The Stability of Simply Supported Rectangular Surfaces in Uniform Subsonic Flow

Abstract

A study is made of the stability of a simply supported flat plate set in an infinite rigid baffle when an inviscid fluid flows uniformly at subsonic speed past one side of the surface. The generalized pressures are derived for low frequencies with two and three-dimensional flows. The three-dimensional generalized pressures are expanded asymptotically for high and low aspect ratios, and analytic forms derived for the critical flow velocity at instability. The asymptotic expansions enable the effect of aspect ratio on stability to be determined. It is shown that the incompressible limit, for two-dimensional flows, is singular but the stability criterion is associated with first-mode divergence and is identical with the three-dimensional high aspect ratio stability result, although there are certain detailed differences in the nature of the instability.