ON MARINE RISER RESPONSES IN TIME- AND DEPTH-DEPENDENT FLOWS

A mathematical formulation for solving the beam equation is developed and applied to describe marine riser motions due to current forces. The method is sufficiently flexible to consider arbitrary currents that vary continuously with depth and time. The relative motions between the riser and the free currents are converted to forces using a simplified formulation, leading to a linear damping and a current drag that is proportional to the square of the current speed. The drag coefficient can vary with time and is used to simulate vortex-induced vibrations where the Strouhal number is permitted to vary along the riser. The expansions for riser displacements are given in terms of time-varying coefficients together with axial varying functions (eigenfunctions). The evolution of the coefficients are determined through a numerical time-integration procedure, while the functions are computed once through an eigenvalue problem. A continuous axial variation of the displacements and bending moments with time are computed using this method. The method is applied to two physical test-cases that have been carried out to study vortex-induced vibrations. The tests employed risers that were approximately 11 and 90 m long. Comparisons between simulated and measured displacements and bending moments revealed a good correspondence between modelled and measured data. This was achieved without tuning of the drag and damping coefficients. The energy-conserving properties of the model are also demonstrated by forcing the model by an impulse load.