Estimation of Rolling Motion of Ship in Random Beam Seas by Efficient Analytical and Numerical Approaches

A steady-state roll motion of ships with nonlinear damping and restoring moments for all times is modeled by a second-order nonlinear differential equation. Analytical expressions for the roll angle, velocity, acceleration, and damping and restoring moments are derived using a modified approach of h...

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Bibliographic Details
Published in:Journal of marine science and application 2021-03, Vol.20 (1), p.55-66
Main Authors: Selvi, M. Salai Mathi, Rajendran, L., Abukhaled, Marwan
Format: Article
Language:English
Subjects:
Acceleration
Damping
Electrical Machines and Networks
Engineering
Geotechnical Engineering & Applied Earth Sciences
Machinery and Machine Elements
Mathematical analysis
Nonlinear differential equations
Offshore Engineering
Perturbation method
Perturbation methods
Power Electronics
Research Article
Rolling (ship motion)
Rolling motion
Ships
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Summary:A steady-state roll motion of ships with nonlinear damping and restoring moments for all times is modeled by a second-order nonlinear differential equation. Analytical expressions for the roll angle, velocity, acceleration, and damping and restoring moments are derived using a modified approach of homotopy perturbation method (HPM). Also, the operational matrix of derivatives of ultraspherical wavelets is used to obtain a numerical solution of the governing equation. Illustrative examples are provided to examine the applicability and accuracy of the proposed methods when compared with a highly accurate numerical scheme.
ISSN:1671-9433
1993-5048
DOI:10.1007/s11804-020-00183-x