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

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

Fotsch, Erika L ; Dankowicz ; Harry

关键词: non-linear dynamics;    pressure relief valve;    chatter;    Shilnikov homoclinic;    unstable manifolds;    stable manifolds;    continuation;    bifurcations;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/90709/FOTSCH-THESIS-2016.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.