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Stochastic analysis of a nonlinear ocean structural system Public Deposited

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/jh343w477

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  • 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.
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