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Exact solutions for discrete breathers in a forced-damped chain
1Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, 32000 Haifa, Israel. ovgend@tx.technion.ac.il
Summary
This study finds exact solutions for symmetric discrete breathers in forced-damped chains with vibro-impact constraints. Stability is analyzed, revealing pitchfork and Neimark-Sacker bifurcations influenced by coupling and forcing amplitude.
Area of Science:
- Nonlinear Dynamics
- Condensed Matter Physics
- Mechanical Vibrations
Background:
- Discrete breathers (DBs) are localized nonlinear oscillations in periodic systems.
- Forced-damped lattices with vibro-impact constraints present complex dynamics.
- Understanding stability is crucial for controlling localized energy in such systems.
Purpose of the Study:
- To derive exact solutions for symmetric on-site discrete breathers.
- To investigate the conditions for the existence and stability of these DBs.
- To analyze the bifurcation mechanisms leading to instability.
Main Methods:
- Analytical derivation of exact solutions for symmetric DBs.
- Application of analytic and numeric methods to establish global stability conditions.
- Investigation of pitchfork and Neimark-Sacker bifurcations.
Main Results:
- Exact solutions for symmetric discrete breathers were obtained.
- Global conditions for DB existence and stability were established.
- Pitchfork and Neimark-Sacker bifurcations identified as primary instability routes.
- Coupling effects on stability were analyzed, showing suppression of pitchfork and promotion of Neimark-Sacker bifurcations.
- Non-monotonous stability dependence on forcing amplitude revealed.
Conclusions:
- The study provides a comprehensive analysis of discrete breathers in forced-damped vibro-impact lattices.
- Bifurcation analysis clarifies stability limits and mechanisms.
- Findings offer insights into controlling localized energy in complex mechanical systems.
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