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Grazing impact oscillations

de Weger J1, van De Water W, Molenaar

  • 1Physics Department, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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This study investigates grazing impacts in mechanical oscillators, revealing a predictable series of period-adding transitions. These dynamics are robust and can be described by simple mathematical models, offering insights into complex oscillatory systems.

Area of Science:

  • Nonlinear Dynamics
  • Mechanical Oscillations
  • Complex Systems

Background:

  • Impact oscillators exhibit complex behaviors when colliding with a boundary.
  • Grazing impacts, characterized by near-zero collision velocities, present unique dynamical phenomena.
  • Period-adding bifurcations are a hallmark of grazing impact dynamics.

Purpose of the Study:

  • To experimentally explore the dynamics of impact oscillators near period-adding transitions.
  • To characterize the system using a minimal set of parameters despite complex harmonic excitation.
  • To validate mathematical models describing grazing impact dynamics.

Main Methods:

  • Experimental setup of a mechanical impact oscillator with controlled driving strength.
  • Observation and analysis of period-M orbits arising from period-adding bifurcations.

Related Experiment Videos

  • Comparison of experimental results with numerical simulations of impacting harmonic oscillators.
  • Evaluation of mathematical mappings, including those with square-root singularities, for describing grazing impacts.

    • Main Results:

    • Observed a geometrically converging series of period-adding transitions in experimental grazing impacts.
    • Successfully characterized the complex dynamics with only three parameters.
    • Demonstrated good agreement between experimental data and numerical simulations.
    • Identified a persistent square-root singularity in mappings describing impact dynamics.

    Conclusions:

    • Grazing impact dynamics exhibit a robust and characteristic period-adding bifurcation scenario.
    • Simple mathematical models with square-root singularities effectively capture the essential dynamics.
    • The observed dynamics are insensitive to experimental nonidealities, suggesting broad applicability.