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.
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ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 26–29, 2018
Quebec City, Quebec, Canada
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-5183-8
PROCEEDINGS PAPER
Bifurcations of Periodic Orbits of a One-Dimensional Pre-Compressed Granular Array
Gizem Dilber Acar,
Gizem Dilber Acar
University of Maryland, College Park, MD
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Balakumar Balachandran
Balakumar Balachandran
University of Maryland, College Park, MD
Search for other works by this author on:
Gizem Dilber Acar
University of Maryland, College Park, MD
Balakumar Balachandran
University of Maryland, College Park, MD
Paper No:
DETC2018-85491, V006T09A006; 6 pages
Published Online:
November 2, 2018
Citation
Acar, GD, & Balachandran, B. "Bifurcations of Periodic Orbits of a One-Dimensional Pre-Compressed Granular Array." Proceedings of the ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 6: 14th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Quebec City, Quebec, Canada. August 26–29, 2018. V006T09A006. ASME. https://doi.org/10.1115/DETC2018-85491
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