Analysis, simulation and visualization of 1D tapping via reduced dynamical models

Denis Blackmore, Anthony Rosato, Xavier Tricoche, Kevin Urban, Luo Zou

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

A low-dimensional center-of-mass dynamical model is devised as a simplified means of approximately predicting some important aspects of the motion of a vertical column comprised of a large number of particles subjected to gravity and periodic vertical tapping. This model is investigated first as a continuous dynamical system using analytical, simulation and visualization techniques. Then, by employing an approach analogous to that used to approximate the dynamics of a bouncing ball on an oscillating flat plate, it is modeled as a discrete dynamical system and analyzed to determine bifurcations and transitions to chaotic motion along with other properties. The predictions of the analysis are then compared-primarily qualitatively-with visualization and simulation results of the reduced continuous model, and ultimately with simulations of the complete system dynamics.

Original languageEnglish (US)
Pages (from-to)14-27
Number of pages14
JournalPhysica D: Nonlinear Phenomena
Volume273-274
DOIs
StatePublished - Apr 15 2014

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Keywords

  • Center of mass model
  • Discrete dynamical model
  • Newtonian models
  • Simulations
  • Visualizations

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