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Analytical Method for Stroboscopically Sampling General Periodic Functions with Arbitrary Frequency Sweep Rates

Publication ,  Journal Article
Sequeira, D; Wang, XS; Mann, B
Published in: Journal of Vibration and Acoustics
December 1, 2018

Parameter sweeps are commonly used to explore the behavior of dynamical systems. This paper derives exact solutions for the instances in time to stroboscopically sample the response of a dynamical system subject to varying input excitations. This work will enable more accurate bifurcation diagrams and Poincare sections in parameter regimes where numerical approaches may lead to incorrect behavior characterization. The simplest case of a linear frequency sweep is first considered before generalizing the results to include more complex functions with nonlinear sweep rates and arbitrary phase shifts.

Duke Scholars

Published In

Journal of Vibration and Acoustics

DOI

EISSN

1528-8927

ISSN

1048-9002

Publication Date

December 1, 2018

Volume

140

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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ICMJE
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Sequeira, D., Wang, X. S., & Mann, B. (2018). Analytical Method for Stroboscopically Sampling General Periodic Functions with Arbitrary Frequency Sweep Rates. Journal of Vibration and Acoustics, 140(6). https://doi.org/10.1115/1.4040046
Sequeira, D., X. S. Wang, and B. Mann. “Analytical Method for Stroboscopically Sampling General Periodic Functions with Arbitrary Frequency Sweep Rates.” Journal of Vibration and Acoustics 140, no. 6 (December 1, 2018). https://doi.org/10.1115/1.4040046.
Sequeira D, Wang XS, Mann B. Analytical Method for Stroboscopically Sampling General Periodic Functions with Arbitrary Frequency Sweep Rates. Journal of Vibration and Acoustics. 2018 Dec 1;140(6).
Sequeira, D., et al. “Analytical Method for Stroboscopically Sampling General Periodic Functions with Arbitrary Frequency Sweep Rates.” Journal of Vibration and Acoustics, vol. 140, no. 6, Dec. 2018. Scopus, doi:10.1115/1.4040046.
Sequeira D, Wang XS, Mann B. Analytical Method for Stroboscopically Sampling General Periodic Functions with Arbitrary Frequency Sweep Rates. Journal of Vibration and Acoustics. 2018 Dec 1;140(6).

Published In

Journal of Vibration and Acoustics

DOI

EISSN

1528-8927

ISSN

1048-9002

Publication Date

December 1, 2018

Volume

140

Issue

6

Related Subject Headings

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