An asymptotic theory for circular cylindrical shells

We derive the two-dimensional shell equations for a circular cylindrical shell by means of an asymptotic expansion of the three-dimensional elastic state. The assumptions involved are of mathematical character only and concern the continuity, di€erentiability and convergence of the series used. A numerical comparison between the frequencies obtained by the two-dimensional shell equations and the three-dimensional state in the case of free vibrations is presented in a few examples