Nonlinear vortex induced vibrations of inclined marine risers

In this paper, we study the nonlinear dynamics of statically deflected offshore structures undergoing vortex induced vibrations. We consider inclined risers that have catenary-like profiles where the riser structure is modelled as an Euler-Bernoulli beam with mid-plane stretching and under self-weight. The statically deflected structure is subjected to vortex induced vibration forces and its equation of motion is coupled with Van der Pol oscillator. Then, we use mode shapes, extracted from the linear eigenvalue problem, in Galerkin method. This reduces the coupled system to a set of nonlinear ordinary differential equations. We use long time integration with Runge-Kutta method to integrate the coupled system and obtain the response while varying the inclination angle, internal velocity, and external velocity. The numerical results reveal the effects of the nonlinearity on the response of the structure, modal interaction, and resonance interactions.