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TECHNICAL PAPERS

Stochastic Dynamics of Impact Oscillators

[+] Author and Article Information
N. Sri Namachchivaya1

Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, 104 South Wright Street, Urbana, IL 61801navam@uiuc.edu

Jun H. Park

Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, 104 South Wright Street, Urbana, IL 61801

1

To whom correspondence should be addressed.

J. Appl. Mech 72(6), 862-870 (Sep 29, 2004) (9 pages) doi:10.1115/1.2041660 History: Received February 04, 2004; Revised September 29, 2004

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.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Phase portrait and graph of system

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Figure 2

Variation of the mean exit time, t, with H

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Figure 3

Stationary density g(h): (a) effect of additive noise (r=1), (b) effect of r(μ2=2)

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Figure 4

Stationary density p(u,v): (a) μ2=1, (b) μ2=2

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Figure 5

Stationary density g(h): (a) effect of additive noise (r=1), (b) effect of r(μ2=2)

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