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# Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using an Asymptotic Perturbation Method

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Department of Mathematics, University of Dayton, Dayton, OH 45469, USA
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Aerospace Engineering & Engineering Mechanics, University of Cincinnati, Cincinnati, OH 45221, USA
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NAMAL Institute, Mianwali 42250, Pakistan
*
Author to whom correspondence should be addressed.
Academic Editors: Nicholas Fantuzzi, Francesco Fabbrocino, Marco Montemurro, Francesca Nanni, Qun Huang, José A.F.O. Correia, Leonardo Dassatti and Michele Bacciocchi
Math. Comput. Appl. 2021, 26(2), 33; https://doi.org/10.3390/mca26020033
Received: 12 March 2021 / Revised: 17 April 2021 / Accepted: 17 April 2021 / Published: 20 April 2021
In this work, the response of a ship rolling in regular beam waves is studied. The model is one degree of freedom model for nonlinear ship dynamics. The model consists of the terms containing inertia, damping, restoring forces, and external forces. The asymptotic perturbation method is used to study the primary resonance phenomena. The effects of various parameters are studied on the stability of steady states. It is shown that the variation of bifurcation parameters affects the bending of the bifurcation curve. The slope stability theorems are also presented. View Full-Text
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MDPI and ACS Style

Usman, M.; Abdallah, S.; Imran, M. Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using an Asymptotic Perturbation Method. Math. Comput. Appl. 2021, 26, 33. https://doi.org/10.3390/mca26020033

AMA Style

Usman M, Abdallah S, Imran M. Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using an Asymptotic Perturbation Method. Mathematical and Computational Applications. 2021; 26(2):33. https://doi.org/10.3390/mca26020033

Chicago/Turabian Style

Usman, Muhammad, Shaaban Abdallah, and Mudassar Imran. 2021. "Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using an Asymptotic Perturbation Method" Mathematical and Computational Applications 26, no. 2: 33. https://doi.org/10.3390/mca26020033

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