A theory of nonlinear wave loading on offshore structures
A theoretical study is made of the nonlinear wave loading on offshore structures using the diffraction theory of hydrodynamics. A nonlinear modification of the classical Morison equation, D≡Fℓ+FD for estimating wave forces on offshore structures is suggested in this paper. The modified equation is f...
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| Format: | Article |
| Language: | English |
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Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171281000446 |
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| _version_ | 1832555932214624256 |
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| author | Lokenath Debnath Matiur Rahman |
| author_facet | Lokenath Debnath Matiur Rahman |
| author_sort | Lokenath Debnath |
| collection | DOAJ |
| description | A theoretical study is made of the nonlinear wave loading on offshore
structures using the diffraction theory of hydrodynamics. A nonlinear modification of the classical Morison equation, D≡Fℓ+FD for estimating wave forces on offshore structures is suggested in this paper. The modified equation is found in the form D≡Fℓ+Fnℓ+FD where Fnℓ≡Fd+Fw+Fq is the nonlinear contribution made up of the dynamic, waterline, and the quadratic forces associated with the irrotational-flow part of the wave loading on structures. The study has then been applied to calculate the linear and the nonlinear wave loadings on a large vertical cylinder partially immersed in an ocean of arbitrary uniform depth. All the linear and nonlinear forces exerting on the cylinder are determined explicitly. A comparison is made between these two kinds of forces. Special attention is given to the nonlinear wave loadings on the cylinder. It is shown that all nonlinear effects come from the interaction between the body's responses to the oncoming wave's fluctuating velocity and its fluctuating extension. It is found that the nonlinear effects are dominated by the sum of the dynamic and waterline forces. The nonlinear correction to Morison's equation increases with increasing kb where b is the characteristic dimension of the body and k is the wave number. This prediction is shown to be contrary to that of the linear diffraction theory which predicted that the Morison coefficient decreases with increasing kb. Several interesting results and limiting cases are discussed in some detail. |
| format | Article |
| id | doaj-art-90af41ee7833418287dadf9b545c7e68 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1981-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-90af41ee7833418287dadf9b545c7e682025-02-03T05:46:44ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251981-01-014358961310.1155/S0161171281000446A theory of nonlinear wave loading on offshore structuresLokenath Debnath0Matiur Rahman1Mathematical Institute, University of Oxford, Oxford, UKHydraulics Laboratory, Division of Mechanical Engineering, National Research Council of Canada, Ottawa, CanadaA theoretical study is made of the nonlinear wave loading on offshore structures using the diffraction theory of hydrodynamics. A nonlinear modification of the classical Morison equation, D≡Fℓ+FD for estimating wave forces on offshore structures is suggested in this paper. The modified equation is found in the form D≡Fℓ+Fnℓ+FD where Fnℓ≡Fd+Fw+Fq is the nonlinear contribution made up of the dynamic, waterline, and the quadratic forces associated with the irrotational-flow part of the wave loading on structures. The study has then been applied to calculate the linear and the nonlinear wave loadings on a large vertical cylinder partially immersed in an ocean of arbitrary uniform depth. All the linear and nonlinear forces exerting on the cylinder are determined explicitly. A comparison is made between these two kinds of forces. Special attention is given to the nonlinear wave loadings on the cylinder. It is shown that all nonlinear effects come from the interaction between the body's responses to the oncoming wave's fluctuating velocity and its fluctuating extension. It is found that the nonlinear effects are dominated by the sum of the dynamic and waterline forces. The nonlinear correction to Morison's equation increases with increasing kb where b is the characteristic dimension of the body and k is the wave number. This prediction is shown to be contrary to that of the linear diffraction theory which predicted that the Morison coefficient decreases with increasing kb. Several interesting results and limiting cases are discussed in some detail.http://dx.doi.org/10.1155/S0161171281000446nonlinear waveswave forcesMorison equationwave loading on structureshydrodynamic diffraction. |
| spellingShingle | Lokenath Debnath Matiur Rahman A theory of nonlinear wave loading on offshore structures International Journal of Mathematics and Mathematical Sciences nonlinear waves wave forces Morison equation wave loading on structures hydrodynamic diffraction. |
| title | A theory of nonlinear wave loading on offshore structures |
| title_full | A theory of nonlinear wave loading on offshore structures |
| title_fullStr | A theory of nonlinear wave loading on offshore structures |
| title_full_unstemmed | A theory of nonlinear wave loading on offshore structures |
| title_short | A theory of nonlinear wave loading on offshore structures |
| title_sort | theory of nonlinear wave loading on offshore structures |
| topic | nonlinear waves wave forces Morison equation wave loading on structures hydrodynamic diffraction. |
| url | http://dx.doi.org/10.1155/S0161171281000446 |
| work_keys_str_mv | AT lokenathdebnath atheoryofnonlinearwaveloadingonoffshorestructures AT matiurrahman atheoryofnonlinearwaveloadingonoffshorestructures AT lokenathdebnath theoryofnonlinearwaveloadingonoffshorestructures AT matiurrahman theoryofnonlinearwaveloadingonoffshorestructures |