The parametric resonance, which could induce severe consequence like fatigue, and further lead to oil-spill risk, has been vastly discussed in about the offshore pipelines. In this paper, a top-tensioned riser has been modelled, and the parametric instability of such structure has been analyzed with Differential Quadrature Method (DQM). Via altering some certain condition parameters such as damping coefficient, internal flow velocity, and unit wet weight, the instability charts of risers under different conditions has been presented. With the illustration of such instability charts, the effect of each parameter on riser’s instability has been discussed with the conclusion that the parametric instability of rise would change drastically with the altering of unit wet weight or damping coefficient, and, however, that the change of internal flow velocity impact slightly on the parametric instability of riser.


Risers has been massively used in offshore structures to convey the fluids between underwater bases and platforms. However, suffering the excitation from the motions of platform and the current of sea water, the security of drilling and oil production would be at risk. In this paper, the parametric instability of riser with internal flow excited by heave motion of platform is discussed with DQM.

The parametric instability has been enormously studied. Hsu CS (1975) found that the straight and vertical configuration of a hanging string in fluid may become unstable if the support point undergoes an up-anddown motion with its frequency and amplitude satisfying certain conditions, and his study introduced the parametric instability of risers into public focus. Meanwhile, the vibration of a long pipe conveying fluid has been proposed (Chen S, 1972; Edelstein WS, Chen S, 1985), and perturbation techniques and the averaging method has been applied to deal with the parametric excited vibration of such model, and he found that tube conveying fluid becomes unstable when the flow velocity exceeds some critical value. Both the heave motion at the top and the excitation from the internal flow would lead to the instability of riser. To make clear the relationship between parametric instability and some certain parameters, various methods have been introduced to cope with the parametric vibration problems of long slender structures under different conditions. Han-Tl Park and Dong-Ho Jung (2002) applied finite element method into the study of long slender marine structures under combined parametric and forcing excitations, and they found that the response amplitude of a combined excitation is much greater than that of a forcing excitation in the even number of instability regions of the Mathieu stability chart. The nonlinear resonance of a slender pipe conveying fluid for marine applications under parametrical excitation has been studied with Keller box method and Modal expansion solution method (I.K Chatjigeorgiou 2004; I.K Chatjigeorgiou 2005). Conclusions were drawn that under specific conditions, the dynamics of the structure in transverse direction could be approximated by the coupled dynamic behavior of a parametrically excited Mathieu-Duffing oscillator and that the inclusion of hydrodynamic drag in the describing model eliminates the impacts of internal resonances excited due to the parametrically imposed motions. Impact of irregular wave in parametric instability of top-tensioned riser has been investigated (Hezhen Yang and Fei Xiao, 2013). And they (Hezhen Yang and Fei Xiao, 2014) have also studied riser under combined vortex and multifrequency parametric excitations.

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