Nonlinear vortex-induced dynamics and post-buckling analysis of fluid-conveying pipelines with complex constraint

The paper investigates the nonlinear vortex-induced vibration (VIV) of fluid-conveying pipelines in the supercritical state under the impact of external fluid, axial tension, and the complex constraints of vertical and torsional springs. The nonlinear governing eqs. are derived by applying Hamilton's principle in conjunction with the van der Pol equation. The numerical modes are received using the differential quadrature method combined with Gauss-Legendre nodes. The nonlinear motion eqs. of the coupled system are discretized by the numerical modes in conjunction with the Galerkin method and are solved utilizing the Runge-Kutta methodology. The results show that the variations of the vertical spring and torsional spring will affect the dynamic stiffness of the pipelines in the pre-buckling and post-buckling regimes, which will lead to a change in the displacement response of the pipelines. The introduction of spring complex constraints significantly enhances the critical velocity of the pipeline, and as the internal fluid velocity increases beyond the critical threshold again, the pipeline transitions into an ultra-supercritical state. The buckling angle exhibits negligible influence on the first-order natural frequency.