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Observation and investigation of a non-monotonic period function for an impact oscillator

Publication ,  Journal Article
Chicone, C; Felts, K; Mann, B
Published in: Communications in Nonlinear Science and Numerical Simulation
May 1, 2009

A mathematical model for a bench-top impact oscillator (a steel pendulum and an aluminum barrier) that incorporates Hertzian contact is analyzed, and predictions derived from our model are compared with experimental data. We report our discovery of a new effect: the existence of a non-monotone period function for the annulus of periodic orbits in the phase plane surrounding the rest point that corresponds to the downward vertical position of the pendulum in the unforced, undamped case. From this non-monotonicity, we predict novel resonance response behavior for the forced, damped oscillator and verify our predictions by experiment. © 2008 Elsevier B.V. All rights reserved.

Duke Scholars

Published In

Communications in Nonlinear Science and Numerical Simulation

DOI

ISSN

1007-5704

Publication Date

May 1, 2009

Volume

14

Issue

5

Start / End Page

2415 / 2425

Related Subject Headings

  • Mathematical Physics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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Chicone, C., Felts, K., & Mann, B. (2009). Observation and investigation of a non-monotonic period function for an impact oscillator. Communications in Nonlinear Science and Numerical Simulation, 14(5), 2415–2425. https://doi.org/10.1016/j.cnsns.2008.06.009
Chicone, C., K. Felts, and B. Mann. “Observation and investigation of a non-monotonic period function for an impact oscillator.” Communications in Nonlinear Science and Numerical Simulation 14, no. 5 (May 1, 2009): 2415–25. https://doi.org/10.1016/j.cnsns.2008.06.009.
Chicone C, Felts K, Mann B. Observation and investigation of a non-monotonic period function for an impact oscillator. Communications in Nonlinear Science and Numerical Simulation. 2009 May 1;14(5):2415–25.
Chicone, C., et al. “Observation and investigation of a non-monotonic period function for an impact oscillator.” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, May 2009, pp. 2415–25. Scopus, doi:10.1016/j.cnsns.2008.06.009.
Chicone C, Felts K, Mann B. Observation and investigation of a non-monotonic period function for an impact oscillator. Communications in Nonlinear Science and Numerical Simulation. 2009 May 1;14(5):2415–2425.
Journal cover image

Published In

Communications in Nonlinear Science and Numerical Simulation

DOI

ISSN

1007-5704

Publication Date

May 1, 2009

Volume

14

Issue

5

Start / End Page

2415 / 2425

Related Subject Headings

  • Mathematical Physics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics