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 Copy

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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