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Modeling of an impact system with a drift
E Pavlovskaia1, M Wiercigroch, C Grebogi
1Department of Engineering, King's College, Aberdeen University, Aberdeen, AB24 3UE, United Kingdom.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
Summary
A new physical model analyzes impact oscillators, revealing complex dynamics. The largest drift occurs at the transition from periodic to chaotic motion, guiding predictions for practical applications.
Area of Science:
- Physics
- Mechanical Engineering
- Nonlinear Dynamics
Background:
- Impact oscillators are crucial in various applications, requiring accurate modeling of their motion.
- Understanding the dynamics of progressive motion, or drift, is essential for system design and performance.
- Viscoelastic impacts introduce complexity that traditional models may not fully capture.
Purpose of the Study:
- To develop and analyze a physical model for impact oscillators.
- To investigate the relationship between motion dynamics and system drift.
- To predict conditions leading to chaotic behavior and loss of periodicity.
Main Methods:
- Development of a physical model incorporating viscoelastic impacts.
- Nonlinear dynamic analysis to study system behavior.
- Construction of a semianalytical solution for periodic regimes.
Main Results:
- The model successfully mimics bounded progressive motion (drift) in impact oscillators.
- System behavior ranges from periodic to chaotic, influenced by stick-slip phases.
- Maximum drift is observed during the transition from periodic to chaotic motion following bifurcations.
Conclusions:
- The developed physical model provides insights into the complex dynamics of impact oscillators.
- The findings highlight the critical transition point for achieving maximum drift.
- The semianalytical solution aids in predicting system progression and loss of periodicity.