Periodic Delay Effects on Cutting Tool Dynamics

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Choi, Youn-Sun

Contributors dc:contributor

• Muncaster, Robert G.

• Engineering, Mechanical

Language dc:language

eng

Identifier

(MiAaPQ)AAI3086033

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86810