Conventional analysis of tension leg platform structures yields natural frequencies which are well separated from wave excitation frequencies. However, the results presented here show that the tethers can have lateral resonant frequencies in the wave frequency range if the platform is deployed in deep water. Analysis which ignores the lateral tether dynamics gives reasonable estimates of platform motions but can seriously underestimate tether displacements. It is usually assumed that tether tension does not vary with time. However, the vertical waves forces, reacted by the tethers, cause the tension to change with time and this can cause a Mathieu type of instability in the platform sway motion. This phenomenon is investigated using a simple energy balance technique and it is shown that square law fluid damping places an upper bound on oscillation amplitude; it is found that platform sway motions due to Mathieu excitation remain acceptable even in large waves.

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