Combined vibration analysis of a top tensioned riser with the geometrical nonlinearity

Abstract

A coupling model representing the interactions between the riser and vortices is proposed, of which the time-varying top tension and the internal nonlinear axial force due to the bending of the riser are considered. In addition, the van der Pol oscillator is introduced to simulate the time-varying characteristic of the vortices. The motion equations are derived and the first-order mode approximation is obtained with the Galerkin approach. The multiple scale method is applied to study the steady-state solutions of the system. Effects of system parameters (the structural damping, nonlinearity, the amplitude ratio of the varying-tension, the shedding frequency) on the responses are investigated in detail. The synchronous and non-synchronous motions between the structure and wake oscillator are studied. The bifurcation diagrams for the responses in terms of the amplitude ratio and the nonlinear parameter are obtained in the large parameter ranges. The results show that responses with different topological properties including quasi-periodic, periodic and chaotic solutions can occur under different parameter conditions. A pair of chaotic attractors can be found for the large parameter range of the amplitude ratio. The joint effects of the amplitude ratio and the nonlinear parameter on the responses in the large parameter range are studied as well, which are further verified by the phase projections and Poincaré sections. The results show that the topological properties of responses can be controlled by the amplitude ratio. These results can be helpful to the dynamic design of the riser in practice.