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Measure synchronization and clustering in a coupled-pendulum system suspended from a common beam
1School of Science, Xi'an University of Posts and Telecommunications, 710121 Xi'an, China.
Chaos (Woodbury, N.Y.)
|October 3, 2019
Summary
Measure synchronization (MS) in coupled pendulums is achieved by decreasing the beam-to-pendulum mass ratio, leading to frequency locking. This study reveals the dynamical mechanism behind these transitions.
Area of Science:
- Nonlinear dynamics
- Coupled oscillator systems
- Mechanical vibrations
Background:
- Coupled pendulum systems exhibit complex dynamics.
- Indirect coupling through a common beam influences system behavior.
- Measure synchronization (MS) is a phenomenon in coupled systems.
Purpose of the Study:
- Investigate measure synchronization (MS) in a nondissipative coupled-pendulum system.
- Determine the influence of the beam-to-pendulum mass ratio (R) on MS.
- Analyze the energy characteristics and dynamical mechanisms of MS.
Main Methods:
- Theoretical analysis of a coupled-pendulum system.
- Varying the mass ratio R to adjust coupling strength.
- Poincaré section analysis to reveal dynamical mechanisms.
Main Results:
- MS, including partial and complete forms, is achieved below a critical mass ratio (Rc).
- Decreasing R enhances coupling strength and promotes MS.
- Pendula exhibit frequency locking during MS transitions.
- Energy characteristics of MS are analyzed.
Conclusions:
- The beam-to-pendulum mass ratio is a critical parameter for achieving MS in this system.
- Frequency locking is a key indicator of MS transitions.
- Poincaré section analysis provides insight into the underlying dynamics of MS.
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