A Nonlinear Delay-Differential Equation with Harmonic Excitation

被引：1

作者：

Lelkes, Janos ^{[1
]}

Kalmar-Nagy, Tamas ^{[1
]}

机构：

[1] Budapest Univ Technol & Econ, Fac Mech Engn, Dept Fluid Mech, H-1111 Budapest, Hungary

来源：

IFAC PAPERSONLINE | 2018年 / 51卷 / 14期

关键词：

delay-differential equation; method of multiple scales; harmonic excitation; Hopf bifurcation; primary resonance; BIFURCATION; SYSTEMS;

D O I：

10.1016/j.ifacol.2018.07.227

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A machining tool can be subject to different kinds of excitations. The forcing may have external sources (such as rotating imbalance or misalignment of the workpiece) or it can arise from the cutting process itself (e.g. chip formation). We investigate the classical tool vibration model which is a delay-differential equation with a quadratic and cubic nonlinearity and periodic forcing. The method of multiple scales gave an excellent approximation of the solution. The resonance curves found here are similar to those for the Duffing-equation, having a hardening characteristic. We found subcritical Hopf and saddle-node bifurcations. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

引用

页码：224 / 229

页数：6

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