Nonlinear Possio integral equation and aeroelastic flutter limit cycle oscillation

Abstract

With a zero thickness wing structure model (Goland) that is linear but aerodynamics that is nonlinear - inviscid isentropic flow characterized by the Euler full potential equation with Kutta-Joukowsky conditions - we show that Flutter is an LCO. The speed is a Hopf Bifurcation point, determined by the linearized model and so is the period. The key relation of the pressure jump to the wing normal velocity is now given by a 2D nonlinear time domain extension of the linear Possio Integral equation. As for the disturbed flow itself, we show that it can be decomposed as the sum of two parts, one part that produces the lift determined by nonlinear Possio equation and does not depend on the value of the ratio of specific heats; and can be linearized; and the other part which produces no lift but may contain discontinuities but not across the wing and cannot be linearized.