Elimination of Subharmonic Resonances of Compliant Marine Structures

Compliant off-shore structures are inherently nonlinear and are prone to potentially dangerous subharmonic resonances under steady ocean waves. In recent work it was emphasized that these resonances could be easily missed in one-off and automated computer simulations and in experimental tests because they often coexist with small-amplitude fundamental solutions, the final steady state observed depending on the starting conditions of the motion. It was also shown that a chaotic, nonperiodic output, governed by a strange attractor, can be generated by a typical deterministic problem. It is shown how the subharmonic resonances can be designed-out by increasing the damping to a prescribed level or by varying other system parameters. Very general mathematical theorems yield a bound on the damping, above which no steady subharmonics can exist. As an example, the bound is shown to be a very good one, by comparison with digital time integrations for the wave-induced motions of an articulated mooring tower to which a massive oil tanker is tied. The values of damping needed to eliminate all subharmonic motions are of the order of magnitude of those that could be achieved in realistic design situations. 11 ref.--AA