2026-09-22T09:41:01Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/90709 2023-07-11 col_2142_5131 com_2142_5130

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 Dankowicz, Harry Fotsch, Erika L 2016-07-07T20:26:40Z 2016-07-07T20:26:40Z 2018-07-08T09:15:36Z 2016-01-20 2016-05 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). No. of bitstreams: 2 FOTSCH-THESIS-2016.pdf: 2882489 bytes, checksum: 7a432e17f0549fca09dc222d606eb94f (MD5) LICENSE.txt: 4209 bytes, checksum: f220c62beb140b992c5d1809f1abc46d (MD5) Previous issue date: 2016-01-20 Embargo set by: Seth Robbins for item 93061 Lift date: 2018-07-07T20:28:14Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 93061 Lift date: 2018-07-07T20:35:34Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system U of I Only Restriction Lifted for Item 93061 on 2018-07-08T09:15:36Z. application/pdf http://hdl.handle.net/2142/90709 en Copyright 2016 Erika Fotsch non-linear dynamics pressure relief valve chatter Shilnikov homoclinic unstable manifolds stable manifolds continuation bifurcations Bifurcation analysis near the cessation of complete chatter and Shilnikov homoclinic trajectories in a pressure relief valve model text text Mechanical Sci & Engineering Mechanical Engineering University of Illinois at Urbana-Champaign Thesis M.S.