Julius Kaplunov j.kaplunov@keele.ac.uk
Vibrations of an elastic cylindrical shell near the lowest cut-off frequency
Kaplunov, J.; Manevitch, L.I.; Smirnov, V.V.
Authors
L.I. Manevitch
V.V. Smirnov
Abstract
A new asymptotic approximation of the dynamic equations in the two-dimensional classical theory of thin-elastic shells is established for a circular cylindrical shell. It governs long wave vibrations in the vicinity of the lowest cut-off frequency. At a fixed circumferential wavenumber, the latter corresponds to the eigenfrequency of in-plane vibrations of a thin almost inextensible ring. It is stressed that the well-known semi-membrane theory of cylindrical shells is not suitable for tackling a near-cut-off behaviour. The dispersion relation within the framework of the developed formulation coincides with the asymptotic expansion of the dispersion relation originating from full two-dimensional shell equations. Asymptotic analysis also enables refining the geometric hypotheses underlying various ad hoc set-ups, including the assumption on vanishing of shear and circumferential mid-surface deformations used in the semi-membrane theory. The obtained results may be of interest for dynamic modelling of elongated cylindrical thin-walled structures, such as carbon nanotubes.
Journal Article Type | Article |
---|---|
Acceptance Date | Apr 5, 2016 |
Publication Date | May 4, 2016 |
Publicly Available Date | Mar 29, 2024 |
Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
Print ISSN | 1364-5021 |
Publisher | The Royal Society |
Peer Reviewed | Peer Reviewed |
Volume | 472 |
Issue | 2189 |
DOI | https://doi.org/10.1098/rspa.2015.0753 |
Keywords | cut-off, shell, elastic, asymptotic, vibration, nanotube |
Publisher URL | https://doi.org/10.1098/rspa.2015.0753 |
Files
2016_KMS_Submitted.pdf
(252 Kb)
PDF
Publisher Licence URL
https://creativecommons.org/licenses/by-nc/4.0/
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