Stochastic analysis procedures have been recently applied to analyze nonlinear
dynamical systems. In this study, nonlinear responses, stochastic and/or chaotic, are
examined and interpreted from a probabilistic perspective. A multi-point-moored
ocean structural system under regular and irregular wave excitations is analytically
examined via a generalized stochastic Melnikov function and Markov process
approach. Time domain simulations and associated experimental observations are
employed to assist in the interpretation of the analytical predictions.
Taking into account the presence of random noise, a generalized stochastic
Melnikov function associated with the corresponding averaged system, where a
homoclinic connection exists near the primary resonance, is derived. The effects of
random noise on the boundary of regions of possible existence of chaotic response
is demonstrated via a mean-squared Melnikov criterion.
The random wave field is approximated as random perturbations on regular
and nearly regular (with very narrow-band spectrum) waves by adding a white noise
component, or using a filtered white noise process to fit the JONSWAP spectrum.
A Markov process approach is then applied explicitly to analyze the response.
The evolution of the probability density function (PDF) of nonlinear stochastic
response under the Markov process approach is characterized by a deterministic
partial differential equation called the Fokker-Planck equation, which in this study is
solved by a path integral solution procedure. Numerical evaluation of the path
integral solution is based on path sum, and the short-time propagator is discretized
accordingly. Short-time propagation is performed by using a fourth order Runge-Kutta scheme to calculate the most probable (i.e. mean) position in the phase space
and to establish the fact that discrete contributions to the random response are locally
Gaussian. Transient and steady-state PDF's can be obtained by repeat application of
the short-time propagation.
Based on depictions of the joint probability density functions and time domain
simulations, it is observed that the presence of random noise may expedite the
occurrence of "noisy" chaotic response. The noise intensity governs the transition
among various types of stochastic nonlinear responses and the relative strengths of
coexisting response attractors. Experimental observations confirm the general
behavior depicted by the analytical predictions. / Graduation date: 1995
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/35512 |
| Date | 02 December 1994 |
| Creators | Lin, Huan |
| Contributors | Yim, Solomon C. S. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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