Complex dynamics of compliant off-shore structures

Abstract

The dynamics of advanced compliant off-shore structures can be extremely complex owing to the inherent nonlinearities. Subharmonic resonances can coexist with stable small-amplitude solutions, the response observed depending solely on the starting conditions of the motion. So care must be taken in digital, analogue and model studies to explore a comprehensive set of initial conditions. ‘Efficient’ automated digital computations could miss an entire subharmonic peak by locking onto a coexisting small-deflexion fundamental solution. Chaotic, non-periodic motions of strange attractors can also arise in well defined deterministic resonance problems. The waveforms of these look like the result of a stochastic process, and because of their extreme sensitivity to initial conditions a statistical description must be sought. Genuinely chaotic solutions can be identified by looking for nearby period-doubling bifurcations, and for the exponential divergence of adjacent starts leading to a loss of correlation. The period-doubling cascades give rise to subharmonics of arbitrarily high order close to the chaotic régimes, so the duration of digital, analogue and laboratory experiments must be long and chosen with care. The resonance of simple bilinear and impact oscillators is used as a vehicle to illustrate these general ideas.