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On the return to equilibrium problem for axisymmetric floating structures in shallow water

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBOCCHI, Edoardo
dc.date.accessioned2024-04-04T02:55:38Z
dc.date.available2024-04-04T02:55:38Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192382
dc.description.abstractEnIn this paper we address the return to equilibrium problem for an axisymmetric floating structure in shallow water. First we show that the equation for the solid motion can be reduced to a delay differential equation involving an extension-trace operator whose role is to describe the influence of the fluid equations on the solid motion. It turns out that the compatibility conditions on the initial data for the return to equilibrium configuration are not satisfied, so we cannot use the result from [3] for the nonlinear problem. Hence, assuming small amplitude waves, we linearize the equations in the exterior domain and we keep the nonlinear equations in the interior domain. For such configurations, the extension-trace operator can be computed explicitly and the delay term in the differential equation can be put in convolution form. The solid motion is therefore governed by a nonlinear second order integro-differential equation, whose linearization is the well-known Cummins equation. We show global in time existence and uniqueness of the solution using the conservation of the total fluid-structure energy.
dc.language.isoen
dc.title.enOn the return to equilibrium problem for axisymmetric floating structures in shallow water
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
dc.subject.halPhysique [physics]/Physique [physics]/Physique Atmosphérique et Océanique [physics.ao-ph]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-01971965
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01971965v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BOCCHI,%20Edoardo&rft.genre=preprint


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