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A robust semi-analytical method for calculating the response sensitivity of a time delay system

Publication ,  Journal Article
Kurdi, MH; Haftka, RT; Schmitz, TL; Mann, BP
Published in: Journal of Vibration and Acoustics
January 1, 2008

It is often necessary to establish the sensitivity of an engineering system's response to variations in the process/control parameters. Applications of the calculated sensitivity include gradient-based optimization and uncertainty quantification, which generally require an efficient and robust sensitivity calculation method. In this paper, the sensitivity of the milling process, which can be modeled by a set of time delay differential equations, to variations in the input parameters is calculated. The semi-analytical derivative of the maximum eigenvalue provides the necessary information for determining the sensitivity of the process stability to input variables. Comparison with the central finite difference derivative of the stability boundary shows that the semi-analytical approach is more efficient and robust with respect to step size and numerical accuracy of the response. An investigation of the source of inaccuracy of the finite difference approximation found that it is caused by discontinuities associated with the iterative process of root finding using the bisection method. Copyright © 2008 by ASME.

Duke Scholars

Published In

Journal of Vibration and Acoustics

DOI

ISSN

1048-9002

Publication Date

January 1, 2008

Volume

130

Issue

6

Related Subject Headings

  • Acoustics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0915 Interdisciplinary Engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering
 

Citation

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MLA
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Kurdi, M. H., Haftka, R. T., Schmitz, T. L., & Mann, B. P. (2008). A robust semi-analytical method for calculating the response sensitivity of a time delay system. Journal of Vibration and Acoustics, 130(6). https://doi.org/10.1115/1.2981093
Kurdi, M. H., R. T. Haftka, T. L. Schmitz, and B. P. Mann. “A robust semi-analytical method for calculating the response sensitivity of a time delay system.” Journal of Vibration and Acoustics 130, no. 6 (January 1, 2008). https://doi.org/10.1115/1.2981093.
Kurdi MH, Haftka RT, Schmitz TL, Mann BP. A robust semi-analytical method for calculating the response sensitivity of a time delay system. Journal of Vibration and Acoustics. 2008 Jan 1;130(6).
Kurdi, M. H., et al. “A robust semi-analytical method for calculating the response sensitivity of a time delay system.” Journal of Vibration and Acoustics, vol. 130, no. 6, Jan. 2008. Scopus, doi:10.1115/1.2981093.
Kurdi MH, Haftka RT, Schmitz TL, Mann BP. A robust semi-analytical method for calculating the response sensitivity of a time delay system. Journal of Vibration and Acoustics. 2008 Jan 1;130(6).

Published In

Journal of Vibration and Acoustics

DOI

ISSN

1048-9002

Publication Date

January 1, 2008

Volume

130

Issue

6

Related Subject Headings

  • Acoustics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0915 Interdisciplinary Engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering