Many studies have tackled the problem of previous termvortex-induced vibrationsnext term (VIV) of a vertical riser with a constant tension and placed in uniform currents. In this study, attention is focused on the cross-flow VIV modelling, time-domain previous termanalysis and predictionnext term of variable-tension vertical risers in linearly sheared currents. The partial-differential equation governing the riser transverse motion is based on a flexural tensioned-beam model with typical pinned–pinned supports. The hydrodynamic excitation model describing the modulation of lift force is based on a distributed van der Pol wake oscillator whose nonlinear equation is also partial-differential due to the implementation of a diffusion term. The variation of empirical wake coefficients with system parameters and the water depth-dependent Reynolds number is introduced. Based on the assumed Fourier mode shape functions obtained by accounting for the effect of non-uniform tension, the Galerkin technique is utilized to construct a low-dimensional multi-mode model governing the coupled fluid-riser interaction system due to VIV. Numerical simulations in the case of varying sheared flow profiles are carried out to systematically evaluate riser nonlinear dynamics and highlight the influence of fluid–structure parameters along with associated VIV aspects. In particular, the effects of shear and tensioned-beam (tension versus bending) parameters are underlined. Some comparisons with published experimental results and observations are qualitatively and quantitatively discussed. Overall parametric previous termanalysis and predictionnext term results may be worthwhile for being a new benchmark against future experimental testing and/or numerical results predicted by an alternative model and methodology.
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