The present work investigates the linear out-of-plane vibrations of catenary risers. The study outlines in detail the complete theoretical procedure for setting up the mathematical formulation that governs the non-linear vibrations of the structure in three dimensions including torsion effects. The governing set is subsequently reduced using valid assumptions, and the equivalent linearized system is eventually derived. It is shown that the linearization procedure uncouples the in-plane and the out-of-plane vibrations of the riser. The reduced linear set of the ordinary differential equations that govern the out-of-plane vibrations is solved in the frequency domain using a centred differences numerical scheme.
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