An asymptotic theory for circular cylindrical shells

We derive the two-dimensional shell equations for a circular cylindrical sh ell by means of an asymptotic expansion of the three-dimensional elastic st ate. The assumptions involved are of mathematical character only and concer n the continuity, differentiability and convergence of the series used. A n umerical comparison between the frequencies obtained by the two-dimensional shell equations and the three-dimensional state in the case of free vibrat ions is presented in a few examples. (C) 2000 Elsevier Science Ltd. All rig hts reserved.