Dynamic response of an axially loaded tendon of a tension leg platform

In this work, a set of nonlinear equations of motion for a coupled axial and transverse vibration of a tower subjected to end tension is derived using Hamilton's principle. The in-plane fluid forces are represented by the Morison equation. The tower is modeled as an elastic beam subjected to end tension with only in-plane motions due to random wave loadings. The dynamic response of the tower is analyzed for various end tensions by the finite difference method. The effects of parameter variations such as an increase in significant wave height, an increase in the constant end tension, and harmonically varying end tension are analyzed both for a reduced model and for an actual tether.It was observed that at low tension, the axial motion is mainly induced by geometry while at higher tension, the axial motion is mainly due to elongation. Analysis of a 260 m tendon showed that increasing the significant wave heights increased the amplitude of transverse response, while the magnitude of axial response remained almost the same. The bending stress in the tendon decreases with an increase in tension due to decreased transverse displacement, but the total stress in the tendon increases with an increase in end tension. The magnitude of transverse displacement could be kept within specific limits by constantly varying the end tension.