{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/21936"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/21936","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Robust bifurcation behavior in the presence of external random excitation","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.\"","abstract_html":""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."","abstract_has_math":false,"creators":["Leng, Gerard Siew Bing"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Aerospace Engineering","degree_department":null,"school":null,"contributors":["Namachchivaya, N. Sri"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:23:43Z","date_published":"2011-05-07T13:23:43Z","updated_at":"2026-07-22T22:25:19Z","subjects":["Engineering, Aerospace"],"languages":["eng"],"rights":["Copyright 1990 Leng, Gerard Siew Bing"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9114312","(UMI)AAI9114312"],"render_values":[{"text":"AAI9114312","href":null,"code":true},{"text":"(UMI)AAI9114312","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/21936","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Namachchivaya, N. 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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.\"","Made available in DSpace on 2011-05-07T13:23:43Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9114312.pdf: 5517789 bytes, checksum: 82c46d30cf9078286a956d7c1661c880 (MD5) Previous issue date: 1990","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:54:12Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:25:10-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Robust bifurcation behavior in the presence of external random excitation"]}]}],"canonical_facts":{"dc:contributor":["Namachchivaya, N. Sri"],"dc:creator":["Leng, Gerard Siew Bing"],"dc:date":["2011-05-07T13:23:43Z","10000-01-01","1990"],"dc:description":["\"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.\"","Made available in DSpace on 2011-05-07T13:23:43Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9114312.pdf: 5517789 bytes, checksum: 82c46d30cf9078286a956d7c1661c880 (MD5) Previous issue date: 1990","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:54:12Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:25:10-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9114312","(UMI)AAI9114312","http://hdl.handle.net/2142/21936"],"dc:language":["eng"],"dc:rights":["Copyright 1990 Leng, Gerard Siew Bing"],"dc:subject":["Engineering, Aerospace"],"dc:title":["Robust bifurcation behavior in the presence of external random excitation"],"dc:type":["text"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:19Z"}