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A. Steindl:
"Application of Dimension Reduction Methods to the Dynamics of a Fluid Conveying Tube";
Talk: 8th World Congress on Computational Mechanics (WCCM8) and 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008), Lido di Venezia; 2008-06-30 - 2008-07-04; in: "5th European Concress on Computational Methods in Applied Sciences and Engineering", B. Schrefler, U. Perego (ed.); (2008), 2 pages.

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 presentation 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, which strongly influences
the applicability of Approximate Inertial Manifolds: Even if a considerable number of eigenfunctions is
chosen as dominating modes, the long term behaviour of the full system and the reduced system differ
considerably. The same difficulty can also be observed in a very simple system with two degrees of
freedom.

Nonlinear Galerkin Method, Approximate Inertial Manifold, Center Manifold, Mode selection.