Modelling and prediction of vortex-induced vibrations (VIV) of marine risers is a challenging task due to the associated multi degrees of freedom in both cross-flow/in-line directions and the multi-mode fluid-structure interactions. In addition, the axial motion and its geometrically nonlinear coupling with lateral responses can be significant, especially at higher-order modes. Nevertheless, several papers in the literature dealing with VIV predictions have often overlooked such aspects. Therefore, this study aims to investigate and understand the effect of axial or longitudinal motion through a theoretical model and numerical approach in time domain.

Attention is paid to VIV of vertical risers subjected to linearly sheared currents. To capture a three-dimensional aspect of the flexible cylinder experiencing VIV, a semi-empirical model is developed consisting of nonlinear equations of cross-flow, in-line and axial structural oscillations which are coupled with the distributed van der Pol-type wake-oscillators modelling the fluctuating fluid lift/drag forces. The mean drag force is also taken into account. These model equations are numerically solved via a space-time finite difference scheme, and the obtained numerical results highlight several aspects of VIV of elastic cylinders along with the axial motion effects.

Apart from the validation of the numerical model with published experimental results, this study reveals how the effect of axial motion and its nonlinear coupling with the two lateral cross-flow/in-line motions can be very important. These depend on the flow velocity, the fluid-structure parameters, the single or multi-mode lock-in condition, and the standing-wave or travelling-wave feature. We recommend that the axial response should be accounted for in VIV analysis and prediction model.

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