Stochastic analysis of a nonlinear ocean structural system

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

A New Method to Predict Vessel Capsizing in a Realistic Seaway

A recently developed approach, in the area of nonlinear oscillations, is used to analyze the single degree of freedom equation of motion of a oating unit (such as a ship) about a critical axis (such as roll). This method makes use of a closed form analytic solution, exact upto the rst order, and takes into account the the complete unperturbed (no damping or forcing) dynamics. Using this method very-large-amplitude nonlinear vessel motion in a random seaway can be analysed with techniques similar to those used to analyse nonlinear vessel motions in a regular (periodic) or random seaway. The practical result being that dynamic capsizing studies can be undertaken considering the shortterm irregularity of the design seaway. The capsize risk associated with operation in a given sea state can be evaluated during the design stage or when an operating area change is being considered. Moreover, this technique can also be used to guide physical model tests or computer simulation studies to focus on critical vessel and environmental conditions which may result in dangerously large motion amplitudes. Extensive comparitive results are included to demonstrate the practical usefulness of this approach. The results are in the form of solution orbits which lie in the stable or unstable manifolds and are then projected onto the phase plane

15th Conference on Dynamical Systems Theory and Applications DSTA 2019 ABSTRACTS

From Preface: This is the fifteen time when the conference „Dynamical Systems – Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and the Ministry of Science and Higher Education. It is a great pleasure that our invitation has been accepted by so many people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcome nearly 255 persons from 47 countries all over the world. They decided to share the results of their research and many years experiences in the discipline of dynamical systems by submitting many very interesting papers. This booklet contains a collection of 338 abstracts, which have gained the acceptance of referees and have been qualified for publication in the conference edited books.Technical editor and cover design: Kaźmierczak, MarekCover design: Ogińska, Ewelina; Kaźmierczak, Mare