Updated semi-discretization method for periodic delay-differential equations with discrete delay. (English) Zbl 1083.70002

Summary: 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.


70-08 Computational methods for problems pertaining to mechanics of particles and systems
70J30 Free motions in linear vibration theory
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