Bifurcation analysis is conducted to investigate the dynamics of a spinning pipe conveying fluid with pulsation. The partial differential equations of the system are obtained by considering the nonlinearity in curvature and inertia. They are then discretized to the ordinary differential equations by means of the Galerkin expansion so that the primary and combination resonance conditions are imposed to the system. Moreover, the multiple scales method is utilized to solve the resultant equations, and the stability of the equilibrium points of the system is determined through the continuation method. The equilibrium solutions are also examined by the numerical integration, by which the existence of double jump, saddle node and Hopf bifurcations are demonstrated for different values of the fluid velocity.

中文翻译：

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脉动输送流体的旋转管道的非线性行为

进行分岔分析以研究带有脉动的旋转管道输送流体的动力学。通过考虑曲率和惯性的非线性得到系统的偏微分方程。然后通过 Galerkin 展开将它们离散为常微分方程，从而对系统施加主共振条件和组合共振条件。此外，利用多尺度法求解所得方程，并通过延拓法确定系统平衡点的稳定性。还通过数值积分检验了平衡解，通过数值积分证明了不同流体速度值下双跳、鞍节点和Hopf分岔的存在。