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Dynamics of rocking semicircular, parabolic, and semi-elliptical disks: Equilibria, stability, and natural frequencies

Publication ,  Journal Article
Mazzoleni, MJ; Krone, MB; Mann, BP
Published in: Journal of Vibration and Acoustics
August 1, 2015

This paper performs a theoretical and experimental investigation of the natural frequency and stability of rocking semicircular, parabolic, and semi-elliptical disks. Horace Lamb's method for deriving the natural frequency of an arbitrary rocking disk is applied to three shapes with semicircular, parabolic, and semi-elliptical cross sections, respectively. For the case of the semicircular disk, the system's equation of motion is derived to verify Lamb's method. Additionally, the rocking semicircular disk is found to always have one stable equilibrium position. For the cases of the parabolic and semi-elliptical disks, this investigation reveals a supercritical pitchfork bifurcation for changes in a single geometric parameter which indicates that the systems can exhibit bistable behavior. Comparisons between experimental validation and theory show good agreement.

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Published In

Journal of Vibration and Acoustics

DOI

EISSN

1528-8927

ISSN

1048-9002

Publication Date

August 1, 2015

Volume

137

Issue

4

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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Mazzoleni, M. J., Krone, M. B., & Mann, B. P. (2015). Dynamics of rocking semicircular, parabolic, and semi-elliptical disks: Equilibria, stability, and natural frequencies. Journal of Vibration and Acoustics, 137(4). https://doi.org/10.1115/1.4030169
Mazzoleni, M. J., M. B. Krone, and B. P. Mann. “Dynamics of rocking semicircular, parabolic, and semi-elliptical disks: Equilibria, stability, and natural frequencies.” Journal of Vibration and Acoustics 137, no. 4 (August 1, 2015). https://doi.org/10.1115/1.4030169.
Mazzoleni MJ, Krone MB, Mann BP. Dynamics of rocking semicircular, parabolic, and semi-elliptical disks: Equilibria, stability, and natural frequencies. Journal of Vibration and Acoustics. 2015 Aug 1;137(4).
Mazzoleni, M. J., et al. “Dynamics of rocking semicircular, parabolic, and semi-elliptical disks: Equilibria, stability, and natural frequencies.” Journal of Vibration and Acoustics, vol. 137, no. 4, Aug. 2015. Scopus, doi:10.1115/1.4030169.
Mazzoleni MJ, Krone MB, Mann BP. Dynamics of rocking semicircular, parabolic, and semi-elliptical disks: Equilibria, stability, and natural frequencies. Journal of Vibration and Acoustics. 2015 Aug 1;137(4).

Published In

Journal of Vibration and Acoustics

DOI

EISSN

1528-8927

ISSN

1048-9002

Publication Date

August 1, 2015

Volume

137

Issue

4

Related Subject Headings

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