Bifurcation analysis of aeroelastic systems with hysteresis by incremental harmonic balance method

The aeroelastic system of an airfoil with a hysteresis nonlinearity in the pitching degree-of-freedom was investigated by the incremental harmonic balance (IHB) method. In the procedure of deducing the IHB iterative scheme, a method of undetermined coefficient was extended to cope with the problem of expanding the hysteresis nonlinearity. Numerical examples show that the limit cycle oscillations (LCOs) obtained by the IHB are in nice agreement with the numerical results. Bifurcations of the attained LCOs with respect to the flow speed, the preload and the freeplay of the hysteresis nonlinearity are analyzed in detail with the help of the Floquet theory. Symmetry breaking, saddle-node bifurcation are detected as the flow speed varying.

► The problem of expanding a hysteresis nonlinearity as Fourier series is solved.
► The incremental harmonic balance method can be applicable in aeroelastic systems with hysteresis.
► Symmetry breaking, saddle-node bifurcations are detected by the above approach.