A theoretical investigation of flow-induced instabilities in compliant coatings

Garrad, A.D.; Carpenter, Peter W.

doi:10.1016/0022-460x(82)90318-2

Cited by 29 publications

(27 citation statements)

References 23 publications

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“…Note that the pole p 1 has negative imaginary part, and so for forcing frequency ω 0 < ω s , there is a spatially unstable wave downstream of the drive point, confirming this result found by Crighton and Oswell [10] and Brazier-Smith and Scott [9]. Similarly, the anomalous waves p 3 , p 4 , with neutral characteristics (real wavenumber) are found for higher frequencies, ω s < ω 0 < ω p whilst there are the usual attenuating terms in x > 0 (p 6 ), x < 0 (p 7 ) for ω 0 > ω p .…”

Section: Response To Continuous Forcingsupporting

confidence: 81%

“…Again, any singularities crossed during deformation result in plate wave contributions to η(x, t). As an example, I 1 yields, on deformation into its steepest descent paths, pole contributions from p 1 , p 2 (ω 0 < ω s ) or p 3 , p 4 or p 6 (ω 0 > ω p ) in x > 0 and p 5 (ω 0 < ω p ) or p 7 (ω 0 > ω p ) in x < 0. The descent integrals yield similar large time behaviour to that given in (3.17) plus the steady contribution.…”

Section: Response To Continuous Forcingmentioning

confidence: 99%

“…[3][4][5][6]). Here the structure is taken to be of finite extent and so a modal expansion for surface deflections can be posed.…”

Section: Introductionmentioning

confidence: 99%

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On transient oscillations of plates in moving fluids

Abrahams

Wickham

2001

Wave Motion

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Section: Response To Continuous Forcingsupporting

confidence: 81%

Section: Response To Continuous Forcingmentioning

confidence: 99%

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On transient oscillations of plates in moving fluids

Abrahams

Wickham

2001

Wave Motion

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“…Dugundji et al 1963;Ishii 1965;Weaver & Unny 1971;Ellen 1973;Garrad & Carpenter 1982;Lucey & Carpenter 1993) requires that the deformation of the flexible panel is written as a sum of orthogonal functions, or eigenmodes, which satisfy the boundary conditions at the panel's ends. The functions most commonly used are the in vacuo modes of the panel.…”

Section: Introductionmentioning

confidence: 99%

On the direct determination of the eigenmodes of finite flow–structure systems

Pitman

Lucey

2008

Proc. R. Soc. A.

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A new method for directly determining the eigenmodes of finite flow-structure systems is presented using the classical problem of the interaction of a uniform incompressible flow with a flexible panel, held at both ends, as an exemplar. The method is a hybrid of theoretical analysis and computational modelling. This method is contrasted with Galerkin and travelling-wave methods, which are most often used to study the hydroelasticity of such systems. The new method does not require an a priori approximation of perturbations via a finite sum of modes. Instead, the coupled equations for the wall-flow system are used to derive a single matrix equation for the system that is a second-order differential equation for the panel-displacement variable. This is achieved in this exemplar by applying a combination of boundary-element and finite-element methods to the discretized system. Standard statespace methods are then used to extract the eigenmodes of the system directly. We present the results for the stability of the case of an unsupported flexible plate, elucidating its divergence and flutter characteristics, and the effect of energy dissipation in the structure. We then present the results for the case of a spring-backed flexible plate, showing that its motion is dominated by travelling waves. Finally, we illustrate the versatility of the approach by extracting the stability diagrams and modes for a panel with spatially varying properties and a panel with non-standard boundary conditions. In doing so, we show how spatial inhomogeneity can modify the energy exchanges between flow and structure, thereby introducing a single-mode flutter instability at pre-divergence flow speeds.

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“…However, later experimental and theoretical work has not provided a definite answer to the question how surface compliance affects drag and noise generation. Theoretical studies (Garrad andCarpenter 1982, Gaster 1985) indicate that transition of a laminar boundary layer to turbulence can be damped by a compliant surface. However, the interaction between a passive compliant surface and a turbulent boundary layer is still not well understood.…”

mentioning

confidence: 99%