Iterative determination of spar lines static equilibrium and improved dynamic modeling by fractional derivatives

Abstract

Polyester mooring systems are used as permanent systems of floating production systems and offshore structures. Compared to other mooring systems, polyester has a highly non linear behavior, thus complicating the overall design. Three important parameters affect the polyester rope stiffness; the mean load, the load range, and the frequency of the loading. Ignoring the 'true' stiffness as influenced by these parameters, may lead to underestimate the load induced riser stresses and damage. Procedures for determining mooring line stiffness that is representative of the in service conditions are developed herein. Two stiffness values, the 'static' and 'dynamic', are iteratively calculated from real time data, and are correlated with laboratory tests. Furthermore, note that fractional derivative models have been extensively proposed in literature for accurately capturing frequency dependent behavior of materials. In this context, a modified Newmark algorithm that takes advantage of the Grunwald-Letnikov fractional derivative representation is developed to treat related structural dynamic problems. In addition, a statistical linearization approach is also developed for random vibration treatment of such systems. The modified Newmark Algorithm is used to conduct Monte Carlo studies demonstrating the reliability of the statistical linearization solution.