The eigenvalue problem of risers is of outmost 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 Touch down Area (TDA) may be modeled as dominated by the suspended part dynamics. Nevertheless, eigenmodes may be strongly affected in this region, as, strictly speaking, this is a nonlinear one-sided (contact type) boundary condition. Actually, we should consider a nonlinear eigenvalue problem. Locally, at TDA, riser flexural rigidity and soil interaction play important roles, affecting the dynamic curvature. Extending and jointing together former analytical solutions on 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.

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