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Vibrations of an elastic cylindrical shell near the lowest cut-off frequency

Kaplunov, J.; Manevitch, L.I.; Smirnov, V.V.

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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

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