Wahi, Pankaj and Chatterjee, Anindya (2005) Regenerative Tool Chatter Near a Codimension 2 Hopf Point Using Multiple Scales. In: Nonlinear Dynamics, 40 (4). pp. 323-338.
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We study a well-known regenerative machine tool vibration model (a delay differential equation) near a codimension 2 Hopf bifurcation point. The method of multiple scales is used directly, bypassing a center manifold reduction. We use a nonstandard choice of expansion parameter that helps understand practically relevant aspects of the dynamics for not-too-small amplitudes. Analytical expressions are then obtained for the double Hopf points. Both sub- and supercritical bifurcations are predicted to occur near the reference point; and analytical conditions on the parameter variations for each type of bifurcation to occur are obtained as well. Analytical approximations are supported by numerics.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Springer.|
|Keywords:||Codimension 2 Hopf bifurcation;Delay differential equation; Method of multiple scales;Regenerative tool chatter|
|Department/Centre:||Division of Mechanical Sciences > Mechanical Engineering|
|Date Deposited:||30 Apr 2007|
|Last Modified:||19 Sep 2010 04:37|
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