Three-dimensional dynamics of fluid-conveying pipe simultaneously subjected to external axial flow

Abstract

In this paper, the instability and three-dimensional (3-D) nonlinear dynamics of a supported pipe subjected concurrently to internal and external axial flows are investigated, for the flow velocity of internal fluid being either steady or pulsatile. For that purpose, a 3-D version of nonlinear governing equations for two perpendicular lateral displacements of the pipe are derived by the use of extended Hamilton's principle. Unlike previous two-dimensional (2-D) versions of governing equation for a supported pipe subjected concurrently to external and internal axial flows, this new 3-D version of governing equations is capable of predicting the non-planar motions of the pipe. Based on linear analyses, it is shown that buckling instability may occur for an internal steady fluid flow while parametric instability can be generated by an internal pulsatile flow. In the nonlinear analyses, the nonlinear dynamics of the pipe with various internal and external flow velocities for different pulsating frequencies and amplitudes are represented by means of bifurcation diagrams, time traces, phase portraits, oscillation trajectories, power spectral density (PSD) diagrams and Poincaré maps. Some interesting dynamical behaviors, including periodic, quasi-periodic and chaotic motions, are detected in a wide range of pulsating frequency of interest. In many cases, non-planar motions of the pipe may be induced by fluid flows. These non-planar motions, however, need to be determined by using the present 3-D theoretical model instead of previously used 2-D ones for supported pipes subjected concurrently to internal and external axial flows.