A fast convergent modal-expansion of the wave potential with application to the hydrodynamic and hydroelastic analysis of floating bodies in general bathymetry

Belibassakis, KA; Athanassoulis, GA

dc.contributor.author	Belibassakis, KA	en
dc.contributor.author	Athanassoulis, GA	en
dc.date.accessioned	2014-03-01T02:51:54Z
dc.date.available	2014-03-01T02:51:54Z
dc.date.issued	2009	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/35742
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-77953118887&partnerID=40&md5=ae2057ba946e57146bd74c06aa2e5177	en
dc.subject.other	Additional mode	en
dc.subject.other	Cnoidal wave	en
dc.subject.other	Elastic body	en
dc.subject.other	Evanescent mode	en
dc.subject.other	Flexural rigidities	en
dc.subject.other	Floating bodies	en
dc.subject.other	Floating structures	en
dc.subject.other	Free surfaces	en
dc.subject.other	General bathymetry	en
dc.subject.other	Hydro-elastic analysis	en
dc.subject.other	Hydrodynamic and hydroelastic analysis	en
dc.subject.other	Ice sheet	en
dc.subject.other	Intermediate depths	en
dc.subject.other	Mass distribution	en
dc.subject.other	Non-linear	en
dc.subject.other	Non-Linearity	en
dc.subject.other	Nonlinear travelling waves	en
dc.subject.other	Nonlinear water waves	en
dc.subject.other	Numerical example	en
dc.subject.other	Numerical investigations	en
dc.subject.other	Numerical solution	en
dc.subject.other	Series expansion	en
dc.subject.other	Thin plate	en
dc.subject.other	Variable bathymetry	en
dc.subject.other	Variable thickness	en
dc.subject.other	Variational principles	en
dc.subject.other	Vertical structures	en
dc.subject.other	Wave potentials	en
dc.subject.other	Wavefields	en
dc.subject.other	Arctic engineering	en
dc.subject.other	Bathymetry	en
dc.subject.other	Hydrodynamics	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Numerical analysis	en
dc.subject.other	Oceanography	en
dc.subject.other	Offshore structures	en
dc.subject.other	Rigid structures	en
dc.subject.other	Thickness control	en
dc.subject.other	Variational techniques	en
dc.subject.other	Water waves	en
dc.subject.other	Waves	en
dc.subject.other	Hydroelasticity	en
dc.title	A fast convergent modal-expansion of the wave potential with application to the hydrodynamic and hydroelastic analysis of floating bodies in general bathymetry	en
heal.type	conferenceItem	en
heal.publicationDate	2009	en
heal.abstract	A non-linear coupled-mode system of horizontal equations has been derived with the aid of Luke's (1967) variational principle, modelling the evolution of nonlinear water waves in intermediate depth and over a general bathymetry Athanassoulis & Belibassakis (2002, 2008). Following previous work by the authors in the case of linearised water waves (Athanassoulis & Belibassakis 1999), the vertical structure of the wave field is exactly represented by means of a local-mode series expansion of the wave potential. This series contains the usual propagating and evanescent modes, plus two additional modes, the free-surface mode and the sloping-bottom mode, enabling to consistently treat the non-vertical end-conditions at the free-surface and the bottom boundaries. The coupled-mode system fully accounts for the effects of non-linearity and dispersion. The main feature of this approach that a small number of modes (of the order of 5-6) are enough for the precise numerical solution, provided that the two new modes (the free-surface and the sloping-bottom ones) are included in the local-mode series. The consistent coupled-mode system has been applied to numerical investigation of families of steady nonlinear travelling wave solutions in constant depth (Athanassoulis & Belibassakis 2007) showing good agreement with known solutions both in the Stokes and the cnoidal wave regimes. In the present work we focus on the hydroelastic analysis of floating bodies lying over variable bathymetry regions, with application to the non-linear scattering of water waves by large floating structures (of VLFS type or ice sheets) characterised by variable thickness (draft), flexural rigidity and mass distributions, modelled as thin plates of variable thickness, extending previous approaches (see, e.g., Porter & Porter 2004, Belibassakis & Athanassoulis 2005, 2006, Bennets et al 2007). Numerical examples are presented, showing that useful results can be obtained for the analysis of large floating elastic bodies or structures very efficiently by keeping only a few terms in the expansion. Ideas for extending our approach to 3D are also discussed. Copyright © 2009 by ASME.	en
heal.journalName	Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE	en
dc.identifier.volume	6	en
dc.identifier.spage	469	en
dc.identifier.epage	476	en