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Stochastic Roll Dynamics of Smooth and Impacting Vessels in Random Waves
Journal
Ocean Engineering
ISSN
00298018
Date Issued
2024-09-01
Author(s)
Kumar, Pankaj
Narayanan, S.
Abstract
Ship instability is frequently associated with extreme roll motion. In this paper smooth and vibro-impact dynamics of vessels rolling under random wave excitations including nonlinearities is investigated. The vessel is represented by a single degree of freedom roll model. The random excitation due to waves and ice is modeled by a sum of random pulses with Poisson arrival rate. Stochastic P-bifurcation analysis is carried out by examining the variation with parameter of the joint probability density functions (jpdf) of the response computed numerically by the solution of the corresponding Fokker–Planck–Kolmogorov (FPK) equation. The finite element (FE), finite difference (FD), path integral (PI) and radial basis neural (RBN) network formulation methods are used in the solution of the FPK equation. The D-bifurcation analysis is analyzed by computing the largest Lyapunov exponent. The mean upcrossing rate is computed using Rice's formula. The random wave excitation is also modeled as the response of a second order linear filter to white noise and the random response of the ship is investigated by solution of the corresponding FPK equation of the four dimensional Markov system by the FD method. Non-smooth coordinate transformations like the Zhuravlev and Ivanov transformations are used converting the discontinuous systems to equivalent smooth systems in the impact dynamics analysis. The adaptive time stepping method (ATSM) approach is used to accurately locate the discontinuity point and a Brownian tree approach is used to direct the integration along the correct Brownian path. Different models for nonlinear damping and the restoring moment are considered and their effects on ship stochastic response such as chaotic motion, unbounded rotational motion, impact modulation motion and ship capsizing are investigated.
Volume
307
Subjects