We study the effect of adding localised stiffness, via a spring support, on the stability of flexible panels subjected to axial uniform incompressible flow. Applications are considered that range from the hydro-elasticity of hull panels of high-speed ships to the aero-elasticity of glass panels in the curtain walls of high-rise building in very strong winds. A two-dimensional linear analysis is conducted using a hybrid of theoretical and computational methods that calculates the system eigen-states but can also be used to capture the transient behaviour that precedes these. We show that localised stiffening is a very effective means to increase the divergence-onset flow speed in both hydro-and aero-elastic applications. It is most effective when located at the mid-chord of the panel and there exists an optimum value of added stiffness beyond which further increases to the divergence-onset flow speed do not occur. For aero-elastic applications, localised stiffening can be used to replace the more destructive flutter instability that follows divergence at higher flow speeds by an extended range of divergence. The difference in eigen-solution morphology between aero-and hydro-elastic applications is highlighted, showing that for the former coalescence of two non-oscillatory divergence modes is the mechanism for flutter onset. This variation in solution morphology is mapped out in terms of a non-dimensional mass ratio. Finally, we present a short discussion of the applicability of the stabilisation strategy in a full three-dimensional system.
A hybrid of computational and theoretical methods is extended and used to investigate the instabilities of a flexible surface inserted into one wall of an otherwise rigid channel conveying an inviscid flow. The computational aspects of the modelling combine finite-difference and boundary-element methods for structural and fluid elements respectively. The resulting equations are coupled in state-space form to yield an eigenvalue problem for the fluid-structure system. In tandem, the governing equations are solved to yield an analytical solution applicable to inserts of infinite length as an approximation for modes of deformation that are very much shorter than the overall length of the insert. A comprehensive investigation of different types of inserts-elastic plate, damped flexible plate, tensioned membrane and spring-backed flexible plate-is conducted and the effect of the proximity of the upper channel wall on stability characteristics is quantified. Results show that the presence of the upper-channel wall does not significantly modify the solution morphology that characterises the corresponding open-flow configuration, i.e. in the absence of the rigid upper channel wall. However, decreasing the channel height is shown to have a very significant effect on instability-onset flow speeds and flutter frequencies, both of which are reduced. The channel height above which channel-confinement effects are negligible is shown to be of the order of the wavelength of the critical mode at instability onset. For spring-backed flexible plates the wavelength of the critical mode is much shorter than the insert length and we show very good agreement between the predictions of the analytical and the state-space solutions developed in this paper. The small discrepancies that do exist are shown to be caused by an amplitude modulation of the critical mode on an insert of finite length that is unaccounted for in the travelling-wave assumption of the analytical model. Overall, the key contribution of this paper is the quantification of the stability bounds of a fundamental fluid-structure interaction (FSI) system which has hitherto remained largely unexplored.
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