Updated semi‐discretization method for periodic delay‐differential equations with discrete delay

descriptionPublicationkeyboard_double_arrow_right Article 21 Jul 2004 English Publisher:WileyJournal:International Journal for Numerical Methods in Engineering, volume 61, pages 117-141 (issn: 0029-5981, eissn: 1097-0207,

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Authors: Insperger, Tamás; Stépán, Gábor;

doi: 10.1002/nme.1061

Updated semi‐discretization method for periodic delay‐differential equations with discrete delay

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Abstract

AbstractAn 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 © 2004 John Wiley & Sons, Ltd.

Related Organizations

Budapest University of Technology and Economics
Hungary

Keywords

Mathieu equation, Free motions in linear vibration theory, Computational methods for problems pertaining to mechanics of particles and systems, transition matrix, linear stability

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