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Dynamics of unforced and vertically forced rocking elliptical and semi-elliptical disks

Publication ,  Journal Article
Wang, XS; Mazzoleni, MJ; Mann, BP
Published in: Journal of Sound and Vibration
March 17, 2018

This paper presents the results of an investigation on the dynamics of unforced and vertically forced rocking elliptical and semi-elliptical disks. The full equation of motion for both rocking disks is derived from first principles. For unforced behavior, Lamb's method is used to derive the linear natural frequency of both disks, and harmonic balance is used to determine their amplitude-dependent rocking frequencies. A stability analysis then reveals that the equilibria and stability of the two disks are considerably different, as the semi-elliptical disk has a super-critical pitchfork bifurcation that enables it to exhibit bistable rocking behavior. Experimental studies were conducted to verify the trends. For vertically forced behavior, numerical investigations show the disk's responses to forward and reverse frequency sweeps. Three modes of periodicity were observed for the steady state behavior. Experiments were performed to verify the frequency responses and the presence of the three rocking modes. Comparisons between the experiments and numerical investigations show good agreement.

Duke Scholars

Published In

Journal of Sound and Vibration

DOI

EISSN

1095-8568

ISSN

0022-460X

Publication Date

March 17, 2018

Volume

417

Start / End Page

341 / 358

Related Subject Headings

  • Acoustics
  • 09 Engineering
  • 02 Physical Sciences
 

Citation

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Wang, X. S., Mazzoleni, M. J., & Mann, B. P. (2018). Dynamics of unforced and vertically forced rocking elliptical and semi-elliptical disks. Journal of Sound and Vibration, 417, 341–358. https://doi.org/10.1016/j.jsv.2017.12.003
Wang, X. S., M. J. Mazzoleni, and B. P. Mann. “Dynamics of unforced and vertically forced rocking elliptical and semi-elliptical disks.” Journal of Sound and Vibration 417 (March 17, 2018): 341–58. https://doi.org/10.1016/j.jsv.2017.12.003.
Wang XS, Mazzoleni MJ, Mann BP. Dynamics of unforced and vertically forced rocking elliptical and semi-elliptical disks. Journal of Sound and Vibration. 2018 Mar 17;417:341–58.
Wang, X. S., et al. “Dynamics of unforced and vertically forced rocking elliptical and semi-elliptical disks.” Journal of Sound and Vibration, vol. 417, Mar. 2018, pp. 341–58. Scopus, doi:10.1016/j.jsv.2017.12.003.
Wang XS, Mazzoleni MJ, Mann BP. Dynamics of unforced and vertically forced rocking elliptical and semi-elliptical disks. Journal of Sound and Vibration. 2018 Mar 17;417:341–358.
Journal cover image

Published In

Journal of Sound and Vibration

DOI

EISSN

1095-8568

ISSN

0022-460X

Publication Date

March 17, 2018

Volume

417

Start / End Page

341 / 358

Related Subject Headings

  • Acoustics
  • 09 Engineering
  • 02 Physical Sciences