Bifurcations of periodic orbits of a one-dimensional pre-compressed granular array

Gizem Dilber Acar, Balakumar Balachandran

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Bifurcations of periodic orbits of a one-dimensional granular array are numerically investigated in this study. A conservative two-bead system is considered without any damping or external forces. By using the Hertzian contact model, and confining the system's total energy to a certain level, changes in in-phase periodic orbit are studied for various pre-compression levels. At a certain pre-compression level, symmetry breaking and period doubling 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 period-two orbit is close to the in-phase orbit at the bifurcation point, the asymmetry of the period-two orbit becomes more pronounced as one moves away from the bifurcation point. This work is meant to serve as an initial step towards understanding how pre-compression may introduce qualitative changes in system dynamics of granular media.

Original languageEnglish
Title of host publication14th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
ISBN (Electronic)9780791851838
DOIs
StatePublished - 2018
EventASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2018 - Quebec City, Canada
Duration: 26 Aug 201829 Aug 2018

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume6

Conference

ConferenceASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2018
Country/TerritoryCanada
CityQuebec City
Period26/08/1829/08/18

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