Determination of offshore spar stochastic structural response accounting for nonlinear stiffness and radiation damping effects

A study of the dynamic behavior of a combined dynamic system comprising a spar structure, a mooring line system, and top tensioned risers (TTR) by buoyancy can is presented. Not only the nonlinear restoring force of the mooring lines, the Coulomb friction at the compliant guides and the spar keel, and the hydrodynamic damping forces are considered, but also the effect of the frequency-dependent radiation damping is readily incorporated in this formulation. The dynamic model is subjected to input force and moment time histories that are compatible with a spectral representation (Jonswap spectrum) of a 100year hurricane in the Gulf of Mexico. The response of the system is first determined by direct numerical integration of the equations of motion. In this regard, particular caution is exercised to treat properly the frequency-dependent terms which involve convolution transforms in the time domain. Next, a novel approach for determining the system responses is proposed. It is based on the technique of statistical linearization which can accommodate readily and efficiently the frequency-dependent elements of the dynamic system. This is achieved by appropriate modification of the system transfer function and by proper accounting for the system nonlinearities. The time domain analysis results are used to demonstrate the reliability of the statistical linearization solution. Further, the effect of the radiation damping, and the effect of the hydrodynamic forces are investigated.