An Interpolation Theory approach to Shell Eigenvalue Problems

The asymptotic behavior of the smallest eigenvalue in linear shell problems is studied, as the thickness parameter tends to zero. In order to cover the widest range of mid-surface geometry and boundary conditions, an abstract approach has been followed, and the Real Interpolation Theory has been used as main tool. A result concerning the ratio between the bending and the total elastic energy is proved. Furthermore, an example of application to cylindrical shells is detailed.