Robust bifurcation behavior in the presence of external random excitation
Leng, Gerard Siew Bing
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Permalink
https://hdl.handle.net/2142/21936
Description
Title
Robust bifurcation behavior in the presence of external random excitation
Author(s)
Leng, Gerard Siew Bing
Issue Date
1990
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)
Engineering, Aerospace
Language
eng
Abstract
"The effects of random external excitation on systems with marginally stable/unstable (critical) modes undergoing a soft loss of stability is examined within the context of bifurcation theory. Physically the problem is motivated by the flight dynamics of aircraft at large angles of attack and sideslip in a turbulent atmosphere. A qualitative criterion for robust bifurcation behavior is suggested and it is found the bifurcation behavior of systems with one critical mode is robust in the sense that the deterministic characteristics carry over to the steady state probability density function for the system in the presence of random external excitation. For systems with two critical modes, exemplified by an aircraft with marginally stable/unstable Dutch roll and spiral modes, the bifurcation behavior is robust under special conditions on the relative degree of mode interaction and excitation intensities. Otherwise, the external excitation will exert a ""stabilizing"" effect on one critical mode only at the expense of the other. The Lyapunov exponent is then introduced as a quantitative measure of the robustness of the steady state response to small perturbations. It is found that while the Lyapunov exponent does not indicate the qualitative changes in the steady state probability density function, it does provide an indication of the relative importance of nonlinear/stochastic effects as system parameters are varied."
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