Eigenoscillations of a thin-walled non-closed shell of revolution

by    I. Gavrilyuk, M. Hermann, V. Trotsenko, Yu. Trotsenko, A. Timokha

Preprint series: 09-03, Reports on Numerical Mathematics

I. Gavrilyuk, M. Hermann, V. Trotsenko, Yu. Trotsenko, A. Timokha

MSC:
65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methods
47J30 Variational methods [See also 58Exx]
34B16 Singular nonlinear boundary value problems

Abstract: In this paper a numerical method is proposed to compute the eigenoscillations of a thin-walled non-closed shell of revolution. The method is based on the well-known Ritz method. The use of special coordinate functions which are adapted to the boundary layer behaviour at the clamped ends guarantees a uniform convergence to the natural modes and their (up to fourth order) derivatives. It is shown that the convergence of the new method does not significantly depend on the thickness of the shell.

Keywords: thin-walled shell, Ritz method, singularly perturbed ODEs, boundary layer behaviour

Upload: 2009-07-09


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