Elimination of sub-harmonic resonances of compliant marine structures

Abstract Compliant off-shore structures are inherently non-linear, and are prone to potentially dangerous subharmonic resonances under steady ocean waves. In recent work we have emphasized how these resonances could be easily missed in one-off and automated computer simulations, as well as in experimental tests, because they often co-exist with small-amplitude fundamental solutions, the final steady state observed depending on the starting conditions of the motion. We have also shown that a chaotic , non-periodic output, governed by a strange attractor can be generated by a typical deterministic problem. In the present paper we show how the sub-harmonic 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 sub-harmonics 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 sub-harmonic motions are of the order of magnitude of those that could be achieved in realistic design situations.