Two-dimensional approximation of eigenvalue problems in shell theory: Flexural shells (Q1976589)

The aim of the paper is the limiting behaviour of eigenvalues and eigenfunctions describing the vibrations of a thin linearly elastic shell, clamped along its lateral surface for \(\varepsilon\to 0\), where \(\varepsilon\) corresponds to the thickness of the shell. The variables in the three-dimensional eigenvalue problem has been rescaled and the result is a problem posed over a fixed domain, where the parameter \(\varepsilon\) now appears in the various bilinear forms. Using suitable a priori estimates the authors obtain the limit problem. It is proved that the order of convergence is \(O(\varepsilon^2)\).