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.
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e-mail: nitingar@ufl.edu
e-mail: mannbr@missouri.edu
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March 2007
Technical Papers
Stability of a Time-Delayed System With Parametric Excitation
Nitin K. Garg,
Nitin K. Garg
Nonlinear Dynamics Lab, Department of Mechanical & Aerospace Engineering,
e-mail: nitingar@ufl.edu
University of Florida
, Gainesville, FL 32611
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Brian P. Mann,
Brian P. Mann
Dynamical Systems Lab, Department of Mechanical & Aerospace Engineering,
e-mail: mannbr@missouri.edu
University of Missouri
, Columbia, MO 65211
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Nam H. Kim,
Nam H. Kim
Structural and Multi-disciplinary Optimization Lab, Department of Mechanical & Aerospace Engineering,
e-mail: nkim@ufl.edu
University of Florida
, Gainesville, FL 32611
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Mohammad H. Kurdi
Mohammad H. Kurdi
Machine Tool Research Center, Department of Mechanical & Aerospace Engineering,
e-mail: mhkurdi@ufl.edu
University of Florida
, Gainesville, FL 32611
Search for other works by this author on:
Nitin K. Garg
Nonlinear Dynamics Lab, Department of Mechanical & Aerospace Engineering,
University of Florida
, Gainesville, FL 32611e-mail: nitingar@ufl.edu
Brian P. Mann
Dynamical Systems Lab, Department of Mechanical & Aerospace Engineering,
University of Missouri
, Columbia, MO 65211e-mail: mannbr@missouri.edu
Nam H. Kim
Structural and Multi-disciplinary Optimization Lab, Department of Mechanical & Aerospace Engineering,
University of Florida
, Gainesville, FL 32611e-mail: nkim@ufl.edu
Mohammad H. Kurdi
Machine Tool Research Center, Department of Mechanical & Aerospace Engineering,
University of Florida
, Gainesville, FL 32611e-mail: mhkurdi@ufl.edu
J. Dyn. Sys., Meas., Control. Mar 2007, 129(2): 125-135 (11 pages)
Published Online: May 11, 2006
Article history
Received:
September 10, 2004
Revised:
May 11, 2006
Citation
Garg, N. K., Mann, B. P., Kim, N. H., and Kurdi, M. H. (May 11, 2006). "Stability of a Time-Delayed System With Parametric Excitation." ASME. J. Dyn. Sys., Meas., Control. March 2007; 129(2): 125–135. https://doi.org/10.1115/1.2432357
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