Noisy Nonlinear Motions of Moored System. Part I: Analysis and Simulations

Abstract

Nonlinear responses of a submerged moored structure are investigated taking into account the presence of environment random noise. Sources of nonlinearity of the system include a quadratic Morison hydrodynamic damping and a geometrically nonlinear restoring force. The random perturbations are modeled by a white-noise process to examine their effects on nonlinear responses analytically and numerically. The analysis procedure includes a generalized Melnikov process to study response stabilities in a global sense and the Fokker-Planck equation to demonstrate response characteristics from a probabilistic perspective. Rich nonlinear phenomena including bifurcations, coexistence of attractors, and chaos are identified and demonstrated. Probability density functions solved from the Fokker-Planck equation are used to depict (co)existing response attractors on the Poincaré section and demonstrate their probabilistic properties. Noise effects on responses are shown via a generalized Melnikov criterion and the probability density function. It is found that the presence of noise may expand the chaotic domain in the parameter space and also cause transitions between coexisting responses.