Single-mode flutter of an elastic plate in the presence of the boundary layer

Abstract

The flutter of an elastic plate in a viscous supersonic gas flow is investigated. The influence of viscous perturbations of the boundary layer on the single-mode flutter is studied considering two different types of a boundary layer profile: the generalized convex boundary layer profile and the profile with a generalized inflection point. It is shown that in the case of the convex layer for thick boundary layers the plate is fully stabilized. In the case of a profile with the generalized inflection point, the thickening of the layer first yields the increase of the growth rates of the perturbations, and the growth is greater than in the inviscid approximation. Numerical simulation of two-dimensional supersonic gas flows with boundary layers (that can have a destabilizing effect on the flutter of an elastic surface) over different curved surfaces is performed. The flow patterns over them are studied: regions of these surfaces, over which stable boundary-layer profiles with a generalized inflection point are formed, are found, and their boundaries are obtained.