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Investigation of rocking semicircular and parabolic disk equilibria, stability, and natural frequencies

Publication ,  Conference
Mazzoleni, MJ; Krone, MB; Mann, BP
Published in: Proceedings of the ASME Design Engineering Technical Conference
January 1, 2014

This paper performs a theoretical and experimental investigation of the natural frequency and stability of rocking semicircular and parabolic disks. Horace Lamb's method for deriving the natural frequency of an arbitrary rocking disk is applied to two shapes with semicircular and parabolic 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 case of the parabolic disk, this investigation unveils a super-critical pitchfork bifurcation for changes in a single geometric parameter which reveals that the system can exhibit bistable behavior. Rapid prototyping technology was used to manufacture sample disks across a wide range of parameters, and a laser tachometer was used to experimentally determine the natural frequency of each disk. Comparisons between experiment and theory show good agreement.

Duke Scholars

Published In

Proceedings of the ASME Design Engineering Technical Conference

DOI

ISBN

9780791846414

Publication Date

January 1, 2014

Volume

8
 

Citation

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MLA
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Mazzoleni, M. J., Krone, M. B., & Mann, B. P. (2014). Investigation of rocking semicircular and parabolic disk equilibria, stability, and natural frequencies. In Proceedings of the ASME Design Engineering Technical Conference (Vol. 8). https://doi.org/10.1115/DETC2014-34396
Mazzoleni, M. J., M. B. Krone, and B. P. Mann. “Investigation of rocking semicircular and parabolic disk equilibria, stability, and natural frequencies.” In Proceedings of the ASME Design Engineering Technical Conference, Vol. 8, 2014. https://doi.org/10.1115/DETC2014-34396.
Mazzoleni MJ, Krone MB, Mann BP. Investigation of rocking semicircular and parabolic disk equilibria, stability, and natural frequencies. In: Proceedings of the ASME Design Engineering Technical Conference. 2014.
Mazzoleni, M. J., et al. “Investigation of rocking semicircular and parabolic disk equilibria, stability, and natural frequencies.” Proceedings of the ASME Design Engineering Technical Conference, vol. 8, 2014. Scopus, doi:10.1115/DETC2014-34396.
Mazzoleni MJ, Krone MB, Mann BP. Investigation of rocking semicircular and parabolic disk equilibria, stability, and natural frequencies. Proceedings of the ASME Design Engineering Technical Conference. 2014.

Published In

Proceedings of the ASME Design Engineering Technical Conference

DOI

ISBN

9780791846414

Publication Date

January 1, 2014

Volume

8