A model for the axial-bending-torsional dynamics of pipes conveying fluid

Abstract

The present work contributes to the ever growing literature on the modelling of flow-induced vibrations in pipes conveying fluid. A three-dimensional nonlinear mathematical model is obtained for a pipe conveying fluid subjected to an external torsional moment. Bending, axial and torsional dynamics are included in the model and nonlinearities up to the cubic order are retained in the equations of motion. The dynamics of the pipe is formulated around the axial and torsional static solutions. The effects of the external torsional moment on the stability of the pipe are characterized as functions of the magnitude and location of the moment. It is shown that there is a critical magnitude, which depends on the location, above which a static instability occurs. Regardless of the magnitude of the torsional moment, it always reduces the critical flow velocity for flutter. While the stability of pipes conveying lighter fluids is shown to be more sensitive to torsional moments applied at the free end, applications at the middle point are more critical for pipes conveying heavier fluids. Depending on the system parameters, divergence and flutter may either coexist, or the system is stabilized over a range of flow velocities before it loses stability again, at higher flow velocities, by flutter. By numerically integrating the nonlinear equations of motion in the time domain, it is also shown that the presence of torsional moments induce three-dimensional motions, even when two-dimensional initial conditions are given.