Bifurcation analysis near the cessation of complete chatter and Shilnikov homoclinic trajectories in a pressure relief valve model

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.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2016

Author dc:creator

• Fotsch, Erika L

Contributors dc:contributor

• Dankowicz, Harry

• non-linear dynamics
• pressure relief valve
• chatter
• Shilnikov homoclinic
• unstable manifolds
• stable manifolds
• continuation
• bifurcations

Statement dc:rights

• Copyright 2016 Erika Fotsch

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/90709

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F90709