Nonlinear Systems Group                                 University of Illinois at Urbana-Champaign

Director: N. Sri. Namachchivaya 306 Talbot Laboratory, 104 South Wright Street Urbana, IL 61801 Phone: (217) 244-0683, Fax: (217) 244-0720 E-mail: navam@uiuc.edu Department of Aerospace Engineering Created: 11/16/2003 Last Updated: 11/16/2003			Non-smooth Dynamical Systems   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.