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Natural frequencies and modal shapes of three-dimensional moonpool with recess in infinite-depth and finite-depth waters
https://orcid.org/0000-0003-2263-1201
Abstract In this study new extensions of the theoretical models developed by Molin (2001) and Molin et al. (2018) are proposed to solve the resonance problem for three-dimensional circular and rectangular moonpools with recesses. Eigenfunction expansions are adopted to describe the velocity potentials in all the subdomains. Then, the velocity potentials and normal velocities are matched at the common boundaries such that the eigenvalue problems are formulated and solved, yielding the natural frequencies and associated modal shapes of the free surface. Both the models for infinite and finite water depths are derived for circular moonpools with recesses. Applications are also made for the three-dimensional rectangular moonpools with recesses. In addition, frozen-mode approximation is derived, which yields simple formulas for prediction of the natural frequencies for piston-mode resonances. The proposed models in this study are validated by comparing the obtained results with the experimental data and the results using other numerical models. Moreover, for the first sloshing mode in rectangular moonpool, simple approximation model is proposed based on the assumption that the half of the wavelength of a standing wave is the same as the moonpool length. The validity of the model is examined by comparing the solutions with the results by the diffraction–radiation code WAMIT.
Highlights Theoretical models are proposed to solve the resonance problem for circular and rectangular moonpools with recesses. The proposed models are validated by comparing the results with the experiments and the solutions by other models. We derive frozen-mode approximation for the piston-mode frequency in finite water depth. For rectangular moonpool with recess, standing-wave approximations are proposed for the first sloshing-mode frequency.
Natural frequencies and modal shapes of three-dimensional moonpool with recess in infinite-depth and finite-depth waters
https://orcid.org/0000-0003-2263-1201
Abstract In this study new extensions of the theoretical models developed by Molin (2001) and Molin et al. (2018) are proposed to solve the resonance problem for three-dimensional circular and rectangular moonpools with recesses. Eigenfunction expansions are adopted to describe the velocity potentials in all the subdomains. Then, the velocity potentials and normal velocities are matched at the common boundaries such that the eigenvalue problems are formulated and solved, yielding the natural frequencies and associated modal shapes of the free surface. Both the models for infinite and finite water depths are derived for circular moonpools with recesses. Applications are also made for the three-dimensional rectangular moonpools with recesses. In addition, frozen-mode approximation is derived, which yields simple formulas for prediction of the natural frequencies for piston-mode resonances. The proposed models in this study are validated by comparing the obtained results with the experimental data and the results using other numerical models. Moreover, for the first sloshing mode in rectangular moonpool, simple approximation model is proposed based on the assumption that the half of the wavelength of a standing wave is the same as the moonpool length. The validity of the model is examined by comparing the solutions with the results by the diffraction–radiation code WAMIT.
Highlights Theoretical models are proposed to solve the resonance problem for circular and rectangular moonpools with recesses. The proposed models are validated by comparing the results with the experiments and the solutions by other models. We derive frozen-mode approximation for the piston-mode frequency in finite water depth. For rectangular moonpool with recess, standing-wave approximations are proposed for the first sloshing-mode frequency.
Natural frequencies and modal shapes of three-dimensional moonpool with recess in infinite-depth and finite-depth waters
https://orcid.org/0000-0003-2263-1201
Abstract In this study new extensions of the theoretical models developed by Molin (2001) and Molin et al. (2018) are proposed to solve the resonance problem for three-dimensional circular and rectangular moonpools with recesses. Eigenfunction expansions are adopted to describe the velocity potentials in all the subdomains. Then, the velocity potentials and normal velocities are matched at the common boundaries such that the eigenvalue problems are formulated and solved, yielding the natural frequencies and associated modal shapes of the free surface. Both the models for infinite and finite water depths are derived for circular moonpools with recesses. Applications are also made for the three-dimensional rectangular moonpools with recesses. In addition, frozen-mode approximation is derived, which yields simple formulas for prediction of the natural frequencies for piston-mode resonances. The proposed models in this study are validated by comparing the obtained results with the experimental data and the results using other numerical models. Moreover, for the first sloshing mode in rectangular moonpool, simple approximation model is proposed based on the assumption that the half of the wavelength of a standing wave is the same as the moonpool length. The validity of the model is examined by comparing the solutions with the results by the diffraction–radiation code WAMIT.
Highlights Theoretical models are proposed to solve the resonance problem for circular and rectangular moonpools with recesses. The proposed models are validated by comparing the results with the experiments and the solutions by other models. We derive frozen-mode approximation for the piston-mode frequency in finite water depth. For rectangular moonpool with recess, standing-wave approximations are proposed for the first sloshing-mode frequency.
Natural frequencies and modal shapes of three-dimensional moonpool with recess in infinite-depth and finite-depth waters
Zhang, Xinshu (author) / Li, Zhanghanyi (author)
Applied Ocean Research ; 118
2021-10-08
Article (Journal)
Electronic Resource
English