COMBINED AXIAL AND LATERAL RESPONSES OF TENSIONED BUOYANT PLATFORM TETHERS

This paper presents the results of an investigation into the combined axial and lateral vibrations of the tethers of tensioned buoyant platforms, (TBPs). Wave-induced motions of the TBP excite tether vibrations through lateral forces at the tether top end (called external or forcing excitation in this paper) combined with a time-varying axial force (called parametric excitation here), Although, the forcing and parametric excitations have been considered separately in the research literature, this paper examines their combined effects - particularly with a view to determining tether behaviour for different water depths, The governing partial differential equation of tether lateral motion is reduced to a nonlinear differential equation and solved by a combination of the Romberg method and the fourth-order Runge-Kutta method. Comparisons for tether vibrations when taking both axial and lateral forcing into account and when considering axial and lateral forcing separately are presented. It is shown that the combined excitation gives greater amplitude of vibration with this feature being particularly dominant in even numbers of the instability region of the Mathieu stability chart. The frequency of oscillation of the combined response is also dependent on the relative magnitudes of axial and lateral excitations. The results demonstrate that the above is true for a wide range of water depths.