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Free hanging catenary and steep wave risers consist of curved portions. The inner flow in the curved portions causes considerable centrifugal forces, yielding dynamic motion. The interaction of the inner fluid flow with the riser motion causes Coriolis forces acting in a direction opposing the motion. The dynamic response of the riser is the consequence of the balance of the centrifugal, Coriolis, inertial, flexural restoring and drag forces. The aim of this study is the analysis of the inner-flow-induced dynamic instability of curved risers made from fibre-reinforced polymer. To this end, the motion equation and boundary conditions are treated with the transfer matrix method. The natural frequencies and the critical inner flow velocities causing instability are calculated. The implementation of the proposed method in representative examples is provided and commented on.

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