ABSTRACT
One of the most common structures used for oil exploitation in deep water are Tension Leg Platforms (TLPs). Compliant structures in the sea are subject to variation in frequency and structural response because of a nonlinear parameter in the equation of motion. Variation of frequency is important in fatigue life study of tethers. In this document, an alternative approach for the analysis and the numerical approximation of this equation of motion, using a variational framework, is presented. This method does not require a small parameter for finding surge motion of TLP. This method can be used to solve a highly nonlinear differential equation of surge motion. We prove that our procedure can never get stuck in local minima, and the error decreases until getting to the original solution independent of the perturbation parameter. A theoretical study of this method is presented. From a design engineer point of view is useful to have a sight of nonlinear vibration behavior of systems which are naturally nonlinear like TLP.
