Stability and vibrations of a flexible pipe under stochastic parametric excitation

Flexible pipes are widely used in engineering applications to transport gas-liquid two-phase flows, such as natural gas and oil. The natural separation, deformation, and mixing of these two fluid phases (gas and liquid) can cause spatiotemporal stochastic variations in total fluid density. In this paper, a mathematical model based on the Gaussian distribution is employed to simulate the stochastic fluctuations in the fluid density of gas-liquid two-phase flow. Subsequently, the nonlinear coupled transversal and axial vibrations of a flexible pipe conveying gas-liquid two-phase flow are developed. The pipe vibration equations are solved using the Galerkin method combined with the Runge-Kutta method. After validating the proposed dynamic model, a comprehensive analysis of the stability and vibration characteristics of the pipe induced by the stochastic fluid density of gas-liquid two-phase flow is conducted. The results indicate that the parametric stability and instability of the pipe can be determined using the Floquet theory. If any frequency component of the stochastic fluid density has a state transition matrix eigenvalue greater than one, the pipe system becomes unstable. In the subcritical flow regime, the pipe vibrations caused by parametric resonances of gas-liquid two-phase flow exhibit chaotic behavior, while in the supercritical regime, the vibrations also display chaotic characteristics due to pipe buckling instability.