Tapping dynamics for a column of particles and beyond

Denis Blackmore, Anthony Rosato, Xavier Tricoche, Kevin Urban, Vishagan Ratnaswamy

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The dynamics of a vertical stack of particles subject to gravity and a sequence of small, periodically applied taps is considered. First, the motion of the particles, assumed to be identical, is modeled as a system of ordinary differential equations, which is analyzed with an eye to observing connections with finite-dimensional Hamiltonian systems. Then, two approaches to obtaining approximate continuum models for large numbers of particles are described: the long-wave approximation that yields partial differential equations and the BSR method that employs integro-partial differential models. These approximate continuum models, which comprise infinite-dimensional dynamical systems, are studied with a focus on nonlinear wave type behavior, which naturally leads to investigating links to infinitedimensional Hamiltonian systems. Several examples are solved numerically to show similarities among the solution properties of the finite-dimensional (lattice-dynamics), and the approximate long-wave and BSR continuum models. Extensions to higher dimensions and more general dynamically driven particle configurations are also sketched.

Original languageEnglish (US)
Pages (from-to)71-86
Number of pages16
JournalJournal of Mechanics of Materials and Structures
Issue number1-4
StatePublished - 2011

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Applied Mathematics


  • BSR approximation
  • Hamiltonian system
  • Long-wave limit
  • Newtonian models
  • Periodic taps


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