Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 61, Issue 1, Pages 117-141Publisher
WILEY
DOI: 10.1002/nme.1061
Keywords
time delay; periodic system; Floquet theory; linear stability
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An updated version of the semi-discretization method is presented for periodic systems with a single discrete time delay. The delayed term is approximated as a weighted sum of two neighbouring discrete delayed state values and the transition matrix over a single period is determined. Stability charts are constructed for the damped and delayed Mathieu equation for different time-period/time-delay ratios. The convergence of the method is investigated by examples. Stability charts are constructed for 1 and 2 degree of freedom milling models. The codes of the algorithm are also attached in the appendix. Copyright (C) 2004 John Wiley Sons, Ltd.
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