Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using an Asymptotic Perturbation Method
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/26/2/33 |
| _version_ | 1797537030712852480 |
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| author | Muhammad Usman Shaaban Abdallah Mudassar Imran |
| author_facet | Muhammad Usman Shaaban Abdallah Mudassar Imran |
| author_sort | Muhammad Usman |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T12:10:16Z |
| format | Article |
| id | doaj.art-18fdccd6741a43e98c91f2c53ebfdeeb |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-10T12:10:16Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-18fdccd6741a43e98c91f2c53ebfdeeb2023-11-21T16:15:51ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472021-04-012623310.3390/mca26020033Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using an Asymptotic Perturbation MethodMuhammad Usman0Shaaban Abdallah1Mudassar Imran2Department of Mathematics, University of Dayton, Dayton, OH 45469, USAAerospace Engineering & Engineering Mechanics, University of Cincinnati, Cincinnati, OH 45221, USANAMAL Institute, Mianwali 42250, PakistanIn 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.https://www.mdpi.com/2297-8747/26/2/33ship-rollingbifurcation curvesasymptotic perturbation method |
| spellingShingle | Muhammad Usman Shaaban Abdallah Mudassar Imran Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using an Asymptotic Perturbation Method Mathematical and Computational Applications ship-rolling bifurcation curves asymptotic perturbation method |
| title | Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using an Asymptotic Perturbation Method |
| title_full | Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using an Asymptotic Perturbation Method |
| title_fullStr | Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using an Asymptotic Perturbation Method |
| title_full_unstemmed | Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using an Asymptotic Perturbation Method |
| title_short | Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using an Asymptotic Perturbation Method |
| title_sort | nonlinear and stability analysis of a ship with general roll damping using an asymptotic perturbation method |
| topic | ship-rolling bifurcation curves asymptotic perturbation method |
| url | https://www.mdpi.com/2297-8747/26/2/33 |
| work_keys_str_mv | AT muhammadusman nonlinearandstabilityanalysisofashipwithgeneralrolldampingusinganasymptoticperturbationmethod AT shaabanabdallah nonlinearandstabilityanalysisofashipwithgeneralrolldampingusinganasymptoticperturbationmethod AT mudassarimran nonlinearandstabilityanalysisofashipwithgeneralrolldampingusinganasymptoticperturbationmethod |