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Title:Periodic Delay Effects on Cutting Tool Dynamics
Author(s):Choi, Youn-Sun
Doctoral Committee Chair(s):Muncaster, Robert G.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Engineering, Mechanical
Abstract:We consider a delay equation whose delay is perturbed by a small periodic fluctuation. In Particular, it is assumed that the delay equation exhibits a Hopf bifurcation when its delay Is unperturbed. The periodically perturbed system exhibits more delicate bifurcations than a Hopf bifurcation. We show that these bifurcations are well explained by the Bogdanov-Takens bifurcations when the ration between the frequencies of the periodic solution of the Unperturbed system (Hopf bifurcation) and the external periodic perturbation is 1:2. Our anaylsis is based on center manifold reduction theory.
Issue Date:2003
Type:Text
Language:English
Description:72 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003.
URI:http://hdl.handle.net/2142/86810
Other Identifier(s):(MiAaPQ)AAI3086033
Date Available in IDEALS:2015-09-28
Date Deposited:2003


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