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Onset instability of a parametrically excited pendulum array.

Weizhong Chen1, Wengang Lin, Yifei Zhu

  • 1The Key Laboratory of Modern Acoustics and Institute of Acoustics, Nanjing University, Nanjing, 210093, China. wzchen@nju.edu.cn

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 16, 2007
PubMed
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Vertical vibration causes instability in a one-dimensional pendulum array, responding subharmonically to forcing frequency. Theoretical predictions for critical conditions and instability waves were experimentally validated for various wavelengths.

Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Mechanical vibrations

Background:

  • The Frenkel-Kontorova chain models phenomena in condensed matter physics.
  • Pendulum arrays exhibit complex dynamics under external forcing.
  • Floquet theory analyzes systems with time-periodic parameters.

Purpose of the Study:

  • Investigate the onset instability of a 1D pendulum array under vertical vibration.
  • Analyze the system's response using Floquet instability analysis.
  • Compare theoretical predictions with experimental results.

Main Methods:

  • Applied continuum approximation to the 1D pendulum array.
  • Utilized Floquet instability analysis to determine critical forcing conditions.
  • Conducted experiments to validate theoretical predictions of instability onset and wavelengths.

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Main Results:

  • Onset instability in the pendulum array consistently responds subharmonically to the forcing frequency.
  • Theoretical predictions for critical forcing conditions and instability wave characteristics were confirmed.
  • Excellent agreement was observed between theoretical calculations and experimental data for both long and short wavelengths.

Conclusions:

  • Floquet instability analysis accurately predicts the subharmonic onset instability in vibrated pendulum arrays.
  • Experimental validation confirms the theoretical framework for understanding instability phenomena in such systems.
  • The study provides a robust model for predicting critical dynamics in macroscopic Frenkel-Kontorova-like systems.