H. Lin et Scs. Yim, NOISY NONLINEAR MOTIONS OF MOORED SYSTEM .1. ANALYSIS AND SIMULATIONS, Journal of waterway, port, coastal, and ocean engineering, 123(5), 1997, pp. 287-295
Nonlinear responses of a submerged moored structure are investigated t
aking into account the presence of environment random noise. Sources o
f nonlinearity of the system include a quadratic Morison hydrodynamic
damping and a geometrically nonlinear restoring force. The random pert
urbations are modeled by a white-noise process to examine their effect
s on nonlinear responses analytically and numerically. The analysis pr
ocedure includes a generalized Melnikov process to study response stab
ilities in a global sense and the Fokker-Planck equation to demonstrat
e response characteristics from a probabilistic perspective. Rich nonl
inear 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 Poincare section and demonstrate their pro
babilistic properties. Noise effects on responses are shown via a gene
ralized 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 respons
es.