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Noisy Impact Oscillators

[+] Author Affiliations
Jun H. Park, N. Sri Namachchivaya

University of Illinois at Urbana-Champaign

Paper No. IMECE2004-60861, pp. 189-200; 12 pages
doi:10.1115/IMECE2004-60861
From:
  • ASME 2004 International Mechanical Engineering Congress and Exposition
  • Applied Mechanics
  • Anaheim, California, USA, November 13 – 19, 2004
  • Conference Sponsors: Applied Mechanics Division
  • ISBN: 0-7918-4702-0 | eISBN: 0-7918-4178-2, 0-7918-4179-0, 0-7918-4180-4
  • Copyright © 2004 by ASME

abstract

The purpose of this work is to develop an averaging approach to study the dynamics of a vibro-impact system excited by random perturbations. As a prototype, we consider a noisy single-degree-of-freedom equation with both positive and negative stiffness and achieve a model reduction; i.e., the development of rigorous methods to replace in some asymptotic regime, a complicated system by a simpler one. To this end, we study the equations as a random perturbation of a two-dimensional weakly dissipative Hamiltonian system with either center type or saddle type fixed points. We achieve the model-reduction through stochastic averaging. Examination of the reduced Markov process on a graph yields mean exit times, probability density functions, and stochastic bifurcations.

Copyright © 2004 by ASME

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