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 Poincaré 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.
Analytical Method for Stroboscopically Sampling General Periodic Functions With Arbitrary Frequency Sweep Rates
Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 12, 2018; final manuscript received April 18, 2018; published online May 10, 2018. Assoc. Editor: Izhak Bucher.
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Sequeira, D., Wang, X., and Mann, B. (May 10, 2018). "Analytical Method for Stroboscopically Sampling General Periodic Functions With Arbitrary Frequency Sweep Rates." ASME. J. Vib. Acoust. December 2018; 140(6): 064701. https://doi.org/10.1115/1.4040046
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