Analysis of a System of Linear Delay Differential Equations

[+] Author and Article Information
Farshid Maghami Asl, A. Galip Ulsoy

Mechanical Engineering Department, University of Michigan, Ann Arbor, MI 48109-2125

J. Dyn. Sys., Meas., Control 125(2), 215-223 (Jun 04, 2003) (9 pages) doi:10.1115/1.1568121 History: Received June 01, 2002; Revised January 01, 2003; Online June 04, 2003
Copyright © 2003 by ASME
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Grahic Jump Location
Roots of the characteristic equation in Eq. (11) when α=T=1, and β=0
Grahic Jump Location
Stability criteria for DDE in Eq. (3) with β=0
Grahic Jump Location
Stability criteria for the generalized first order DDE in Eq. (3)
Grahic Jump Location
Principal (k=0), second (k=1), and third (k=2) modes in the free solution form for Eq. (15)
Grahic Jump Location
Free solution for Eq. (15) for large values of N and parameter values α=1, β=1, and T=1
Grahic Jump Location
Convergence of the free solution for Eq. (15) for large values of N and parameter values α=1, β=1, and T=1
Grahic Jump Location
Free solution for Eq. (15) for different values of time delay with α=1, β=1, and T=0,0.5,1,2,4
Grahic Jump Location
Complete solution for Eq. (20) for a unit step input and parameter values α=1, β=1, and T=1
Grahic Jump Location
Stability lobes for the chatter equation




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