Three-dimensional dynamics and synchronization of two coupled fluid-conveying pipes with intermediate springs

Abstract

A system of two coupled oscillating structures may experience dynamical synchronization under coupling effects. Dynamical synchronization refers to the process in which two vibrating structures under coupling effects may display similar dynamics and vibrational behaviors even though their important parameters are not equivalent. In this study, the three-dimensional dynamics and synchronization behaviors of two coupled fluid-conveying pipes connected with linear springs are investigated. In the analytical model, the geometric nonlinearities due to axial elongation of the two pipes and the extension of linear springs are considered. The flow velocities of the internal fluid of the two pipes may be steady or pulsatile. In the case of the flow velocities of the two pipes being steady, the lowest several natural frequencies and the post-buckling behavior of the two-pipe system are obtained by changing the flow velocities in the two pipes. When one pipe conveys pulsatile fluid and the other conveys steady fluid, the dynamical bifurcation and synchronization behaviors of the two-pipe system are analyzed, with several typical synchronization patterns being explored by means of time traces, phase portraits, power spectral density (PSD) diagrams, Poincaré maps, etc. It is shown that making use of synchronization characteristics of the two-pipe system may provide a possible way to control the vibrations of the two-pipe system and to achieve some special engineering objectives.