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A. Steindl, H. Troger:
"Dimension Reduction of Fluid Conveying Tubes: A Nontrivial Problem";
in: "IUTAM Symposium on Fluid-Structure Interaction in Ocean Engineering", E. Kreuzer (ed.); issued by: IUTAM; Springer-Verlag, Heidelberg, 2008, ISBN: 978-1-4020-8629-8, 273 - 284.

We consider various Galerkin methods for the
dimension reduction in the dynamics
of a fluid conveying tube.

Due to the presence of viscous internal damping\index{viscous internal
damping}, the
spectrum\index{spectrum} of the linear operator has a finite
accumulation point, as shown in \Fig{Eigval}, which
strongly influences the applicability of the Approximate Inertial
Manifold method. It could be shown by numerical calculations
that even if a considerable number of active modes is chosen,
the long term behaviour of the full system and the
reduced system differ considerably.

Hence the choice of the ansatz-functions seems of crucial importance.
Several different choices are discussed.

Moreover also the construction of the reduced order system is far from
being straight-forward.

ansatz functions, linear and nonlinear Ritz-Galerkin methods