Quasi-periodic aeroelastic response analysis of an airfoil with external store by incremental harmonic balance method

Abstract

This paper presents an investigation on the nonlinear aeroelastic system of an airfoil with external store by incremental harmonic balance (IHB) method. Besides solving limit cycle (LC) solutions, the IHB method is implemented to obtain quasi-periodic (QP) solutions by introducing multiple irreducible time scales. Steady state responses such as LC and QP oscillations obtained by the presented method are verified by numerical examples. One pair of Floquet multipliers for LC solutions first leave and then enter a unit cycle at complex conjugate values, indicating the existence of a secondary Hopf bifurcation and its reversal one. Along with the fundamental frequency of LC oscillation, an additional frequency arises at the secondary bifurcation, and finally disappears at the reversal bifurcation. The appearance and disappearance of the irreducible frequency cause the steady state responses changing from LC to QP and back to LC oscillation.