Membrane flutter induced by radiation of surface gravity waves on a uniform flow

Labarbe, Joris; Kirillov, Oleg N.

doi:10.1017/jfm.2020.533

Cited by 4 publications

(28 citation statements)

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“…New complete dispersion relation has been derived and analyzed with the perturbation theory for multiple roots of polynomials [48] to obtain an explicit analytical approximation to the critical flutter velocity that is in excellent agreement with the numerical computation of the full stability map. Moreover, we have identified in [26] a new instability domain arising from a conical singularity in the parameter space that could not be detected in the restrictive assumptions of [27]. This new domain is associated with a low-frequency flutter for short wavelengths and corresponds to the case when the velocity of propagation of elastic waves in the membrane is much smaller than the velocity of the flow.…”

Section: Introductionmentioning

confidence: 86%

“…In a recent work [26] attention was paid to an overlooked classical model that appears to be a perfect candidate for the role of the Lamb oscillator in the field of radiation-induced instabilities. This is the model, proposed by Nemtsov in 1985, of an elastic membrane resting on the bottom of a uniformly flowing fluid layer of finite depth and loosing its stability due to emission of surface gravity waves [27].…”

Section: Introductionmentioning

confidence: 99%

“…In [26] we extended analysis of Nemtsov's membrane with infinite chord to the case of dispersive surface gravity waves by allowing the fluid layer to have arbitrary depth and the added mass ratio parameter to take arbitrary non-negative values. New complete dispersion relation has been derived and analyzed with the perturbation theory for multiple roots of polynomials [48] to obtain an explicit analytical approximation to the critical flutter velocity that is in excellent agreement with the numerical computation of the full stability map.…”

Section: Introductionmentioning

confidence: 99%

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Radiation-induced instability of a finite-chord Nemtsov membrane

Labarbe

Kirillov

2022

Physics of Fluids

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We consider a problem of stability of a membrane of an infinite span and a finite chord length that is submerged in a uniform flow of finite depth with free surface. In the shallow water approximation, Nemtsov (1985) has shown that an infinite-chord membrane is susceptible to flutter instability due to excitation of long gravity waves on the free surface if the velocity of the flow exceeds the phase velocity of the waves and placed this phenomenon into the general physical context of the anomalous Doppler effect. In the present work we derive a full nonlinear eigenvalue problem for an integro-differential equation in the case of the finite-chord Nemtsov membrane in the finite-depth flow. In the shallow-and deep water limits we develop a perturbation theory in the small added mass ratio parameter acting as an effective dissipation parameter in the system, to find explicit analytical expressions for the frequencies and the growth rates of the membrane modes coupled to the surface waves. This result reveals a new intricate pattern of instability pockets in the parameter space and allows for its analytical description. The case of an arbitrary depth flow with free surface requires numerical solution of a new non-polynomial nonlinear eigenvalue problem. We propose an original approach combining methods of complex analysis and residue calculus, Galerkin discretization, Newton method and parallelization techniques implemented in MATLAB to produce high-accuracy stability diagrams within an unprecedentedly wide range of system's parameters. We believe that the Nemtsov membrane appears to play the same paradigmatic role for understanding radiation-induced instabilities as the famous Lamb oscillator coupled to a string has played for understanding radiation damping.

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Section: Introductionmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Radiation-induced instability of a finite-chord Nemtsov membrane

Labarbe

Kirillov

2022

Physics of Fluids

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“…Notons qu'une méthode de type Complex Mapping est également mise en oeuvre pour traiter les problèmes radiés. Le problème diffracté ainsi que les problèmes radiés sont finalement résolus en utilisant le logiciel libre FreeFEM++ (HECHT et al, 2005) basé sur la méthode des éléments finis. On est ainsi en mesure de reconstruire le potentiel total donné par l'équation (10) puis la pression via l'équation de Bernoulli (4).…”

Section: Méthode De Résolutionunclassified

“…Ces deux extensions pourraient permettre de se rapprocher davantage des cas réels, et font partie des perspectives de cette étude. Par ailleurs, les études de stabilité récentes de (MOUGEL & MICHELIN, 2020) et (LABARBE & KIRILLOV, 2020), dans des configurations simplifiées de membranes infiniment longues, mettent en lumière des phénomènes d'instabilité résultants du couplage surface libre/courant/membrane flexible. La généralisation de ces études au cas d'une membrane de longueur finie semble être une piste prometteuse pour affiner la compréhension des mécanismes de récupération d'énergie décrits dans cet article.…”

Section: èMes Journées Nationales Génie Côtier -Génie Civilunclassified

Etude théorique de l'effet d’un faible courant sur les interactions houle/membrane flexible : application à la récupération d’énergie

Achour¹,

Mougel²,

Jacono³

et al. 2020

XVIèmes Journées, Le Havre

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Dans la perspective de l'utilisation de structures flexibles pour la récupération d'énergies renouvelables, nous nous intéressons dans cette étude à l'effet d'un faible courant sur les performances d'un récupérateur d'énergie de la houle par une membrane flexible. La configuration étudiée théoriquement correspond au forçage par une houle incidente monochromatique, d'une membrane flexible immergée parallèlement à la surface libre en présence d'un courant et reliée à un amortisseur linéaire ponctuel modélisant l'extraction d'énergie. L'effet de l'écoulement incident (vagues/courant) sur l'efficacité de la récupération d'énergie est étudié pour un récupérateur aux caractéristiques données (immersion, propriétés structurelles et dimensions fixées). L'étude révèle notamment que la présence d'un faible courant peut augmenter significativement l'efficacité de la récupération d'énergie des vagues.

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Membrane flutter in three-dimensional inviscid flow

Mavroyiakoumou

Alben

2022

J. Fluid Mech.

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We develop a model and numerical method to study the large-amplitude flutter of rectangular membranes (of zero bending rigidity) that shed a trailing vortex-sheet wake in a three-dimensional (3-D) inviscid fluid flow. We apply small initial perturbations and track their decay or growth to large-amplitude steady-state motions. For 12 combinations of boundary conditions at the membrane edges we compute the stability thresholds and the subsequent large-amplitude dynamics across the three-parameter space of membrane mass density, pretension and stretching rigidity. With free side edges we find good agreement with previous 2-D results that used different discretization methods. We find that the 3-D dynamics in the 12 cases naturally forms four groups based on the conditions at the leading and trailing edges. The deflection amplitudes and oscillation frequencies have scalings similar to those in the 2-D case. The conditions at the side edges, although generally less important, may have small or large qualitative effects on the membrane dynamics – e.g. steady vs unsteady, periodic vs chaotic or the variety of spanwise curvature distributions – depending on the group and the physical parameter values.

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Membrane flutter induced by radiation of surface gravity waves on a uniform flow

Abstract: Abstract

Cited by 4 publications

References 66 publications

Radiation-induced instability of a finite-chord Nemtsov membrane

Radiation-induced instability of a finite-chord Nemtsov membrane

Etude théorique de l'effet d’un faible courant sur les interactions houle/membrane flexible : application à la récupération d’énergie

Membrane flutter in three-dimensional inviscid flow

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