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Communication Dans Un Congrès Année : 2018

Nonlinear dynamics of slender inverted flags in axial flow

Résumé

A nonlinear fluid-elastic continuum model of a slender cantilevered plate subjected to axial flow directed from the free end to the clamped one, also known as the inverted flag problem, is proposed. A nonlinear unsteady slender wing theory is employed to express the fluid-related forces acting on the plate. It is based on potential flow theory for inviscid fluids. The Euler-Bernoulli beam theory with exact kinematics and inextensibility is employed to derive the nonlinear partial integro-differential equation governing the dynamics of the plate. Discretization in space is carried out via a conventional Galerkin scheme using the linear modeshapes of the cantilevered beam. A Newton solver is implemented to obtain equilibrium solutions and integration in time is conducted using Gear's backward differentiation formula. A bifurcation diagram in terms of flow velocity is constructed in order to gain insight on the stability and post-critical behaviour of the system. It is shown that the undeflected static equilibrium is stable prior to a supercritical Hopf bifurcation giving rise to a flapping motion around the undeflected static equilibrium. By further increasing the flow velocity, the flag displays flapping motions around deflected static equilibria and change to fully-deflected static states at even higher flow velocities. These predictions are in excellent agreement with existing experimental data available in the literature.
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Dates et versions

hal-01812870 , version 1 (11-06-2018)

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Paternité - Partage selon les Conditions Initiales

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  • HAL Id : hal-01812870 , version 1

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Mohammad Tavallaeinejad, Mathias Legrand, Michael Païdoussis. Nonlinear dynamics of slender inverted flags in axial flow. 9th International Symposium on Fluid-Structure Interactions, Flow-Sound Interactions, Flow-Induced Vibration & Noise, Jul 2018, Toronto, Canada. ⟨hal-01812870⟩
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