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Synchronization of spring pendula
Dawid Dudkowski1, Tomasz Kapitaniak1
1Department of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-537 Lodz, Poland.
Chaos (Woodbury, N.Y.)
|July 18, 2025
Summary
This study reveals how coupled spring pendula synchronize, detailing conditions for synchronous states and exploring their coexistence with desynchronization. Findings advance understanding of mechanical oscillator synchronization and complex dynamics.
Area of Science:
- Mechanical Engineering
- Nonlinear Dynamics
- Complex Systems
Background:
- Coupled oscillators exhibit complex behaviors, including synchronization, which is crucial in various physical and biological systems.
- Understanding synchronization in systems with elastic elements and damping is essential for designing stable and predictable mechanical systems.
Purpose of the Study:
- To investigate the synchronization phenomenon in coupled spring pendula with varying lengths.
- To determine the regions of synchronous states and analyze coexistence scenarios with other dynamical behaviors.
- To examine the influence of elastic element characteristics and damping on synchronous configurations.
Main Methods:
- Modeling two self-excited nodes with elastic elements suspended on a horizontally oscillating support.
- Analyzing the regions of appearance of synchronous states and co-existing behaviors.
- Presenting and explaining typical solutions to illustrate pendula and spring oscillation relationships.
- Investigating properties of synchronous configurations, including damping effects.
Main Results:
- Identified regions for the appearance of synchronous states in coupled spring pendula.
- Described coexistence scenarios between different dynamical behaviors, including synchronization and desynchronization.
- Demonstrated the influence of elastic element properties and damping on system synchronization.
- Showcased that coherent dynamics and desynchronization can coexist.
Conclusions:
- Uncovered novel mechanisms for synchronization in mechanical oscillators.
- Contributed to a deeper understanding of complex dynamical systems.
- Provided insights into the behavior of coupled spring pendula under varying conditions.
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