Bifurcation analysis of a two-degree-of-freedom aeroelastic system with freeplay structural nonlinearity by a perturbation-incremental method

A perturbation-incremental (PI) method is presented for the computation, continuation and bifurcation analysis of limit cycle oscillations (LCO) of a two-degree-of-freedom aeroelastic system containing a freeplay structural nonlinearity. Both stable and unstable LCOs can be calculated to any desired degree of accuracy and their stabilities are determined by the Floquet theory. Thus, the present method is capable of detecting complex aeroelastic responses such as periodic motion with harmonics, period-doubling (PD), saddle-node bifurcation, Neimark–Sacker bifurcation and the coexistence of limit cycles. Emanating branch from a PD bifurcation can be constructed. This method can also be applied to any piecewise linear systems.