Updated semi-discretization method for periodic delay-differential equations with discrete delay
Updated semi-discretization method for periodic delay-differential equations with discrete delay
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DOI：
10.1002/nme.1061
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发表时间：
2004-09-07
影响因子：
2.9
通讯作者：
Stépán, G
中科院分区：
文献类型：
--
作者：
Insperger, T;Stépán, G
针对具有单个离散时滞的周期系统，提出了一种改进的半离散化方法。将延迟项近似为两个相邻离散延迟状态值的加权和，并确定单个周期内的转移矩阵。对于不同的时间周期/时滞比，给出了阻尼型和滞后型Mathieu方程的稳定性图。通过算例研究了该方法的收敛性能。建立了1自由度和2自由度铣削模型的稳定性图。该算法的代码也附在附录中。版权所有(C)2004 John Wiley Sons，Ltd.
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.