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Title:Bifurcation analysis near the cessation of complete chatter and Shilnikov homoclinic trajectories in a pressure relief valve model
Author(s):Fotsch, Erika L
Department / Program:Mechanical Sci & Engineering
Discipline:Mechanical Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:M.S.
Genre:Thesis
Subject(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.
Issue Date:2016-01-20
Type:Thesis
URI:http://hdl.handle.net/2142/90709
Rights Information:Copyright 2016 Erika Fotsch
Date Available in IDEALS:2016-07-07
Date Deposited:2016-05


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