The stability of the equilibrium of a wing in an unsteady flow

Abstract

The stability of the equilibrium position of a wing is investigated. The wing is modelled by a heavy rigid body with a fixed point and is close in shape to a thin plate. The wing is fastened using a viscoelastic material which can be modelled by non-linear viscoelastic springs that keep the wing in a position close to horizontal. The motion of the wing is described by a system of non-linear ordinary integrodifferential equations which, using the model adopted, take account of the unsteady nature of the flow past the wing and the viscoelastic properties of the spring material. The stability of the equilibrium under persistent disturbances is analysed. This analysis is based on the use of series similar to those in the first Lyapunov method. The stability of the equilibrium for purely rotational motions of the wing about the longitudinal axis is investigated in the critical case of a single zero root of the characteristics equation. The Lyapunov constants which solve the stability problem are indicated.