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Two-dimensional map for impact oscillator with drift.

Ekaterina Pavlovskaia1, Marian Wiercigroch, Celso Grebogi

  • 1Centre for Applied Dynamics Research, Department of Engineering, King's College, Aberdeen University, Aberdeen AB24 3UE, United Kingdom. E.Pavlovskaia@eng.abdn.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 5, 2004
PubMed
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This study analyzes an impact oscillator with drift, separating bounded oscillations from progressive motion. A new 2D map method simplifies analysis and accurately predicts system dynamics, validated against differential equations.

Area of Science:

  • * Mechanical Engineering
  • * Nonlinear Dynamics
  • * Physics of Complex Systems

Background:

  • * Impact oscillators are crucial in various applications, exhibiting complex dynamics.
  • * Modeling progressive motion and bounded oscillations in these systems presents analytical challenges.

Purpose of the Study:

  • * To develop a simplified analytical model for an impact oscillator with drift.
  • * To separate and analyze bounded oscillations from the system's drift motion.
  • * To introduce a novel graphical method for iterating a 2D analytical map.

Main Methods:

  • * A coordinate transformation was employed to decouple oscillations and drift.
  • * A two-dimensional analytical map was developed to study bounded dynamics.

Related Experiment Videos

  • * Numerical iterations of the 2D map were performed and compared with the original system's differential equations.

    • Main Results:

    • * The transformation successfully separated bounded oscillations from drift motion.
    • * The 2D analytical map accurately represents the system's bounded dynamics.
    • * Bifurcation diagrams from the map closely matched those from the original differential equations.

    Conclusions:

    • * The proposed 2D map and graphical iteration method offer an effective tool for analyzing impact oscillators with drift.
    • * The findings simplify the study of complex dynamics in such systems, with implications for engineering applications.