A nonlinear model for the dynamic behavior of tubular beams such as marine risers, pipelines, legs of tension leg platforms, and drill strings is developed. The formulation includes three translational degrees of freedom of the riser cross section and three rotational degrees of freedom for shear and torsion. Nonlinear constitutive equations for cross sections of unequal principal stiffnesses and extensible material are derived. Initial structural imperfections which are inherent in long risers are modeled in the form of initial curvature and geometric torsion which do not induce strains. The inertia forces due to the motion of the riser and internal fluid motions are formulated. The external hydrodynamic and hydrostatic forces are integrated on the riser surface as pressure and traction forces. The model is a comprehensive consistent nonlinear formulation of the riser dynamics and can be used for evaluation of the significance of nonlinear effects.
Bifurcation analysis of vortex-induced vibration of low-dimensional models of marine risers
