Stability analysis of an articulated flexible pipe conveying fluid with a rotational spring

The stability of an articulated flexible pipe conveying fluid by altering its structural parameters is investigated in this paper. Utilizing generalized Hamilton's principle, the governing equations for the motion of both the upper and lower pipe segments of the system are established. The equations are then discretized using the Galerkin's method, which leads to a generalized eigenvalue problem. To validate the mathematical model, the eigenvalue branches of a degenerated system are compared with prior findings by using extreme values for the structural parameters. The results indicate that the instability characteristics of the pipe system are heavily influenced by these parameters. A reduction in the length of the upper segment causes the system to exhibit characteristics similar to either a pinned-free or cantilevered pipe, contingent upon the stiffness of the rotational spring. Secondary flutter phenomena manifest after the third or fourth mode instability as the flow velocity increases. When the upper and lower segments are of equal lengths, the critical flow velocity stabilizes when the spring stiffness surpasses a certain threshold. The inclusion of a flexible joint between the segments increases the system's susceptibility to higher-mode instability. Additionally, an extended upper segment may result in intricate instability behaviors, including a sequence of “instability-restabilization-instability” as the flow velocity rises. These innovative numerical findings provide theoretical perspectives on the dynamic behavior of articulated fluid-conveying pipes.