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• W1514540062 abstract "A versatile computational model is described for the two-dimensional fluid-structure interaction between a fluid flow and a thin flexible plate held at its leading edge. This fundamental system may be con- sidered representative of many engineered or natural systems in which a plate or membrane experiences spon- taneous, and often sustained, vibration. The energy exchanges between the fluid and structure that underpin such motions may be either desirable (for example in sound-production or as a fluid-energy extraction device) or damaging (for example, producing material fatigue or instability in paper-rolling processes). The system studied requires that the governing fluid equations are solved concurrently with those of the flexi- ble plate with compatibility of motion and continuity of stresses at the fluid-structure interface. The former is written as a kinematic boundary condition on the solution of the Laplace equation for the fluid flow. While this implies an inviscid and irrotational flow, viscous effects are implicitly included through a streamwise distribu- tion of bound-vorticity (i.e. boundary-layers are assumed to be infinitely thin) and the imposition of a Kutta condition that effectively sets the correct sum of bound vorticity. Thus, the model developed is appropriate to flows with high Reynolds number that are most commonly found in applications. Continuity of stress for an inviscid fluid requires that the pressure matches the stresses due to the flexible-plate's inertial forces and its bending stiffness. Finally, as the plate moves, its changing shape means that the lift it generates - the sum of the pressure forces that drive the plate motion - also changes. This lift variation then requires that vorticity is continuously shed from the trailing edge in order to satisfy Kelvin's circulation theorem and this yields a near-field wake that influences the flow over the flexible plate. In our computational model we deploy a boundary-element method, using first-order vortex panels, along the surface of the flexible plate. A Kutta condition is enforced at the trailing edge of the deforming surface while the Kelvin circulation theorem is used to determine the strengths of discrete Gaussian vortex blobs that are shed and then convected with the mean flow to form the downstream wake. We assume small-amplitude disturbances of the flexible plate that permits linearisation of the kinematic condition and the wake dynamics. The flexible plate is modelled by the beam equation that is solved using finite-differences. The system can then be written as a single matrix equation for the beam deflection and its time derivatives at the collocation points and a sum of wake-vortex effects. When the latter are excluded and a steady flow is assumed, system eigenmodes can be extracted using state-space methods to determine the vibration frequencies of the fluid-structure system and the stability of such oscillations. Alternatively, numerical simulations of the full system are conducted to study the response to an applied initial excitation. In this paper, we explore the effect on the stability of the fluid-loaded plate when a point mass is added to an otherwise homogeneous plate. It is shown that this effect can be either stabilising or destabilising depending upon the location of the added mass and that its inclusion modifies the energy exchanges of the fluid-structure interaction of the 'standard' system." @default.
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• W1514540062 date "2009-01-01" @default.
• W1514540062 modified "2023-09-27" @default.
• W1514540062 title "Fluid-structure modelling of a flexible lifting surface in a fluid flow" @default.
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