Single-mode plate flutter taking the boundary layer into account

The stability of an elastic plate in supersonic gas flow is investigated using asymptotic methods and taking the boundary layer formed on the plate surface into account. It is shown that the effect of the boundary layer can be of two types depending on its profile. In the case of generalized convex profiles (characteristic of accelerated flow) supersonic and subsonic plate oscillations are stabilized and destabilized, respectively. In the case of profiles with a generalized inflection point located in the subsonic part of the layer (characteristic of homogeneous and decelerated flows) supersonic perturbations are destabilized in the thin boundary layer and stabilized when the layer is fairly thick; subsonic perturbations are damped.