Nonlinear free vibrations and vortex-induced vibrations of fluid-conveying steel catenary riser

This paper presents a model formulation that can be used for analyzing the three-dimensional vibration behaviors of an inclined extensible steel catenary riser (SCR). The virtual work-energy functional, which involves strain energy due to axial stretching and bending rigidity of the riser and virtual work done by the gravitational, inertial and external drag forces, is formulated. The method of Galerkin finite element is used to obtain the mass and stiffness matrices. Then the eigenvalue problem is solved to determine its natural frequencies and corresponding mode shapes. A new nonlinear model capable of analyzing the vortex-induced vibration of SCR in the ocean current was addressed. The unsteady hydrodynamic forces associated with cross-flow vibrations are modeled as distributed van der Pol wake oscillators. Depending on the vortex-excited out-of-plane modes and system fluid-structure parameters, the parametric studies are carried out to determine the maximum response amplitudes of SCR, along with the occurrence of the mode transition phenomenon. The obtained results highlight the effect of internal fluid velocities and top tension on the nonlinear dynamics of riser undergoing vortex-induced vibration.