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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 100-year 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.
