Refined theories are employed to study nonlinear vibrations of elastic rings in the mth flexural mode away from autoparametric resonances involving other flexural modes. A top-down modeling approach is followed to describe the rings undergoing all deformation modes in space by the Special Cosserat theory of curved rods. The specialization to extensional-flexural-shearing, then to extensional-flexural, and finally to purely flexural planar motions is illustrated. Free undamped extensional-flexural nonlinear motions involving the mth mode and its companion mode are investigated via a direct asymptotic approach based on the method of multiple scales applied to the geometrically exact equations of motion and it is shown that these motions are softening for linearly elastic rings while there are thresholds in the constitutive laws separating softening from hardening behaviors.
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ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 4–7, 2013
Portland, Oregon, USA
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-5596-6
PROCEEDINGS PAPER
Nonlinear Flexural Vibrations of Unshearable Elastic Rings
Walter Lacarbonara,
Walter Lacarbonara
Sapienza University of Rome, Rome, Italy
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Andrea Arena,
Andrea Arena
Sapienza University of Rome, Rome, Italy
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Stuart S. Antman
Stuart S. Antman
University of Maryland, College Park, MD
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Walter Lacarbonara
Sapienza University of Rome, Rome, Italy
Andrea Arena
Sapienza University of Rome, Rome, Italy
Stuart S. Antman
University of Maryland, College Park, MD
Paper No:
DETC2013-12427, V07AT10A061; 9 pages
Published Online:
February 12, 2014
Citation
Lacarbonara, W, Arena, A, & Antman, SS. "Nonlinear Flexural Vibrations of Unshearable Elastic Rings." Proceedings of the ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 7A: 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Portland, Oregon, USA. August 4–7, 2013. V07AT10A061. ASME. https://doi.org/10.1115/DETC2013-12427
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