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A. Steindl:
"Application of Dimension Reduction Methods to the Dynamics of a Fluid Conveing Tube";
Vortrag: Fifth EUROMECH Nonlinear Dynamics Conference, Eindhoven; 07.08.2005 - 12.08.2005; in: "Proceedings ENOC-2005", D. H. van Campen, M.D. Lazurko, W.P.J.M. van den Oever (Hrg.); (2005), ISBN: 90-386-2667-3; Paper-Nr. 06-443, 8 S.

Realistically modelled mechanical systems usually are represented in an infinite dimensional phase space creating great difficulties in analyzing their dynamics. Hence one will try to reduce the original system to a low dimensional system. However this is useful only if a good approximation of the original dynamics is achieved.

In this paper we consider dimension reduction methods for the simulation of the discretized equations for a fluid conveying tube. Due to the presence of viscous internal damping in the equations of motion the spectrum of the linear operator has a finite accumulation point, as indicated in Fig. 4, which strongly influences the applicability of Approximate Inertial Manifolds: Even if a considerable number of modes is chosen as dominating modes, the long term behaviour of the full system and the reduced system differ considerably. The difficulty can also be observed in a very simple system with two degrees of freedom.

Numerical calculations indicate, that the eigenfunctions of the linear operator do not behave as well as expected. We therefore investigate different methods to construct appropriate linear bases. The basis from a coarser discretization of the system looks promising, because in simulations with different element sizes only small differences were observed.

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