The effect of a weak nonlinearity on the lowest cut-off frequencies of a cylindrical shell

被引：0
作者：
I. V. Andrianov
J. Kaplunov
A. K. Kudaibergenov
L. I. Manevitch
机构：
[1] RWTH Aachen University,Institut fur Allgemeine Mechanik
[2] Keele University,School of Computing and Mathematics
[3] Al-Farabi Kazakh National University,undefined
[4] Semenov Institute of Chemical Physics RAS,undefined
来源：
Zeitschrift für angewandte Mathematik und Physik | 2018年 / 69卷
关键词：
Shell; Asymptotic; Nanotube; Nonlinear; Cut-off; 41 Approximations and expansions; 74 Mechanics of deformable solids;
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摘要：
The plane strain problem for a thin circular cylindrical shell is considered within the framework of the Sanders–Koiter theory. The relative shell thickness and displacement amplitude are chosen to be of the same asymptotic order. The leading nonlinear correction to the lowest cut-off frequencies is derived using the method of multiple scales. In contrast to the traditional two-mode Galerkin expansions assuming inextensibility of the shell transverse cross section, the developed fourth-order asymptotic scheme operates with five angular modes. The obtained results reveal asymptotic inconsistency of previous approximate solutions to the problem.
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