AN INVESTIGATION OF STABILITY IN THE LARGE BEHAVIOUR OF A CONTROL SURFACE WITH STRUCTURAL NON-LINEARITIES IN SUPERSONIC FLOW

It is well known that the presence of non-linearities may significantly affect the aeroelastic response of an aerospace vehicle structure. In this paper, the aeroelastic behaviour at high Mach numbers of an all-moving control surface with a non-linearity in the root support is investigated. Very often, a stable equilibrium point, corresponding to zero displacement of the structure, together with an unstable limit cycle arising from a sub-critical Hopf bifurcation results from the presence of the non-linearity. The stable equilibrium point will then possess a domain of attraction. In this paper, this situation is investigated by first applying the averaging method to obtain a new set of aeroelastic equations in which the limit cycle is replaced by an unstable equilibrium point. A fourth order power series approximation to the stable manifold in the neighbourhood of this equilibrium point is then determined. From the stable manifold, predictions of the domain of attraction of the stable equilibrium point may then be made. The method is applied to two examples in which the non-linearity in the root support was due to either a cubic hardening restoring moment or the presence of freeplay. The approximation to the stable manifold was sufficient to enable significant information about the domain of attraction of the stable equilibrium point of the control surface to be obtained; agreement with predictions from numerical integration of the aeroelastic equations in the time domain was shown to be generally good in the cases considered, though outside the region of validity of the stable manifold expansion, discrepancies will occur. The averaging method was shown to be sufficiently accurate for this analysis even when the non-linearities could not be considered as weak.