Identifying route to stall flutter through stochastic bifurcation analysis

Abstract

The interaction of an elastic structure such as an airfoil and fluid flow can give rise to nonlinear phenomenon such as limit cycle oscillations, period doubling or chaos. These phenomena are indicated by a change in the stability behaviour of the dynamical known as bifurcations. Presence of viscous effects in the fluid flow can give rise to flow separation which causes a stability change in the system that is identified to happen via a Hopf bifurcation. In such cases, the airfoil exhibits limit cycle oscillations which are torsionally dominant, known as stall flutter. Despite identifying the route to stall flutter under uniform flow conditions, investigating a stall problem under stochastic wind has received minimal attention. The ability of fluctuating flows to change the stability boundaries and disrupt the route to flutter, compels the need to carry out a stochastic analysis of stalling airfoils. Study of stall flutter in such systems under the influence of a time varying sinusoidal gust is undertaken and the route to flutter is identified by carrying out a stochastic bifurcation analysis.