dynamics of homogeneous granular chains with no precompression. / Starosvetsky, Yuli; Jayaprakash, K. R.; Vakakis, Alexander F.; Kerschen, Gaëtan; Manevitch, Leonid I.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 85, No. 3, 036606, 28.03.2012.

Research output: Contribution to journalArticle

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