Stability analysis of axially moving pipes with internal fluid flow

We study the dynamic stability of a slender pipe traveling horizontally between two supports, with an incompressible fluid flowing through it. The pipe is modeled as a tensioned Euler–Bernoulli beam. We introduce a first-order damping term, similar to a beam resting upon a distribution of viscous dampers, which, in turn, may model the presence of surrounding air. The governing equations of motion are derived using the extended Hamilton principle. These are then analyzed for stability employing the Galerkin method. Subsequently, stability regimes are identified in the parameter space of the velocities of the pipe and the fluid, which are then verified by explicitly solving the governing equations through direct numerical integration. A key novelty of this work is that we study the coupled problem of a translating pipe and a pipe with internal axial fluid flow, capturing the interplay between structural and hydrodynamic effects. Finally, we develop a reduced order model for the nonlinear system that successfully captures its stability characteristics and highlights the role of tension nonlinearity.