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Stability of a time-delayed system with parametric excitation

Publication ,  Journal Article
Garg, NK; Mann, BP; Kim, NH; Kurdi, MH
Published in: Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME
March 1, 2007

This paper investigates two different temporal finite element techniques, a multiple element (h-version) and single element (p-version) method, to analyze the stability of a system with a time-periodic coefficient and a time delay. The representative problem, known as the delayed damped Mathieu equation, is chosen to illustrate the combined effect of a time delay and parametric excitation on stability. A discrete linear map is obtained by approximating the exact solution with a series expansion of orthogonal polynomials constrained at intermittent nodes. Characteristic multipliers of the map are used to determine the unstable parameter domains. Additionally, the described analysis provides a new approach to extract the Floquet transition matrix of time periodic systems without a delay. Copyright © 2007 by ASME.

Duke Scholars

Published In

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

DOI

ISSN

0022-0434

Publication Date

March 1, 2007

Volume

129

Issue

2

Start / End Page

125 / 135

Related Subject Headings

  • Industrial Engineering & Automation
  • 40 Engineering
  • 09 Engineering
 

Citation

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ICMJE
MLA
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Garg, N. K., Mann, B. P., Kim, N. H., & Kurdi, M. H. (2007). Stability of a time-delayed system with parametric excitation. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 129(2), 125–135. https://doi.org/10.1115/1.2432357
Garg, N. K., B. P. Mann, N. H. Kim, and M. H. Kurdi. “Stability of a time-delayed system with parametric excitation.” Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME 129, no. 2 (March 1, 2007): 125–35. https://doi.org/10.1115/1.2432357.
Garg NK, Mann BP, Kim NH, Kurdi MH. Stability of a time-delayed system with parametric excitation. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME. 2007 Mar 1;129(2):125–35.
Garg, N. K., et al. “Stability of a time-delayed system with parametric excitation.” Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, vol. 129, no. 2, Mar. 2007, pp. 125–35. Scopus, doi:10.1115/1.2432357.
Garg NK, Mann BP, Kim NH, Kurdi MH. Stability of a time-delayed system with parametric excitation. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME. 2007 Mar 1;129(2):125–135.

Published In

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

DOI

ISSN

0022-0434

Publication Date

March 1, 2007

Volume

129

Issue

2

Start / End Page

125 / 135

Related Subject Headings

  • Industrial Engineering & Automation
  • 40 Engineering
  • 09 Engineering