Hill Instability Analysis of TLP Tether Subjected to Combined Platform Surge and Heave Motions

This paper presents the Hill instability analysis of Tension Leg Platform (TLP) tether in deep sea. The 2-D nonlinear beam model, which is undergoing coupled axial and transverse vibrations, is applied. The governing equations are reduced to nonlinear Hill equation by use of the Galerkin's method and the modes superposition principle. The Hill instability charted up to large parameters is obtained. An important parameter M is defined and can be expressed as the functions of tether length, the platform surge and heave motion amplitudes. Some example studies are performed for various environmental conditions. The results demonstrate that the nonlinear coupling between the axial and transverse vibrations has a significant effect on the response of structure. It needs to be considered for the accurate dynamic analysis of long TLP tether subjected to the combined platform surge and heave motions.