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, the spectrum of the lineal-operator has a finite accumulation point, as shown in Fig. 4, 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.
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