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" Nonlinear Dynamics of Inverted Flags: "
Tavallaeinejad, Mohammad
Legrand, Mathias
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Latin Dissertation
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| Language of Document
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English
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| Record Number
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1112102
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TLpq2516720108
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| Main Entry
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Legrand, Mathias
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Tavallaeinejad, Mohammad
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| Title & Author
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Nonlinear Dynamics of Inverted Flags:\ Tavallaeinejad, MohammadLegrand, Mathias
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| College
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McGill University (Canada)
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| Date
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2020
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| student score
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2020
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| Degree
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Ph.D.
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| Page No
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224
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| Abstract
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Inverted flags—clamped-free elastic thin plates subjected to a fluid flowing axially and directed from the free end towards the clamped end—have been observed experimentally and computationally to exhibit large-amplitude flapping beyond a critical flow velocity. The motivation for further research on the dynamics of this system is partly due to its presence in some engineering and biological systems, and partly because of the very rich dynamics it displays. In the present thesis, our goal is to develop nonlinear analytical models for the dynamics and stability of inverted flags. More specifically, two theoretical aerodynamic models are proposed, according to the flag aspect ratio (i. e. height-to-length ratio). For asymptotically small aspect ratio, where the length of the flag is assumed to be infinite, the fluid forces are calculated using slender body theory; an extension of elongated-body theory to large-amplitude rotations of the plate mid-plane along with Bollay's nonlinear wing theory are employed to formulate the fluid-related forces acting on the plate. For high aspect ratios, where the height of the flag is assumed to be much larger than its length, two-dimensional flow theories are relevant; in this case, the inviscid fluid flow is modelled via the quasi-steady version of Theodorsen's unsteady aerodynamic theory, also utilizing the Polhamus leading edge suction analogy to model flow separation effects from the leading edge at moderate angles of attack. On the structural front, the flag is modelled via a geometrically-exact Euler-Bernoulli beam theory, assuming the flag to be inextensible. A Hamiltonian framework is employed to derive the nonlinear fluid-elastic continuum models in terms of the rotation angle of the flag cross-section. Discretization in space is carried out via the Galerkin technique. Gear's backward differentiation formula and a pseudo-arclength continuation technique are employed to solve the resultant discretized equations. It was found from numerical results that, for flags of small aspect ratio, the undeflected static equilibrium is stable prior to a subcritical pitchfork bifurcation. For flags of high aspect ratio, however, the undeflected stable static equilibrium is subjected to a supercritical pitchfork bifurcation, which is associated with static divergence (buckling) of the flag. At higher flow velocities, past the pitchfork bifurcation, a supercritical Hopf bifurcation materialises, generating a flapping motion around the deflected static equilibrium. At even higher flow velocities, flapping motion becomes symmetric, around the undeflected static equilibrium. Interestingly, it was also found that heavy flags may exhibit large-amplitude flapping right after the initial static equilibrium, provided that they are subjected to a sufficiently large disturbance. Numerical results suggest that a fluidelastic instability may be the underlying mechanism for the flapping motion of high aspect ratio inverted flags. In other words, flapping may be viewed as a self-excited vibration. Finally, experiments with cantilevered flexible plates in reverse axial flow were conducted in a subsonic wind tunnel to shed light on the effect of different system parameters on the stability and global dynamics of inverted flags. The experimental observations are compared withthe simulation results obtained via the proposed models. Reasonably good agreement with theoretical predictions was obtained
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Flags
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Fluid mechanics
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Heat transfer
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Physics
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Vibration
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Vortices
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