Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T19:59:05.578Z Has data issue: false hasContentIssue false
  • English
  • Français

Hydroelastic response of floating elastic discs to regular waves. Part 2. Modal analysis

Published online by Cambridge University Press:  16 April 2013

F. Montiel ,
L. G. Bennetts ,
V. A. Squire ,
F. Bonnefoy  and
P. Ferrant
F. Montiel*
Affiliation:
Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand
L. G. Bennetts
Affiliation:
School of Mathematical Sciences, University of Adelaide, Adelaide, South Australia 5005, Australia
V. A. Squire
Affiliation:
Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand
F. Bonnefoy
Affiliation:
Laboratoire de recherche en Hydrodynamique, Énergétique et Environnement Atmosphérique, École Centrale de Nantes, 1 rue de la Noë, Nantes, France
P. Ferrant
Affiliation:
Laboratoire de recherche en Hydrodynamique, Énergétique et Environnement Atmosphérique, École Centrale de Nantes, 1 rue de la Noë, Nantes, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Validation of a linear numerical model of wave interactions with floating compliant discs is sought using data obtained from the wave basin experiments reported in Part 1 (Montiel et al. J. Fluid Mech., vol. 723, 2013, pp. 604–628). Comparisons are made for both single-disc tests and the two-disc tests in which wave interactions between discs are observed. The deflection of the disc or discs is separated into the natural modes of vibration in vacuo. The decomposition allows the rigid-body motions and flexural motions to be analysed separately. Rigid-body motions are accurately replicated by the numerical model but, although passable agreement is found, the amplitudes of flexural modes are consistently overestimated. Extensions of the numerical model are used to discount the experimental configuration as a source of the discrepancies. An enhanced viscoelastic model for the discs is also proposed, which results in improved model/data agreement for the flexural motions but cannot account for all of the disagreement.

JFM classification

Waves/Free-surface Flows: Wave scattering Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 723 , 25 May 2013 , pp. 629 - 652
Copyright
©2013 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allen, J. B. & Rabiner, L. R. 1977 A unified approach to short-time Fourier analysis and synthesis. Proc. IEEE 65, 1558–1564.Google Scholar
Altenbach, H. & Eremeyev, V. A. 2009 On the bending of viscoelastic plates made of polymer foams. Acta Mechanica 204, 137–154.CrossRefGoogle Scholar
Amon, R. & Dundurs, J. 1968 Circular plate with supported edge-beam. J. Engng Mech. Div.-ASCE 94, 731–742.CrossRefGoogle Scholar
Andrianov, A. I. & Hermans, A. J. 2005 Hydroelasticity of a circular plate on water of finite or infinite depth. J. Fluids Struct. 20, 719–733.Google Scholar
Balmforth, N. J. & Craster, R. V. 1999 Ocean waves and ice sheets. J. Fluid Mech. 395, 89–124.Google Scholar
Bennetts, L. G. 2007 Wave scattering by ice sheets of varying thickness. PhD thesis, University of Reading.Google Scholar
Biot, M. A. 1955 Dynamics of viscoelastic media. In Proceedings of the Second Midwestern Conference on Solid Mechanics, pp. 94–108. Purdue University.Google Scholar
Chen, X., Wu, Y., Cui, W. & Jensen, J. J. 2006 Review of hydroelasticity theories for global response of marine structures. Ocean Engng 33, 439–457.Google Scholar
Cohen, L. 1989 Time-frequency distributions—a review. Proc. IEEE 77, 941–981.CrossRefGoogle Scholar
Deverge, M. & Jaouen, L. 2004 A review of experimental methods for the elastic and damping characteristics of acoustical porous materials. In Proceedings of the 33rd International Congress and Exposition on Noise Control Engineering, Prague, Czech Republic. The Institute of Noise Control Engineering of the USA (INCE/USA).Google Scholar
Falnes, J. 2002 Ocean Waves and Oscillating Systems: Linear Interactions Including Wave-Energy Extraction. Cambridge University Press.Google Scholar
Flügge, W. 1975 Viscoelasticity, 2nd edn. Springer.Google Scholar
Fox, C. & Squire, V. A. 1991 Coupling between the ocean and an ice shelf. Ann. Glaciol. 15, 101–108.Google Scholar
Itao, K. & Crandall, S. H. 1979 Natural modes and natural frequencies of uniform, circular, free-edge plates. Trans. ASME: J. Appl. Mech. 46, 448–453.Google Scholar
Kagemoto, H. & Yue, D. K. P. 1986 Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method. J. Fluid Mech. 166, 189–209.Google Scholar
Kohout, A. L., Meylan, M. H. & Plew, D. R. 2011 Wave attenuation in a marginal ice zone due to the bottom roughness of ice floes. Ann. Glaciol. 52, 118–122.Google Scholar
Kohout, A. L., Meylan, M. H., Sakai, S., Hanai, K., Leman, P. & Brossard, D. 2007 Linear water wave propagation through multiple floating elastic plates of variable properties. J. Fluids Struct. 23, 643–649.CrossRefGoogle Scholar
Love, A. E. H. 1944 A Treatise on the Mathematical Theory of Elasticity. Dover.Google Scholar
Marsault, P. 2010 Étude des interactions houle/glace de mer. Master’s thesis, École Centrale de Nantes (in French).Google Scholar
Meylan, M. H. & Squire, V. A. 1996 Response of a circular ice floe to ocean waves. J. Geophys. Res. 101, 8869–8884.CrossRefGoogle Scholar
Montiel, F. 2012 Numerical and experimental analysis of water wave scattering by floating elastic plates. PhD thesis, University of Otago.Google Scholar
Montiel, F., Bennetts, L. G. & Squire, V. A. 2012 The transient response of floating elastic plates to wavemaker forcing in two dimensions. J. Fluids Struct. 28, 416–433.CrossRefGoogle Scholar
Montiel, F., Bonnefoy, F., Ferrant, P., Bennetts, L. G., Squire, V. A. & Marsault, P. 2013 Hydroelastic response of floating elastic discs to regular waves. Part 1. Wave basin experiments. J. Fluid Mech. 723, 604–628.Google Scholar
Peter, M. A., Meylan, M. H. & Chung, H. 2003 Wave scattering by a circular plate in water of finite depth: a closed form solution. In Proceedings of the 13th International Offshore and Polar Engineering Conference, pp. 180–185. The International Society of Offshore and Polar Engineers.Google Scholar
Squire, V. A. 2007 Of ocean waves and sea-ice revisited. Cold Reg. Sci. Technol. 49, 110–133.Google Scholar
Squire, V. A. 2011 Past, present and impendent hydroelastic challenges in the polar and subpolar seas. Phil. Trans. R. Soc. A 369, 2813–2831.CrossRefGoogle ScholarPubMed
Stuart, R. J. & Carney, J. F. 1974 Vibration of edge reinforced annular plates. J. Sound Vib. 35 (1), 23–33.CrossRefGoogle Scholar
Timoshenko, S. & Goodier, J. N. 1951 Theory of Elasticity. McGraw-Hill.Google Scholar
Watanabe, E., Utsunomiya, T. & Wang, C. M. 2004 Hydroelastic analysis of pontoon-type VLFS: a literature survey. Engng Struct. 26, 245–256.Google Scholar
Williams, T. D. & Porter, R. 2009 The effect of submergence on the scattering by the interface between two semi-infinite sheets. J. Fluids Struct. 25 (5), 777–793.CrossRefGoogle Scholar