Free vibration analysis of large sag catenary with application to catenary jumper

The main goal of this study is to investigate the free vibration analysis of a large sag catenary with
application to the jumper in hybrid riser system. The equation of motion is derived by using the variational
method based on the virtual work principle. The finite element method is applied to evaluate the numerical
solutions. The large sag catenary is utilized as an initial configuration for vibration analysis. The nonlinearity
due to the large sag curvature of static configuration is taken into account in the element stiffness matrix. The natural frequencies of large sag catenary and their corresponding mode shapes are determined by solving the eigenvalue problem. The numerical examples of a large sag catenary jumpers are presented. The influences of bending rigidity and large sag shape on the free vibration behaviors of the catenary jumper are provided. The results indicate that the increase in sag reduces the jumper natural frequencies. The corresponding mode shapes of the jumper with large sag catenary shape are comprised of normal and tangential displacements. The large sag curvature including in the element stiffness matrix increases the natural frequency especially for a case of very large sag shape. Mostly, the mode shapes of jumper are dominated by the normal displacement, however, the tangential displacement significantly occurs around the lowest point of sag. The increase in degree of inclination of the catenary tends to increase the natural frequencies.