Viscous damping issues in the dimension reduction of a fluid conveying tube

Abstract

We consider the dimension reduction of an already discretized model for a fluid-conveying tube by the linear and non-linear Galerkin method. We show, how the viscous damping parameter affects the distribution of the eigenvalues for the system and how this distribution influences the convergence of the approximation. By a simple mechanical model, it is also demonstrated that the Galerkin method may fail completely, if the energy dissipation is governed by the stable modes.