Nonlinear vortex-induced vibrations of fluid-conveying tensioned pipes in super-critical regimes

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Nonlinear vortex-induced vibration (VIV) properties of the fluid-conveying pipes in super-critical regimes subjected to the combined action of external fluid and axial tension are investigated. A new nonlinear dynamic model taking into account the variation of axial tension and the action of external flow is proposed. According to the van der Pol equation, the interaction between the pipe and external flow is evaluated. More specifically, the nonlinear governing equations are established based on Hamilton's principle, and they are then discretized via the Galerkin method and solved by the fourth-order Runge-Kutta method. The VIV amplitudes obtained from the present theoretical model are compared with the published experimental results, which validates the effectiveness and accuracy of the proposed nonlinear dynamic model. It is found that keeping the external fluid velocity constant, with the increase of internal fluid velocity, the growth rates of the maximum response amplitudes in different directions of the buckled pipe are the same under different tensions. When the internal fluid velocity is kept constant, for the pipe in post-buckling state, increasing the tension will be accompanied by decreasing the dynamic stiffness of the pipe, which leads to the increase of the dynamic displacement response. When the pipe in super-critical regime is subjected to variable tension, the increase of the time-varying tension amplitude can either enhance the maximum response amplitude in the cross-flow (CF) direction of the pipe or suppress it.