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Center for Nonlinear Studies |
In the present talk we address the problem of shell vibration from the mathematical standpoint. We are interested in the asymptotic behavior of the shell for small thicknesses, and the related effects on the numerical discretization of the problem. After a brief review of the classical asymptotic analysis of shells (source problem), we consider the asymptotic study of the first eigenvalue and related eigenmodes. In particular, we show how in general the latter problem is more complex, and that the so called "mixed bending-membrane" cases are often encountered. As a consequence, in the finite element analysis of shell vibrations the locking pathology must in general be dealt with even in shells with a "non-flexural" geometry. Finally, in order to obtain a wider understanding, the particular case of a clamped cylindrical shell is analyzed more in deep. During the talk various numerical tests are shown; such tests confirm the above theory and underline the effects of the locking phenomenon.
Host: Mikhail Shashkov