Abstract
In a previous paper [D. H. Trivett, J. Acoust. Soc. Am. Suppl. 1 75, S77 (1984)] the existence of a low‐frequency, low phase velocity axisymmetric mode in a thin cylindrical shell was demonstrated. This mode is not obtained as a solution to the equations of present thin shell theories, a result which can be traced to the invalidity of the assumptions of Kirchhoff's theory of plates when applied to a cylindrical shell (the application of Kirchhoff's assumptions to cylindrical shells is due to Love and most subsequent researchers, not Kirchhoff. In this paper the thin shell assumptions are discussed and numerical solutions to the exact linear elastic equations are presented demonstrating their invalidity at low frequency.
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