Dynamics of Randomly Perturbed Nonlinear Structural and Mechanical Systems With Resonances
Choi, Seunggil
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https://hdl.handle.net/2142/85077
Description
Title
Dynamics of Randomly Perturbed Nonlinear Structural and Mechanical Systems With Resonances
Author(s)
Choi, Seunggil
Issue Date
2003
Doctoral Committee Chair(s)
Namachchivaya, N. Sri
Department of Study
Aerospace Engineering
Discipline
Aerospace Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Language
eng
Abstract
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.
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