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.
Zeitschrift für angewandte Mathematik und Physik – Springer Journals
Published: Dec 12, 2017
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