Dynamics of one-dimensional granular arrays with pre-compression

Gizem Dilber Acar, Balakumar Balachandran

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Bifurcations of periodic orbits and band zones of a one-dimensional granular array are numerically investigated in this study. A conservative two-bead system is first considered without any dissipation or external forcing. By using the Hertzian contact model, and confining the system’s total energy to a certain level, changes in the in-phase periodic orbit are studied for various pre-compression levels. At a certain pre-compression level, symmetry breaking and period doubling simultaneously occur, and an asymmetric period-two orbit emerges from the in-phase periodic orbit. Floquet analysis is conducted to study the stability of the in-phase periodic solution and to detect the bifurcation location. Although the trajectory of the period-two orbit is close to the in-phase orbit at the bifurcation point, the asymmetry of the period-two orbit becomes more pronounced away from the bifurcation point. Pre-compression is found to affect the periodic orbit frequencies, which in turn result in changes in the wave propagation band zones. These changes are illustrated by studying vibration transmission through a granular chain at different frequencies to ascertain the band zone limits.

Original languageEnglish
Pages (from-to)707-720
Number of pages14
JournalNonlinear Dynamics
Volume99
Issue number1
DOIs
StatePublished - 1 Jan 2020

Keywords

  • Bifurcations
  • Granular media
  • Period doubling
  • Pre-compression
  • Symmetry breaking

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