Stability of a time-delayed system with parametric excitation
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.
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- Industrial Engineering & Automation
- 40 Engineering
- 09 Engineering
Citation
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Industrial Engineering & Automation
- 40 Engineering
- 09 Engineering