Noise-induced transitions in nonlinear responses of a submerged moored structure are investigated from both global stability and probability points of view. The analysis procedure includes a stochastic Melnikov process to identify potential chaotic domains, and the Fokker-Planek equation to investigate and demonstrate response probabilistic characteristics. With the presence of weak perturbations, highly nonlinear phenomena including coexistence of attractors and chaos are found to exist. It is indicated that the presence of noise expands the potential chaotic domain in the parameter space and causes transitions between coexisting responses, which may not occur otherwise.
Complex nonlinear responses of moored ocean systems under deterministic settings has been elucidated analytically and numerically via period-doubling cascades and the (co)existence of harmonic, subharmonie and ultraharmonie responses (Gottlieb and Yim, 1992). Near resonances, coexisting (and competing) nonlinear moored structural responses have been found with different initial conditions, and the cascade of local bifurcations (and sudden explosions in some eases) often leads to chaotic responses. An experimental investigation (Yim et al, 1993) examining nonlinear response behavior of a single-degree-of-freedom (SDOF) moored structural system identifies the existence of subharmonie and ultraharmonie as well as period-doubling bifurcations. Despite of good agreement between analytical predictions and numerical results, there are experimental observations which can not be explained using conventional deterministic analysis procedures. Figure 1 shows the time history of a sample experimental structural response subjected to "deterministic" monochromatic wave excitation. The response resides in a harmonic mode for a relatively long duration (about 120 seconds, Fig. la) and then transitions to a subharmonic steady state (Figs. lb-e). The existence of unexpected transition indicates the presence of random noise caused by imperfect wave conditions (e.g., diffraction, reflection and re-reflection), which may lead the response trajectory to visit other coexisting attractors (Lin and Yim, 1995).
