{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/90709"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/90709","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Bifurcation analysis near the cessation of complete chatter and Shilnikov homoclinic trajectories in a pressure relief valve model","abstract":"The student, Erika Fotsch, submitted this Thesis for approval on 2016-01-19 at 09:37.","abstract_html":"The student, Erika Fotsch, submitted this Thesis for approval on 2016-01-19 at 09:37.","abstract_has_math":false,"creators":["Fotsch, Erika L"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Dankowicz, Harry"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-07-07T20:26:40Z","date_published":"2016-07-07T20:26:40Z","updated_at":"2026-07-22T22:26:34Z","subjects":["non-linear dynamics","pressure relief valve","chatter","Shilnikov homoclinic","unstable manifolds","stable manifolds","continuation","bifurcations"],"languages":["en"],"rights":["Copyright 2016 Erika Fotsch"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/90709","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dankowicz, Harry"]},{"key":"dc:creator","label":"Author","values":["Fotsch, Erika L"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2016-07-07T20:26:40Z","2018-07-08T09:15:36Z","2016-01-20","2016-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["non-linear dynamics","pressure relief valve","chatter","Shilnikov homoclinic","unstable manifolds","stable manifolds","continuation","bifurcations"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2016 Erika Fotsch"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/90709"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The student, Erika Fotsch, submitted this Thesis for approval on 2016-01-19 at 09:37.","This Thesis was approved for publication on 2016-01-20 at 11:02.","DSpace SAF Submission Ingestion Package generated from Vireo submission #9039 on 2016-07-07 at 13:48:04","This thesis investigates bifurcations associated with periodic orbits with complete chatter, as well as bifurcations associated with homoclinic trajectories, in the dynamics of a pressure relief valve model. A combination of original numerical implementations with analytical tools found in the existing literature enables a deeper understanding of the dependence of the valve dynamics on system parameters. In particular, the transition from complete to incomplete chatter along a family of periodic orbits is explored to find a cascade of bifurcations that are then investigated further using a discrete-time approximation to the system dynamics. In addition, a toolbox that formulates a boundary value problem associated with a complete chatter sequence is developed within the computational framework of the continuation package coco. Lastly, a Shilnikov-type homoclinic bifurcation is located and the global manifold structure near this bifurcation point is explored using continuation methods applied to appropriate boundary value problems.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2018-05-01","The student, Erika Fotsch, accepted the attached license on 2016-01-19 at 09:30.","Made available in DSpace on 2016-07-07T20:26:40Z (GMT). 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A combination of original numerical implementations with analytical tools found in the existing literature enables a deeper understanding of the dependence of the valve dynamics on system parameters. In particular, the transition from complete to incomplete chatter along a family of periodic orbits is explored to find a cascade of bifurcations that are then investigated further using a discrete-time approximation to the system dynamics. In addition, a toolbox that formulates a boundary value problem associated with a complete chatter sequence is developed within the computational framework of the continuation package coco. Lastly, a Shilnikov-type homoclinic bifurcation is located and the global manifold structure near this bifurcation point is explored using continuation methods applied to appropriate boundary value problems.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2018-05-01","The student, Erika Fotsch, accepted the attached license on 2016-01-19 at 09:30.","Made available in DSpace on 2016-07-07T20:26:40Z (GMT). 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