Bifurcation analysis of vortex-induced vibration of low-dimensional models of marine risers

A low-dimensional model of a top-tensioned riser under excitations from vortices and time-varying tension is proposed, where the van der Pol wake oscillator is used to simulate the loading caused by the vortex shedding. The governing partial differential equations describing the fluid–structure interactions are formulated and multi-mode approximations are obtained using the Galerkin projection method. The one mode approximation is applied in this study and two different resonances are investigated by employing the method of multiple scales. They are the 1:1 internal resonance between the structure and wake oscillator (also known as ‘lock-in’ phenomenon) and the combined 1:1 internal and 1:2 parametric resonances. Bifurcations under the varying nondimensional shedding frequency for different mass–damping parameters are investigated and the results of multiple-scale analysis are compared with direct numerical simulations. Analytical responses are calculated using the continuation method and their stability is determined by examining the eigenvalues of the corresponding characteristic equations. Effects of the system parameters including the amplitude of the tension variation, vortex shedding frequency and mass–damping parameter on the system bifurcations have been investigated. The analytical approach has allowed to probe bifurcations occurring in the system and to identify stable and unstable responses. It is shown that the combined resonances can induce large-amplitude vibration of the structure. Counter-intuitively, the amplitude of such responses increases rapidly as the amplitude of the tension variation grows. Comparisons between the analytical and numerical results confirm that the span of the system vibration can be accurately predicted analytically with respect to the obtained response amplitudes of responses. The proposed multi-mode approximation and presented findings of this study can be used to enhance design process of top tension risers.