Abstract:
The vortex-induced vibration (VIV) response characteristics of a flexible cantilevered pipe with a concentrated mass block at the free end are numerically investigated based on the wake oscillator model under three typical flow profiles: linear shear flow, exponential shear flow, and real stepped flow. First, a coupling model is developed between the structural oscillator of the flexible cantilevered pipe and the wake oscillator. Then, the coupling model is discretized using a second-order central difference scheme and solved through iterative methods. Finally, the vibration displacement, dominant vibration frequency, and other response features of the structure are systematically analyzed under the influence of the three flow profiles. Numerical results show that, for the cantilevered pipe with a tip mass, the VIV responses along the pipe axis under all three flow conditions exhibit multi-frequency characteristics. The dominant modal orders of vibration are very close for different flow profiles. The structural vibration patterns feature a combination of standing and traveling waves, with the traveling waves consistently propagating from the upper region with higher flow velocity toward the lower region with slower flow velocity, indicating a common propagation trend. Despite these similarities, notable differences in VIV responses are observed among the three flow profiles. Under linear shear flow and exponential shear flow, the maximum vibration displacement of the pipe appears at the free end. However, under the real stepped flow profile, the maximum displacement occurs at a lower or middle section of the pipe. Moreover, the VIV frequency energy distribution under linear shear flow is more concentrated, forming a “clustered peak” spectrum and showing quasi-periodic vibration characteristics. In contrast, under exponential shear flow and real stepped flow, the frequency energy distribution becomes more dispersed, presenting a broadband spectrum and a more chaotic vibration behavior.