Bifurcation analysis of aircraft pitching motions about large mean angles of attack

Abstract

Bifurcation theory is used to analyze the nonlinear dynamic stability characteristics of an aircraft'subject to single-degree-of-freedom pitching-motion perturbations about a large mean angle of attack. The requisite aerodynamic information in the equations of motion can be represented in a form equivalent to the response to finite-amplitude pitching oscillations about the mean angle of attack. It is shown how this information can be deduced from the case of infinitesimal -amplitude oscillations. The bifurcation theory analysis reveals that when the mean angle of attack is increased beyond a critical value at which the aerodynamic damping vanishes, new solutions representing finite-amplitude periodic motions bifurcate from the previously stable steady motion. The sign of a simple criterion, cast in terms of aerodynamic properties, determines whether the bifurcating solutions are stable (supercritical) or unstable (subcritical). For flat-plate airfoils flying at supersonic/hypersonic speed, the bifurcation is subcritical, implying either that exchanges of stability between steady and periodic motion are accompanied by hysteresis phenomena, or that potentially large aperiodic departures from steady motion may develop.