Dynamics of Randomly Perturbed Nonlinear Structural and Mechanical Systems With Resonances

179 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003.In the second part, we investigate the dynamics of 1-DOF systems excited by both periodic and random perturbation. The near resonant motion of such systems is not well understood. We will study this problem in depth with the aim of discovering a common geometric structure in the phase space, and determine the effects of noisy perturbations on the passage of trajectories through the resonance zone. We consider the noisy, periodically driven Duffing equation as a prototypical 1-DOF system and achieve a model-reduction through stochastic averaging. The solution of the reduced model can be approximated by a Markov process. Depending on the strength of the noise, the reduced Markov process takes its values on a line or on a graph with certain gluing conditions at the vertices of the graph. The reduced model will provide a framework for computing standard statistical measures of dynamics and stability. This work will also explain a counter-intuitive phenomenon of stochastic resonance.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD