Free vibrations for some Koiter shells of revolution

The asymptotic behaviour of the smallest eigenvalue in linear Koiter shell problems is studied, as the thickness parameter tends to zero. In particular, three types of shells of revolution are considered. A result concerning the ratio between the bending and the total elastic energy is also provided, by using the general theory detailed in [L. Beirão da Veiga, C. Lovadina, An interpolation theory approach to Shell eigenvalue problems (submitted for publication); L. Beirão da Veiga, C. Lovadina, Asymptotics of shell eigenvalue problems, C.R. Acad. Sci. Paris 9 (2006) 707–710].