{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/85077"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/85077","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Dynamics of Randomly Perturbed Nonlinear Structural and Mechanical Systems With Resonances","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Choi, Seunggil"],"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":2015,"date_issued":"2015-09-25T22:34:20Z","date_published":"2015-09-25T22:34:20Z","updated_at":"2026-07-22T22:26:24Z","subjects":["Applied Mechanics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3086032"],"render_values":[{"text":"(MiAaPQ)AAI3086032","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/85077","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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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.","Made available in DSpace on 2015-09-25T22:34:20Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3086032.pdf: 6299862 bytes, checksum: 02763ce8f42059af1f5fd5b85440ca67 (MD5) Previous issue date: 2003","Embargo set by: Seth Robbins for item 86358 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","179 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003."]},{"key":"dc:title","label":"Title","values":["Dynamics of Randomly Perturbed Nonlinear Structural and Mechanical Systems With Resonances"]}]}],"canonical_facts":{"dc:contributor":["Namachchivaya, N. Sri"],"dc:creator":["Choi, Seunggil"],"dc:date":["2015-09-25T22:34:20Z","10000-01-01","2003"],"dc:description":["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.","Made available in DSpace on 2015-09-25T22:34:20Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3086032.pdf: 6299862 bytes, checksum: 02763ce8f42059af1f5fd5b85440ca67 (MD5) Previous issue date: 2003","Embargo set by: Seth Robbins for item 86358 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","179 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003."],"dc:identifier":["http://hdl.handle.net/2142/85077","(MiAaPQ)AAI3086032"],"dc:language":["eng"],"dc:subject":["Applied Mechanics"],"dc:title":["Dynamics of Randomly Perturbed Nonlinear Structural and Mechanical Systems With Resonances"],"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":"2026-07-22T22:26:24Z"}