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 M. Salai Mathi Selvi,L. Rajendran,Marwan Abukhaled.Estimation of Rolling Motion of Ship in Random Beam Seas by Efficient Analytical and Numerical Approaches[J].Journal of Marine Science and Application,2021,(1):55-66.[doi:10.1007/s11804-020-00183-x]
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Estimation of Rolling Motion of Ship in Random Beam Seas by Efficient Analytical and Numerical Approaches


Estimation of Rolling Motion of Ship in Random Beam Seas by Efficient Analytical and Numerical Approaches
M. Salai Mathi Selvi1 L. Rajendran1 Marwan Abukhaled2
M. Salai Mathi Selvi1 L. Rajendran1 Marwan Abukhaled2
1. Department of Mathematics, AMET (Deemed to be University), Chennai, Tamil Nadu, India;
2. Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE
Nonlinear dampingSteady-state roll motionUltraspherical waveletsHomotopy perturbation methodAnalytical solution
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.


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Received date:2019-11-18;Accepted date:2020-05-12。
Foundation item:The authors are thankful to Shri J. Ramachandran, Chancellor, Col. Dr. G. Thiruvasagam, Vice-Chancellor, Academy of Maritime Education and Training (AMET), Deemed to be University, Chennai, for their support.
Corresponding author:Marwan Abukhaled, mabukhaed@aus.edu
Last Update: 2021-06-10