Mathematical Models and Methods in Applied Sciences c ° World Scienti¯c Publishing Company AN INTERPOLATION THEORY APPROACH TO SHELL EIGENVALUE PROBLEMS

Revised (Day Month Year) Communicated by (xxxxxxxxxx) The asymptotic behaviour 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