Abstract
The eigenvalue problem of risers is of utmost importance, particularly if vortex-induced vibration (VIV) is concerned. Design procedures rely on the determination of eigenvalues and eigenmodes. Natural frequencies are not too sensitive to the proper consideration of boundary condition, within a certain extent where dynamics at the touchdown area (TDA) may be modeled as dominated by the dynamics of the suspended part. However, eigenmodes may be strongly affected in this region because, strictly speaking, this is a nonlinear one-side (contact-type) boundary condition. Actually, we shall consider a nonlinear eigenvalue problem. Locally, at TDA, riser flexural rigidity and soil interaction play important roles and may affect the dynamic curvature. Extending and merging former analytical solutions on touchdown point (TDP) dynamics and on the eigenvalue problem, obtained through asymptotic and perturbation methods, the present work critically address soil and bending stiffness effects a little further. As far as linear soil stiffness and planar dynamics hypotheses may be considered valid, it is shown that penetration in the soil is small and that its effect does not change significantly the bending loading that is mainly caused by the cyclic excursion of the TDP and corresponding dynamic tension. A comparison of the analytical results with a full nonlinear time-domain simulation shows a remarkable agreement for a typical steel catenary riser. The WKB approximation for the eigenvalue problem gives good estimates for TDP excursion. As the dynamic tension caused solely by VIV is very small, the merged analytical solution may be used as a first estimate of the curvature variation at TDP in the cases of current perpendicular to the “riser plane.”
