University of Illinois Urbana-Champaign

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

Fotsch, Erika L

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

Description

Title
Bifurcation analysis near the cessation of complete chatter and Shilnikov homoclinic trajectories in a pressure relief valve model
Author(s)
Fotsch, Erika L
Issue Date
2016-01-20
Director of Research (if dissertation) or Advisor (if thesis)
Dankowicz, Harry
Department of Study
Mechanical Sci & Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
  • non-linear dynamics
  • pressure relief valve
  • chatter
  • Shilnikov homoclinic
  • unstable manifolds
  • stable manifolds
  • continuation
  • bifurcations
Abstract
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.
Graduation Semester
2016-05
Type of Resource
text
Permalink
http://hdl.handle.net/2142/90709
Copyright and License Information
Copyright 2016 Erika Fotsch

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