This paper considers the theoretical response of a base-excited post-buckled beam. A mass that can be varied was attached to the midspan of the clamped-clamped beam. The theoretical model for the post-buckled beam was first investigated by applying the extended Hamilton principle to obtain a partial differential equation for beam motion carrying a central mass. This equation was used to analyze the behavior of the pre- and post-buckled natural frequencies in terms of the axial load. The first three buckled configurations were then examined, and plots showing the pre- and post-buckled modal frequencies were constructed. It was found that the addition of a central mass to the beam significantly lowered its first natural frequency, while the second frequency was relatively unaffected. A set of experiments were performed and it was shown that adding a mass on the beam increased the occurrence of snap through behavior. This nonlinear behavior produced large displacements and chaotic behavior.
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ASME 2010 Dynamic Systems and Control Conference
September 12–15, 2010
Cambridge, Massachusetts, USA
Conference Sponsors:
- Dynamic Systems and Control Division
ISBN:
978-0-7918-4418-2
PROCEEDINGS PAPER
Investigations of Natural Frequencies and Vibration Mode Shapes for a Post-Buckled Beam With Different Attached Masses
Pascaline Cette,
Pascaline Cette
Duke University, Durham, NC
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Adam J. Sneller,
Adam J. Sneller
Duke University, Durham, NC
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Brian P. Mann
Brian P. Mann
Duke University, Durham, NC
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Pascaline Cette
Duke University, Durham, NC
Adam J. Sneller
Duke University, Durham, NC
Brian P. Mann
Duke University, Durham, NC
Paper No:
DSCC2010-4025, pp. 569-576; 8 pages
Published Online:
January 25, 2011
Citation
Cette, P, Sneller, AJ, & Mann, BP. "Investigations of Natural Frequencies and Vibration Mode Shapes for a Post-Buckled Beam With Different Attached Masses." Proceedings of the ASME 2010 Dynamic Systems and Control Conference. ASME 2010 Dynamic Systems and Control Conference, Volume 2. Cambridge, Massachusetts, USA. September 12–15, 2010. pp. 569-576. ASME. https://doi.org/10.1115/DSCC2010-4025
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