Book ChapterDOI
Solving the Problem of Nonlinear Ship Roll Motion Using Stochastic Dynamics
Jeffrey Falzarano,Zhiyong Su,Arada Jamnongpipatkul,Abhilash Somayajula +3 more
- pp 423-435
TLDR
In this paper, two techniques from the theory of stochastic dynamics are applied to study the probabilistic nature of roll motion in irregular seas, where the roll response moment equation is formulated from a six dimensional state space rolling model with a fourth order linear filter using the Ito differential rule.Abstract:
Due to nonlinear viscous damping and the softening characteristic of the stiffness, the roll motion of a ship exhibits complex dynamics. Specifically predicting the probabilistic characteristics of roll response in an irregular seaway is still a challenging problem and continues to be of interest for both practitioners and researchers. In this work two techniques from the theory of stochastic dynamics are applied to study the probabilistic nature of roll motion in irregular seas. The first method is the “Moment Equation method” where the roll response moment equation is formulated from a six dimensional state space rolling model with a fourth order linear filter using the Ito differential rule. The resulting moment equations are solved using a cumulant neglect technique. Alternatively in the second approach, the probability density function of the rolling response is evaluated by solving the corresponding Fokker Planck Equation of the system using “Path Integral method”.read more
Citations
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Journal ArticleDOI
Parametric roll vulnerability of ships using Markov and Melnikov approaches
TL;DR: A previously developed analytical model for roll restoring moment, which was found to be effective in modeling the problem of parametric roll, is analyzed using the Melnikov approach and the nature of random response is analyzed to determine whether the vessel exhibits any chaotic dynamics.
References
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Book
Random vibration and statistical linearization
J.B. Roberts,Pol D. Spanos +1 more
TL;DR: In this paper, a comprehensive account of statistical linearization with related techniques allowing the solution of a very wide variety of practical non-linear random vibration problems is given, and the principal value of these methods is that they are readily generalized to deal with complex mechanical and structural systems and complex types of excitation such as earthquakes.
Book
Probability and Random Processes with Applications to Signal Processing
Henry Stark,John W. Woods +1 more
TL;DR: This chapter concludes with a Summary, Problems, and References of the Introduction to Probability, which explains the motivation for studying Probability and some useful classification of Random Processes.
Journal ArticleDOI
Efficient path integration methods for nonlinear dynamic systems
Arvid Naess,V. Moe +1 more
TL;DR: In this paper, a splines interpolation method is applied to the logarithm of the calculated PDF to obtain an accurate representation of the PDF over the whole domain and not only at the chosen grid points.
Journal ArticleDOI
Application of global methods for analyzing dynamical systems to ship rolling motion and capsizing
TL;DR: This analysis is based on determining criteria which can predict the qualitative nature of the invariant manifolds which represent the boundary between safe and unsafe initial conditions, and how these depend on system parameters for a specific ship model.
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