Effectiveness of the segment method in absolute and joint coordinates when modelling risers

Abstract

This paper presents two formulations of the segment method: one with absolute coordinates and the second with joint coordinates. The nonlinear equations of motion of slender links are derived from the Lagrange equations by means of the methods used in multibody systems. Values of forces and moments acting in the connections between the segments are defined using a new and unique procedure which enables the mutual interaction of bending and torsion to be considered. The models take into account the influence of the velocity of the internal fluid flow on the riser's dynamics. The dynamic analysis of a riser with fluid flow requires calculation of the curvature by approximation of the Euler angles with polynomials of the second order. The influence of the sea environment, such as added mass of water, drag and buoyancy forces as well as sea current, is considered. In addition, the influence of torsion is discussed. Validation is carried out for both models by comparing the authors' own results with those obtained from experimental measurements presented in the literature and from COMSOL, Riflex and Abaqus software. The validation is concerned with vibrations of cables and the riser with internal fluid flow as well as with frequencies of free and forced vibrations of a riser fully or partially submerged in water. The numerical effectiveness of both formulations is examined for dynamic analysis of the riser, whose top end is moving in a horizontal plane. Conclusions concerned with the effectiveness of both formulations of the segment method and the influence of torsional vibrations on numerical results are formulated.